Microbial adaptation, differentiation, and
community structure
by
Jonathan Friedman
Submitted to the Program in Computational and Systems Biology
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2013
© Massachusetts Institute of Technology 2013. All rights reserved.
Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Program in Computational and Systems Biology
February 28, 2013
Certified by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Eric J. Alm
Associate Professor
Thesis Supervisor
Certified by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Daniel H. Rothman
Professor
Thesis Supervisor
Accepted by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Christopher B. Burge
Chair, Computational and Systems Biology Ph.D. Graduate
Committee
Microbial adaptation, differentiation, and community
structure
by
Jonathan Friedman
Submitted to the Program in Computational and Systems Biology
on February 28, 2013, in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy
Abstract
Microbes play a central role in diverse processes ranging from global elemental cycles
to human digestion. Understanding these complex processes requires a firm understanding of the interplay between microbes and their environment. In this thesis, we
utilize sequencing data to study how individual species adapt to different niches, and
how species assemble to form communities. First, we study the potential temperature
and salinity range of 16 marine Vibrio strains. We find that salinity tolerance is at
odds with the strains’ natural habitats, and provide evidence that this incongruence
may be explained by a molecular coupling between salinity and temperature tolerance. Next, we investigate the genetic basis of bacterial ecological differentiation by
analyzing the genomes of two closely related, yet ecologically distinct populations of
Vibrio splendidus. We find that most loci recombine freely across habitats, and that
ecological differentiation is likely driven by a small number of habitat-specific alleles. We further present a model for bacterial sympatric speciation. Our simulations
demonstrate that a small number of adaptive loci facilitates speciation, due to the opposing roles horizontal gene transfer (HGT) plays throughout the speciation process:
HGT initially promotes speciation by bringing together multiple adaptive alleles, but
later hinders it by mixing alleles across habitats. Finally, we introduce two tools for
analyzing genomic survey data: SparCC, which infers correlations between taxa from
relative abundance data; and StrainFinder, which extracts strain-level information
from metagenomic data. Employing these tools, we infer a rich ecological network
connecting hundreds of interacting species across 18 sites on the human body, and
show that 16S-defined groups are rarely composed of a single dominant strain.
Thesis Supervisor: Eric J. Alm
Title: Associate Professor
Thesis Supervisor: Daniel H. Rothman
Title: Professor
2
Acknowledgments
Numerous people have provided guidance, support, and friendship during my thesis
work. The following does but little to convey the extent of my gratefulness.
My deepest gratitude is given to my thesis advisors, Eric Alm and Daniel Rothman, for showing me how to practice science, and how to enjoy the process. Whatever
scientific taste I possess is owed to them. Thanks to past and present members of the
Alm and Rothman labs for providing a stimulating and vibrant scientific environment.
In particular, Lawrence David, Jesse Shapiro, Alex Petroff and Olivier Devauchelle
have been a constant source of both inspiration and humility. Martin Polz and his
group have provided a much needed tether to the natural world. It is also my pleasure
to acknowledge members of my thesis advisory committee and my collaborators for
their contributions to this thesis.
Thanks to Tracy, Michelle, Christoph, Alon, Alex, Olivier, Lawrence, Jesse, Otto
and Francisco for their continued friendship and support. To Arne and Celine, for
demonstrating that there is life after kids. To Amit and Tamar, for six years of friendship, philosophy, and indian food. To Tova and Moti, for their unconditional support.
To my siblings, Dana, Yael, Moran, Uzi, and Neta, who put up with it all, and remind
me where home is. To my grandfather, in whose footsteps I am trying to follow. To
my parents for both nature and nurture, and for fostering my inquisitiveness, even
when it led me to the origin of flags and the salaries of international referees. Above
all, to Liraz, Ella and Sammy, for being my girls.
3
Contents
I
Introduction
II
5
Contributions
10
1 Shape and evolution of the fundamental niche in marine Vibrio
12
2 Population Genomics of Early Events in the Ecological Differentiation of Bacteria
33
3 Sympatric speciation: when is it possible in bacteria?
44
4 Inferring Correlation Networks from Genomic Survey Data
66
5 Inferring Strain Diversity from Metagenomic Data
93
III
Conclusion
107
IV
Bibliography
111
4
Part I
Introduction
5
Microbes play a central role in diverse processes ranging from global elemental
cycles [1] to human digestion. Gleaning insights regarding such complex natural systems depends critically on data availability. A primary source of data for microbial
ecology is the rapidly increasing amounts of fully sequenced bacterial genomes, and
genomic surveys [2]. These data provide a unique opportunity for investigating ecological processes and the forces that drive them, as genomes bear the markings of
their evolutionary history, and genomic surveys record the taxonomic and functional
composition of entire microbial communities.
Extracting meaningful insights from biological sequence data requires overcoming
several challenges. Sequence data typically provide a comprehensive characterization
of individual genomes or a broad characterization of whole communities, each presenting its own challenges. Individual genomes, though providing a record of their
evolutionary history, do so in a non-trivial way, integrating the effects of multiple
selective pressures whose relative importance changes over time and across environments. Moreover, bacterial genome are often comprised of sequence blocks that have
evolved under distinct sets of selective pressures, due to the fact that bacteria engage
in a non-hereditary exchange of genetic material between potentially distantly related
individuals, a phenomenon known as horizontal gene transfer (HGT) [3]. Despite the
fact that genomic surveys provide broad coverage, they give incomplete representations of the surveyed communities: surveys based on specific marker genes provide
limited phylogenetic resolution [4] and do not capture flexible or mobile elements
[5]; and metagenomic surveys provide broad coverage of the genomic makeup of a
community, but offer limited information regarding the linkage between the observed
elements [6].
The works presented in this thesis attempt to overcome the aforementioned challenges and leverage both full genomes and genomic surveys to elucidate the interplay
between microbes and their environment, on scales ranging from individual strains
to entire communities. First, Chapter 1, is concerned with the potential ecological
niche species can occupy in the absence of inter-species competition, a topic prevalent
in the theoretical literature, but surprisingly scant in the experimental one. In this
6
chapter, we present a novel experimental apparatus to jointly measure the potential
temperature and salinity range of individual strains, and develop a conceptual framework for linking these ranges to the coupling between underlying molecular stress
response pathways. Applying these tools to 16 marine Vibrio strains, we find that
only a subset of possible stress coupling mechanisms are observed, though we could
not detect a selective signature for this finding. We further show that salinity tolerance is at odds with the strains’ natural habitats, and provide evidence that this
inconsistency may be explained by coupling between salinity and temperature tolerance at the molecular level. The theory and analysis included in this work are my
own, whereas the experimental work was conducted by my co-authors.
Chapters 2 and 3 are focused on the genetic basis of adaptation and ecological
differentiation in bacteria. One popular model for the evolutionary dynamics of ecological adaptation is the stable ecotype model [7]. In this model individuals that
acquire novel adaptive alleles proceed to take over their ecological niche in a selective
sweep that purges all the genetic diversity within the niche. However, akin to the
effect of recombination in sexual eukaryotes, HGT may break the linkage between the
adaptive alleles and the genetic background in which they arise, and thus preserve
some genome-wide diversity [7]. In previous work, I have used stochastic simulations
to show that the amount of genome-wide diversity following a selective sweep at a
particular adaptive loci depends critically on the recombination rate and the strength
of selection [8].
In light of these ideas, in Chapter 2, we analyze the genomes of two closely related,
yet ecologically distinct populations of the marine bacteria Vibrio splendidus. We find
that most loci recombine freely across habitats, and ecological differentiation is likely
driven by a small number of habitat-specific alleles. Moreover, we show that there is
reduced gene flow between habitats, and propose that the separation of gene pools
between the populations may gradually increase over time. Such a separation of gene
pools across habitats is consistent with the stable ecotype model, which may apply
to later stages of ecological differentiation in recombining bacteria. My contributions
to this work include the flexible genome analysis that demonstrated the reduced gene
7
flow across habitats, and the identification of several habitat specific genes that may
contribute to habitat adaptation.
The results of a simulation study designed to better understand the role HGT
plays in ecological differentiation and sympatric speciation are presented in Chapter
3. These simulations extend our previous work to include two distinct, yet genetically
coupled niches, rather than a single niche. Our simulations demonstrate that HGT has
opposing effects during early and late stages of the differentiation process. Initially,
HGT promotes adaptation by bringing together multiple adaptive alleles into a single
genome. In contrast, in the absence of genetic isolation, HGT later on mixes different
niche-adapted genomes and creates unfit intermediates. We show that, without timevarying recombination rates, this tradeoff is resolved when only a small number of
loci are required in order to adapt to a new niche.
The final two chapters present algorithms used to extract information regarding community structure from genomic surveys, whose popularity has been rapidly
increasing over recent years. Chapter 4 presents SparCC, an algorithm capable of
inferring correlations between genes or species from relative abundance data, which
is a first step on the road to identifying ecological interactions. Analysis of both
simulated data and datasets collected from 18 sites on the human body demonstrates
that, as genomic survey data give only relative abundances, traditional correlation
analysis may yield erroneous results. We further show that the accuracy of standard
correlations depends critically on the diversity of the community studied and on the
density of the true correlation network, and that spurious correlations prevail in several real-world datasets. In contrast, such artifact are absent from the rich interaction
networks inferred by SparCC.
In Chapter 5, we introduce StrainFinder, an algorithm which uses metagenomic
data to identify strains at a higher phylogenetic resolution than that offered by 16S
profiling. Such high resolution data are crucial for detecting migration between environments, and provide a unique opportunity for gleaning insights into the assembly of
natural communities. StrainFinder leverages the fact that alleles found in a common
set of strain should have similar proportions in a metagenomic dataset, a fact that
8
is formalized in a probabilistic framework that also accounts for the sampling noise,
and facilitates the inference of strain abundances. When applied to metagenomic
data sampled from human cheeck and feces, we find that operational taxonomic units
(OTUs) identified in corresponding 16S surveys are rarely composed of a single dominant strain. Moreover, we find that strain diversity differs consistently between OTUs
across individuals, and that these differences cannot be accounted for by the sampling
body site.
9
Part II
Contributions
10
Chapter 1
Shape and evolution of the
fundamental niche in marine
Vibrio
Arne C. Materna*, Jonathan Friedman*, Claudia Bauer, Christina
David, Sara Chen, Ivy B. Huang, April Gillens, Sean A. Clarke, Martin
F. Polz and Eric J. Alm
*These authors contributed equally to this work.
This chapter is presented as it originally appeared in ISME Journal 320, 1081
(2008). Corresponding Supplementary Material is appended.
Chapter 1
Shape and evolution of the
fundamental niche in marine
Vibrio
Hutchinson’s fundamental niche, defined by the physical and biological
environments in which an organism can thrive in the absence of interspecies interactions, is an important theoretical concept in ecology. However, little is known about the overlap between the fundamental niche
and the set of conditions species inhabit in nature, and about natural
variation in fundamental niche shape and its change as species adapt to
their environment. Here, we develop a custom-made dual gradient apparatus to map a cross-section of the fundamental niche for several marine
bacterial species within the genus Vibrio based on their temperature and
salinity tolerance, and compare tolerance limits to the environment where
these species commonly occur. We interpret these niche shapes in light
of a conceptual model comprising five basic niche shapes. We find that
the fundamental niche encompasses a much wider set of conditions than
those strains typically inhabit, especially for salinity. Moreover, though
the conditions strains typically inhabit agree well with the strains temperature tolerance, they are negatively correlated with the strains salinity
12
tolerance. Such relationships can arise when the physiological response to
different stressors is coupled, and we present evidence for such a coupling
between temperature and salinity tolerance. Finally, comparison with well
documented ecological range in V. vulnificus suggests that biotic interactions limit the occurrence of this species at low temperature - high salinity
conditions. Our findings highlight the complex interplay between the ecological, physiological and evolutionary determinants of niche morphology,
and caution against making inferences based on a single ecological factor.
13
Introduction
In his often-cited 1957 essay, G. E. Hutchinson introduced the concept of the fundamental niche as the combination of all environmental conditions (biotic and abiotic)
that permit a species to sustain its population in the absence of interference from
other species [9]. Since that time, the niche concept has been one of the most studied and one of the most debated concepts in theoretical ecology [10–13]. Despite its
central importance, few empirical studies have been undertaken to map the fundamental niche space associated with non-consumable environmental factors (NEFs),
such as temperature, salinity and pH [14, 15]. Rather, studies have primarily focused
on the effects of multiple consumable environmental resources (e.g., nutrients) on
inter-species competition [11, 12, 16–18].
Hutchinson considered whether niche shapes, i.e., the two-dimensional cross-section
of a pair of environmental factors, could prove informative regarding the physiological
response of an organism toward those factors. He deduced that independently acting factors should map out a rectangular fundamental niche, because the maximum
tolerance to either factor is independent of the other, and supposed that interactions
between factors could lead to more complex shapes. In this way, a species niche
shape reflects the organism’s physiological response, e.g., whether the stress response
pathways for each factor are independent.
In a broader evolutionary context, the population-wide variation in niche shape
and the plasticity of these shapes with respect to mutation will have profound effects
on how species adapt to new or changing environments. For example, if niche shapes
are highly constrained within species, then large changes in environmental factors
can lead to significant changes in community composition with many species being
displaced. On the other hand, if variation is high within populations, community
composition could be robust to large changes in environmental parameters.
In this study, we combine theory and experiment to address the following fundamental questions: (i) What basic classes of two-dimensional niche shapes are anticipated based on considerations of organismal physiology? (ii) Which niche shapes are
14
observed? (iii) How does the fundamental niche relate to the environment species
typically inhabit? (iv) How do niche shapes vary within and between populations?
Although our scientific questions and theoretical development apply generally to any
model system and any environmental factors, we focused our experimental efforts on
the salinity-temperature niche of 17 environmental isolates of the bacterial genus Vibrio, representing 11 well-characterized and genetically diverse species, isolated from a
range of different environments (Table 1.1) [19–21]. Bacteria constitute a convenient
model system since their growth can be assayed in high throughput over a range of
tightly controlled environmental conditions. The Vibrio genus is an excellent model
system because it is found in a notable range of environmental temperatures and salinities [22], which have been shown to be the strongest environmental determinants of
microbial community composition [23, 24]. Moreover, there is evidence that temperature and salinity are prominent factors in Vibrio ecology, population dynamics,
physiological stress response, and evolution [25–29].
Materials and methods
Bacterial strains and isolates
The following bacterial strains were used in this study: V. parahaemolyticus EB101
(ATCC 17802), V. fischeri MJ11 (ATCC 7744), V. cholerae N16961 (ATCC 39315),
V. metecus strains OP6B# and OP3H#, Listonella (formerly Vibrio) anguillarum
NCMB 6 (ATCC 19264), Vibrio sp. (DAT7222), Vibrio sp. MED222 , and the V.
splendidus strains 12B1*, 12F1*, 12A10*, 14B11*, 12E10*, Vibrio sp. F12*, V. crassostreae 1C5*, V. cyclitrophicus strains 1-273 and Z-264. Strains marked with * and #
where isolated from seawater collected at the Plum Island (PIE) Long-term Ecological
Research (LTER) site (http://ecosystems.mbl.edu/pie/data/est/EST.htm) [30] and
Oyster Pond, Woods Hole, MA [31], respectively. Vibrio sp. DAT7222 was isolated
from aquaculture tanks used to raise marine mud-crab larvae in Australia, Darwin,
Northern Territory and was kindly provided by Yan Boucher [32] Vibrio sp. MED222
15
16
c
b
17.27
16.20
16.27
20.38
15.05
15.77
19.72
21.03
15.98
19.70
16.26
17.33
17.49
23.33
16.92
17.09
19.59
15.88
18.50
TM in
(°C)
21.95
21.68
20.49
21.71
25.50
23.79
25.33
26.71
22.02
24.36
26.34
25.04
25.45
29.61
27.51
26.99
30.94
33.05
28.32
TOpt
(°C)
Plum Island Long-term Ecological Research.
Biological replicates.
Estimated value.
29.16
26.62
27.08
28.05
29.79
25.61
30.15
30.99
33.15
30.00
33.22
33.16
32.48
40.35
33.96
31.55
40.24
36.16
41.02
V. splendidus 12A10
V. splendidus 14B11
V. splendidus 12B1-1b
V. splendidus 12B1-2b
V. splendidus 12F1
V. splendidus 12E10
V. sp. MED222
V. cyclitrophicus 1273
V. cyclitrophicus Z-264
V. sp. F12
V. crassostrea 1C5
V. fischeri MJ11-1b
V. fischeri MJ11-2b
V. parahaemolyticus
V. sp. DAT7222
Listonella anguillarum
V. metecus OP6B
V. metecus OP3H
V. cholerae N16961
a
TM ax
(°C)
Experiment
7.21
4.94
6.59
6.34
4.29
1.82
4.82
4.28
11.13
5.64
6.88
8.12
7.03
10.74
6.45
4.56
9.30
3.11
12.70
RangeHot
(°C)
1.08
0.99
1.07
1.1
1.13
1.03
1.21
1.25
1.35
1.17
1.23
1.38
1.3
1.55
1.27
1.17
1.19
1.32
1.28
SM ax
(M NaCl)
1
0.90
0.90
0.83
0.77
0.84
0.83
0.87
0.73
0.90
0.72
0.77
0.78
0.68
0.88
0.75
0.64
0.69
0.66
MHot
16
16
16
16
16
22
16
16
16
16
NA
NA
20–30c
NA
25
25
NA
PIE-LTER
PIE-LTER
NW Mediterranean Sea, 1 m depth
PIE-LTER
PIE-LTER
PIE-LTER
PIE-LTER
North sea
Dried sardines (shirasu), Japan
Aquafarm, Darwin, NT, Australia
Ulcerous lesion in cod
Oyster pond, MA, USA
Oyster pond, MA, USA
Stool of cholera patient, Bangladesh
Tisolation
(°C)
PIE-LTERa
PIE-LTER
PIE-LTER
Isolation environment
NA
0.52c
NA
0.07
0.07
NA
0.52–0.58
0.52–0.58
NA
NA
NA
0.52–0.58
0.52–0.58
NA
0.52–0.58
0.52–0.58
0.52–0.58
Sisolation
(M NaCl)
Table 1.1: Measured niche shape parameters and strain isolation conditions
was kindly provided by Jarone Pinhassi, University of Kalmar, Sweden. Note that
strains obtained from the ATCC may have undergone periods of replication in constant laboratory conditions.
Cultures and growth conditions
To ensure clonality of cultures, cells were streaked out to single colonies on solid
medium (all analyzed strains lack a swarming motility phenotype on solid medium);
subsequently a single colony was picked for inoculating liquid medium. This isolation
step was generally applied before and after storage of a strain at -80C. To prepare
cultures for -80C storage, autoclaved glycerol was added to a final concentration of
25% v/v. Cultures were maintained in tryptic soy broth (TSB) supplemented with 2%
w/v additional sodium chloride (NaCl). For preparation of solid TSB medium, Bacto
Agar (BD, Franklin Lakes, NJ, USA) was added to a concentration of 1.5% w/v.
Cultures were grown at 22C with gentle shaking (190 rpm). For all experiments on
2D gradients, salinity-adjusted medium (LB-S) was prepared following the protocol
for lysogeny broth (LB) medium with the NaCl concentration adjusted as required.
We relied solely on NaCl for adjusting the salinity of the growth medium since Stanley
and coworkers [33] have shown that NaCl is the most effective salt with respect to
restoring normal temperature tolerance in bacteria when replenishing dilute seawater.
Other deviations from standard LB medium were that the pH of LB-S medium was
adjusted to 8.0 using 1N NaOH and the concentration of agar in solid LB-S was raised
from 1.2% to 1.5% wv.
Preparation of 2-dimensional (2D) salinity/temperature gradients
Orthogonal salinity and temperature gradients were established in disposable, nonvented 241 x 241 x 20 mm bio-assay polystyrene dishes (Nunc, Thermo Fisher Scientific, Roskilde, Denmark). Salinity gradients were established by diffusion between
two adjacent medium layers [14] using the following procedure: The dish was tilted
17
by raising one side by 5 mm and a wedge-shaped high salinity base layer was poured,
using 170 ml solid LB-S medium containing 2.2 M NaCl. After solidification the plate
was leveled and the top layer was poured using 170 ml solid LB-S medium without
additional NaCl (0 M, Fig. S1). The gradient was equilibrated for 43 h to ensure
diffusion-driven formation of the salinity gradient along one axis of the bio-assay dish.
Prior to inoculation, any residual water (from condensation during cooling of the solid
medium) was removed from the surface of the gradient followed by drying for 10 min
under sterile laminar air flow.
Stable and reproducible temperature gradients were established using a custom
made device (supporting text), into which the bio-assay dish was installed after establishment of a salinity gradient (Fig. S1).
Inoculation of 2D salinity/temperature gradients
After colony purification on solid TSB medium, cultures were grown overnight in
liquid LB-S containing 0.5 M NaCl. After adjusting OD600 to 0.07 using a NanoDrop
1000 (Thermo Scientific, Wilmington, DE, USA) spectrophotometer (1 mm optical
path length), the cultures were further diluted in LB-S 0.5 M NaCl to a density of
6 ∗ 107 cells/ml. Cells were then spotted onto the surface of the salinity gradient in a
regularly spaced grid of 24 x 24 spots using a 96-well replicator, rather than spread
across the surface to avoid cell density effects (e.g., colonies that extend into regions
that otherwise do not support growth from individual cells). Assuming that each pin
of the 96-well replicator transfers a volume of 2-20ul, the number of cells inoculated
onto each spot is estimated to be on the order of 105 − 106 . The distance of 0.9
mm between neighboring culture spots corresponds to the pins on a 96-well plate
replicator.
Data acquisition from 2D salinity/temperature gradients
Gradient plates were incubated for 24h +/-2h after inoculation. Zero Net Growth
Isoclines (ZNGIs) were determined from the most extreme temperature/salinity val-
18
ues that developed visible colonies within this time frame (Fig. 1.2A), and were used
as proxies for niche boundaries. The salinity of all culture spots along the ZNGI and
the temperature gradient were measured, and a digital image of the experiment was
taken. Since temperature gradients proved stable along the salinity axis (Fig. S3B,
Fig. S5D), the temperature of culture spots along the ZNGI could be inferred from
the temperature gradient, rather than measured for each spot individually. In each
experiment, temperature was measured in 1 cm intervals along the temperature axis,
using a handheld IR thermometer, with four replicate measurements taken at each
point. These measurements were fit to a cubic function, which was then used to infer
the temperature at the ZNGI culture spots. By contrast, the salinity gradients were
more variable along the temperature axis (Fig. S4D, Fig. S5B), necessitating the direct measurement of salinity at each of the ZNGI culture spots. At each spot, a small
core sample was taken, and separated into liquid and solid components by centrifugation for 30 min at 20,800 x g. The liquid phase was diluted in deionized H2O, and
ppt salinity measured using a refractometer. A standard curve was used to convert
the measured salinities into mol/l NaCl (Fig. S2). Two duplicate measurements were
performed on each core, and their mean was taken as the spots salinity.
Phylogenetic analysis and independent contrasts
A phylogenetic tree of the studied strains plus E. coli K12 (outgroup for rooting)
was constructed based on partial sequences from 8 housekeeping genes: hsp60, recA,
gyrB, sodA, adk, mdh, pgi, and chiA. Sequences for strains Vibrio sp. MED222, V.
parahaemolyticus, and V. fischeri MJ11, and Listonella anguillarum were obtained
from complete genomes available on GenBank. For all other strains, partial sequences
were obtained during previous studies using multilocus sequencing [31, 34, and references therein]. Sequences were aligned using MUSCLE [35], and manually trimmed
before concatenating all alignments. A phylogenetic tree was inferred using PhyML
[36] with default settings. We note that this tree reflects the strains evolutionary
history, rather than the evolutionary history of particular genes that determine the
niche shape.
19
Felsensteins independent contrasts method [37, 38] was implemented in the Python
programming language, and used to compute correlations between shape parameters
and the statistical significance of these correlations. This method is utilized since
standard Pearson correlations do not take into account the phylogenetic relationships
between strains, which may lead to spurious correlations. The method of independent
contrasts circumvents this problem by constructing new, independent variables, which
are differences between the parameters of different strains. This method is based on
the assumptions that trait evolution is consistent with a neutral Brownian motion
model, and that dependencies arise from shared evolutionary ancestry. The validity of
these assumptions was assessed using two different methods, as suggested by Garland
et al. [39]. First, under the model assumptions normalized contrasts are predicted to
be independent of the square root of the sum of their branch lengths. This expectation
was validated by performing a linear ordinary least-squares fit between these variables.
Contrasts that were clear outliers with respect to any of the niche parameters were
excluded from further analysis (e.g. Fig. S8). These contrasts corresponded to
nodes with extremely short branch length, and are known to be very sensitive to
measurement errors [40]. Second, the model prediction that contrasts be normally
distributed was assessed using the Shapiro-Wilk test for normality (Table S1).
Theory
Theory of niche shapes and corresponding classes of stress
interactions
To avoid ambiguity, we formally define the fundamental niche and related terms, as
used in this paper. Following Hutchinson, the fundamental niche represents the combination of environmental conditions that permit a species to maintain its populations
in the absence of other species. Each combination of permissive conditions can be
represented as a point in a high-dimensional space in which each coordinate represents
the magnitude of a single environmental factor. The collection of all such points is
20
termed the niche space, and the niche boundary is defined as the curve encapsulating
all permissive conditions in the niche space. Equivalently, for a given species, let g(E)
be the species net growth rate at environmental conditions E. The fundamental niche
corresponds to the set of conditions for which g(E)0, and the niche shape to the set
of conditions for which g(E) = 0. Because it is not possible to characterize the full
(multi-dimensional) extent of the niche space for an organism, we focus on a crosssection in which two non-consumable environmental factors (NEFs), temperature and
salinity, are systematically varied. Changing other environmental factors, such as pH
or type of media, can affect the shape of the temperature-salinity fundamental niche
since a different cross-section of the full niche space might be measured.
Five basic classes of niche shapes are illustrated in Fig. 1.1. These shapes capture
the effect of two NEFs (with levels E1 and E2) on a single population, with all other
parameters held constant. We assume there exists a unique optimal condition E1opt ,
E2opt that supports the largest sustainable population, and defined the origin to be
this condition. The axes thus correspond to deviations from optimal conditions, or
stress levels. The curves represent niche boundaries, and contained between a curve
and the axes is the area corresponding to the fundamental niche. It is important
to note that different quadrants represent different types of stress (e.g., heat stress
vs. cold stress), which may have entirely different response pathways and couplings.
Thus, the niche shape may vary between quadrants. Fig. 1.1 represents only one
quadrant of the niche shape, in which both NEF are at, or above their optimal level.
We focus on basic niche shapes that can be interpreted in terms of the physiology
underlying the organisms stress response, rather than developing complex models
that are able to capture the finer details of niche shapes. To do so, we considered
shapes corresponding to zero, linear, and non-linear interactions between stresses,
with the restrictions that the type of stress interaction is independent of the stress
levels (i.e., the niche boundary does not cross the additivity line), and that the sign
of the curvature of the boundary is constant. An analogous approach is widely used
in multicomponent drug therapeutics [41, 42], where it is known as isobolographic
analysis [43].
21
These assumptions result in five basic shapes: concave, diagonal, convex, rectangular, and super-convex (Fig. 1.1 and Table 1.2). The simplest case is that of
non-interacting stressors, which lead to a rectangular niche shape since the maximal
tolerance to either stressor is independent of the level of the other stressor. One way
stresses can interact is through both creating demand for a common, limiting cellular resource, such as ATP. That is, some amount of the common cellular resource is
dedicated to alleviate the effects of either stress. If the stress level maps to limiting
resource consumption in a linear fashion, the fundamental niche boundary will be diagonal. On the other hand, if the resource consumption increases faster or slower than
linear with stress levels, niche shapes can be concave or convex, respectively. Other
shapes can arise when the concentration or activity of some cellular components (e.g.,
proteins or pathways) affects both stresses simultaneously. These components may
not compete for cellular resources, but instead change the physicochemical properties
of the cell. For example, the permeability of the cell membrane is altered by the concentration of porins, and can influence the effect of multiple stresses. Super-convex
shapes can arise if the effects of one stress alleviate the effects of another, and concave
shapes can result if the optimal activity of these cellular components is different.
These basic niche shapes are a simplification and an idealization, which is not
expected to be precisely reproduced in observed niche shapes. Rather, they enable
the identification of the dominant features of stress response physiology. For instance,
though stress response is typically multifaceted, if a nearly diagonal shape is observed
(e.g., Fig. 1.2C), it is likely that the main response pathways of the two stresses
compete for the same cellular resource.
22
10
9
8
Super-convex
(Anagonistic)
7
S2
S2
6
Rectangular (Noninteracting)
5
Convex
(Antagonistic)
4
Diagnonal
(Additive)
Concave
(Synergistic)
3
2
1
0
0
1
2
3
4
5
6
7
8
9
10
S1
S1
Figure 1.1: Five classes of fundamental niche morphology and underlying stress
interactions. Axes measure the deviations from the optimal conditions (the origin), i.e.,
the stress due to the environmental factors. The curves represent niche boundaries, with
the area contained between a curve and the axes corresponding to the fundamental niche
area. Each curve is labeled according to its shape, with the corresponding type of stress
interaction indicated in parentheses. Note that only the positive quadrant (both NEFs
above their optimal levels) is depicted.
Results
Measurement of 2-dimensional (2D) salinity-temperature gradients
We designed an inexpensive platform to create 2D orthogonal gradients of temperature and salinity on solid media, which allowed estimation of niche shapes realized in
natural populations and their comparison to our simple theoretical model. We focused
on the high temperature/high salinity quadrant, because our experimental apparatus
did not allow us to examine sufficiently low temperatures for many strains. In addition, we found that upon removal of the temperature stress, new colonies developed
at the cold temperature region, whereas no new colonies form at the high tempera-
23
B
0.4 M
temperature gradient
1.7 M
A
temperature [˚C]
1.4
1.4
SMax
ATot
salinity (NaCl) gradient
1.3
salinity [M NaCl]
1.2
1.2
SMin, cold
AFN
1.1
Sal [M NaCl]
1.3
1.1
1
1.0
0.9
0.9
0.8
0.8
0.7
SMin, hot
TExt, cold
TOpt
TExt, hot
0.6
0.5 ˚C
40.0 ˚C
0.00 M
1.0 ˚C
0.10 M
0.05 M
0.6
1.5 ˚C
0.7
14
14
16
16
18
18
20
22
22
24
24
26
26
28
28
30
30
32
32
34
34
T [˚C]
15.0 ˚C
C
1.25
1.25
V. metecus OP6B
1.40
1.4
1.10
1.1
V. fischeri MJ11
1.30
1.3
1.05
1.05
1.10
1.1
1.20
1.2
1.001
1.05
1.05
1.001
0.95
0.95
0.90
0.9
0.85
0.85
M = AFN/ATot
M
= 0.64
1.10
1.1
1.001
M = AFN/ATot
0.90
0.9
= 0.77
[˚C]
TT [˚C]
0.90
0.9
0.80
0.8
M = AFN/ATot
M
= 0.90
0.75
0.75
0.7
0.70
20
20 22 24
24 26
26 28
28 30
30 32
32 34 36 38
38 40 42
42
V. splendidus 12B1
0.95
0.95
0.85
0.85
M
0.80
0.8
0.80
0.8
0.75
0.75
Sal [M NaCl]
1.15
1.15
Sal [M NaCl]
Sal
NACl]
Sal [M
[M NaCl]
1.20
1.2
18
18
20
20
22
22
24
24
26
[˚C]
TT [˚C]
28
28
30
32
32
17 18 19
19 20 21 22 23
23 24 25 26
26 27
27 28
28
[˚C]
TT [˚C]
Figure 1.2: Zero Net Growth Isoclines (ZNGI) on 2 dimensional salinitytemperature gradients.
(A) Example of a 2-dimensional solid-medium salinitytemperature gradient established in 24x24 cm square culture dishes. White spots are bacterial colonies. Dark spots are locations along the estimated ZNGI where salinity was
measured directly by destructive coring. The outer plot along the x-axis shows the temperature values (bottom plot, solid lines) and their measurement error (upper plot, diamonds)
along the test gradient, when a low (blue) or high (red) temperature range setup was employed. Corresponding plots for salinity are shown along the y-axis (for details see Materials
& Methods, supporting text). (B) Example of a measured ZNGI (open circles) and niche
shape parameters. Parameters are shown for both the high temperature and low temperature quadrants, though our analysis focuses on the high temperature quadrant (see main
text). TExt,hot (TM ax ) - highest permissive temperature. TExt,cold - lowest permissive temperature. TOpt - optimal temperature (as defined in main text). SM ax - highest permissive
salinity. SM in - lowest permissive salinity. AF N - area of the fundamental niche (shaded).
AT ot - area of the fundamental niche if the stresses acted independently. (C) Examples of
the three classes of niche shapes observed: diagonal, convex and rectangular (from left to
right). Shaded areas correspond to the niche area in the high-temperature quadrant.
24
ture region within an additional 24 hours, consistent with previous studies showing
resuscitation following a temperature increase [44]. Therefore, at low temperatures
there was ambiguity between no growth and slow growth phenotypes, while the effect
of higher temperatures was cell death, making analysis more straightforward. Our
motivation to focus on the high salinity region was to achieve greater resolution and
to be able to use the same rich medium for all strains. Assaying lower salinities would
require using strain-specific media, which may differentially affect niche morphology,
convoluting niche comparisons.
Niche morphology was quantified using the following parameters: highest permissive temperature (TM ax ), highest permissive salinity (SM ax ), optimal temperature
(TOpt ), and niche morphology index (M ). The niche morphology index, which summarizes how interactions between stressors affect niche boundaries, was defined to
objectively classify the different niche shapes. M is defined as the area spanned by
the niche divided by the area of the rectangular niche that would be observed had
the two stressors been acting independently (Fig. 1.2). Table 1.2 illustrates how M
values correspond to different classes of niche shape: concave - M < 0.5; diagonal M = 0.5; convex - 0.5 < M < 1; rectangular - M = 1; super-convex - M > 1. We
note that while SOpt was outside the measured salinity range the inferred M values
are representative of those of the full high temperature/high salinity quadrant, as long
as the class of niche shape is consistent in this quadrant (note that no such switches
were observed in the measured range of any of the strains).
In general, TOpt can be a function of salinity and requires detailed growth curves
at each position to measure directly. We avoided this added complexity by approximating TOpt using two independent methods: (i) we took TOpt as the temperature
that allows growth in the highest salinity (SM ax ), and (ii) we defined TOpt as the
midpoint of the range of temperatures in which the largest colonies formed. We note
that the first approach is not applicable to super-convex shapes. However, the second
method, which is capable of detecting super-convex shapes, yielded nearly identical
results, with no super-convex shapes. Therefore, we report results based on the first,
more straightforward approach.
25
Observed niche shapes
M values fell in a narrow range between 0.64-1.00, and the observed niche shapes
were all convex, ranging from nearly diagonal, to nearly rectangular (Table 1.1, Fig.
1.3). No concave or super-convex shapes were observed. Niche shape parameters for
all strains are summarized in Table 1.1, and niche shapes of all strains are depicted
in Fig. S6. We note that classes of niche shapes in the low temperature/high salinity
quadrant are consistent with those of the high temperature/high salinity quadrant
(Fig. S7), and were excluded solely because we have less confidence in their accuracy,
as detailed in the previous section.
Maximal permissible temperatures, ranging from 25C to 41C, were consistent with
realistic environmental conditions, whereas permissible salinities, ranging from 0.99
M NaCl to 1.55 M NaCl, far exceeded that typical of marine environments of 0.6
M NaCl [45]. Moreover, though the conditions strains typically inhabit agrees well
with the strains temperature tolerance, they are negatively correlated with the strains
salinity tolerance (Fig. 1.3). This is exemplified by the fact that V. cholerae strains
from warm estuarine and freshwater environments display high temperature and salt
tolerance, whereas V. splendidus strains from a colder marine environment have a
markedly lower temperature and salt tolerance.
Additionally, we observe that the various niche parameters do not vary independently. Salinity and temperature tolerance are positively correlated with each other,
and negatively correlated with M values (Fig. 1.3). Thus, strains that display niche
shapes consistent with independent responses to both stressors generally have lower
overall tolerance to those stressors. By contrast, strains with high tolerances to a
single stress tend to also have a high tolerance to the other stressor, and have a
niche shape consistent with the existence of coupling between the stress responses.
Although these trends appear highly significant, spurious correlations between independently evolving factors can arise because of the phylogenetic structure of the
data. To control for phylogenetic effects, we used Felsensteins method of independent
contrasts [37, 38] to compute correlations between niche shape parameters and eval-
26
Smax
Mhot
Legend:
0.1
0.1
Tmax
TMax
SMax
MHot
Smax
Tmax
Mhot
27
0.1
0.1
Legend:
Tmax
0.1
Legend:
Tmax
Figure 1.3: Evolution of the fundamental niche. (A) ZNGIs of all strains at the high
temperature/high salinity quadrant, colored by M values. ZNGIs tend to be located along
the diagonal from the bottom-left corner to the top-right corner, indicating a correlation
between temperature and salinity tolerance. Additionally, as strains become more tolerant
their niche shape varies from rectangular to diagonal (decreasing M value). (B) Maximal
permissive temperature (TM ax ) vs. maximal permissive salinity (SM ax ) and M -value. Each
point represents the values measured for a single strain. Note that the correlations were
calculated using Felsensteins method of independent contrasts (see main text). (C) MLSA
phylogenetic tree of all strains. Corresponding values of TM ax , SM ax and M are given by
the color bars to the right.
V.spl1C5
V.spl13C1
V.splZ264
V.splI273
V.spMED222
V.spl12E10
V.spl12F1
V.spl12B1
V.spl14B11
V.spl12A10
TMax
S
Mhot
38
Mhot
MHot
Smax
Mhot
36
MMax
Smax
Hot
34
S
Tmax
MMax
Smax
Hot
32
0.1
0.1
30
0.1
0.1
SMax [M NaCl]
1.4
1.3
1.2
V.chN16961
V.chN16961
V.chOP4A
V. cholera N16961
V.psOP3H
V.psOP3H
OP3H
metecusN16961
V. cholera
V.chN16961
V.chN16961
V.chOP4A
V.
V.psOP6B
V.psOP6B
OP6B
metecus
V.
V.psOP3H
V.psOP3H
V.chN16961
OP3H
metecus
V.
V.chN16961
V. cholera N16961
L.anguill
L.anguill
anguillarum
L.
V.psOP6B
V.psOP6B
V.psOP3H
OP6B
metecus
V.
V.psOP3H
OP3H
metecus
V.
V.harveyi
V.harveyi
L.anguill
DAT7222
sp.
V.
L.anguill
V.psOP6B
anguillarum
L.
V.psOP6B
OP6B
V. metecus
V.parahaem
V.parahaem
parahaemolyticus
V.
V.harveyi
V.harveyi
L.anguill
DAT7222
sp.
V.
L.anguill
anguillarum
L.
V.fischeri
V.fischeri
MJ11
fischeri
V.
V.parahaem
V.parahaem
V.harveyi
V.
V.harveyi
sp. DAT7222
V. parahaemolyticus
V.spl1C5
V.spl1C5
1C5
crassostrea
V.
V.fischeri
V.fischeri
V.parahaem
MJ11
fischeri
V.
V.parahaem
parahaemolyticus
V. sp.
V.spl13C1
V.spl13C1
F12
V.
V.spl1C5
V.spl1C5
1C5
crassostrea
V.
V.fischeri
V.fischeri
MJ11
fischeri
V.
V.splZ264
V.splZ264
Z-264
cyclitrophicus
V. sp.
V.spl13C1
V.spl13C1
V.spl1C5
F12
V.
V.spl1C5
1C5
crassostreaV.splI273
V.splI273
1-273
cyclitrophicus
V. cyclitrophicus
V.splZ264
V.splZ264
Z-264
V.
V.spl13C1
V.spl13C1
V. sp. F12
V.spMED222
V.spMED222
MED222
sp.
V.
V.splI273
V.splI273
1-273
cyclitrophicus
V.
V.splZ264
V.splZ264
Z-264
V. cyclitrophicus
V.spl12E10
V.spl12E10
splendidus
V. sp.
V.spMED222
V.spMED222
MED22212E01
V.
V.splI273
V.splI273
1-273
V. cyclitrophicus
V.spl12F1
V.spl12F1
12F01
splendidus 12E01
V. splendidus
V.spl12E10
V.spl12E10
V.
V.spMED222
V.spMED222
MED222
sp.
V.
V.spl12B1
V.spl12B1
12B01
splendidus
V.
V.spl12F1
V.spl12F1
12F01
splendidus
V.
V.spl12E10
V.spl12E10
12E01
splendidus
V.
V.spl14B11
V.spl14B11
14B11
splendidus 12B01
V. splendidus
V.spl12B1
V.spl12B1
V.spl12F1
V.
V.spl12F1
12F01
V.spl12A10
V.spl12A10
12A10
splendidus
V.
V.spl14B11
V.spl14B11
V.
V.spl12B1
V.spl12B1
12B01
splendidus 14B11
V. splendidus
V.spl12A10
V.spl12A10
V.spl14B11
V. splendidus 12A10
V.spl14B11
14B11
V.spl12A10
V.spl12A10
V. splendidus 12A10
V.chOP4A
SMax
MHot
0.8
1.1
1.0
40
MHot
28
28
28
Max
TMax [˚C]
30 32 34 36
30 T32 34
36
Max [˚C]
30 T32
34 36
[˚C]
V.spl12A10
V.chN16961
V.chOP4A
V.psOP3H
V.chN16961
V.chOP4A
V.psOP6B
V.psOP3H
V.chN16961
L.anguill
V.psOP6B
V.psOP3H
V.harveyi
L.anguill
V.psOP6B
V.parahaem
V.harveyi
L.anguill
V.fischeri
V.parahaem
V.harveyi
V.spl1C5
V.fischeri
V.parahaem
V.spl13C1
V.spl1C5
V.fischeri
V.splZ264
V.spl13C1
V.spl1C5
V.splI273
V.splZ264
V.spl13C1
V.spMED222
V.splI273
V.splZ264
V.spl12E10
V.spMED222
V.splI273
V.spl12F1
V.spl12E10
V.spMED222
V.spl12B1
V.spl12F1
V.spl12E10
V.spl14B11
V.spl12B1
V.spl12F1
V.spl12A10
V.spl14B11
V.spl12B1
V.spl12A10
V.spl14B11
V.chOP4A
had a correlation of -0.56 (p-value 4.6e-2).
Legend: TMax
Tmax
Legend: T
SMax
Max
Tmax
0.1
0.1
28
Mhot
26
Mhot
V.chOP4A
T
M
S ax
M
M ax
Ho
t
0.9
Legend:
0.1
0.1
V.chN16961
V.chN16961
V. cholera N16961
V.psOP3H
V.psOP3H
V. metecus OP3H
V.psOP6B
V.psOP6B
V. metecus OP6B
L.anguill
L. anguillarum L.anguill
V.harveyi
V.harveyi
V. sp. DAT7222
V.parahaem
V.parahaem
V. parahaemolyticus
V.fischeri
V.fischeri
V. fischeri MJ11
V.spl1C5
V. crassostrea V.spl1C5
1C5
V.spl13C1
V.spl13C1
V. sp. F12
V.splZ264
V.splZ264
V. cyclitrophicus Z-264
V.splI273
V.splI273
V. cyclitrophicus
1-273
V.spMED222
V. sp. MED222V.spMED222
V.spl12E10
V.spl12E10
V. splendidus 12E01
V.spl12F1
V.spl12F1
V. splendidus 12F01
V.spl12B1
V.spl12B1
V. splendidus 12B01
V.spl14B11
V.spl14B11
V. splendidus 14B11
V.spl12A10
V.spl12A10
V. splendidus 12A10
0.1
26
26
26
1.5
Smax
Mhot
40
40
40
SMax
S
MMax
Hot
SMax
M
Hot
MHot
1.6
Smax
40
0.68 0.72 0.76 0.80 0.84 0.88 0.92 0.96
0.68 0.72 0.76 0.80 0.84 0.88 0.92 0.96
0.68 0.72 0.76 0.80 0.84 0.88 0.92 0.96
0.68 0.72 0.76 0.80 0.84 0.88 0.92 0.96
0.1
B
Tmax
Smax
35
C
C
C
30
35
35
35
0.6
Legend:
30
Temp [˚C]
30 [˚C]
Temp
30 [˚C]
Temp
Temp [˚C]
0.8
MHot
25
25
25
1.4
MHot
MHot
0.1
20
20
20
1.6
1.6
1.5
1.6
1.5
1.5
1.4
1.4
1.3
1.4
1.3
1.2
1.3
1.2
1.1
1.2
1.1
1.1
1.0
1.0
0.9
1.0
0.9
0.9
1.6
0.4
0.4
MHot
0.6
0.6
0.4
25
0.8
0.8
0.6
C
20
1.0
1.0
0.8
B
B
B
1.0
1.2
1.2
1.0
Legend:
1.4
1.4
1.2
0.4
[M
NaCl]
[M
NaCl]
SalSal
[MSal
NaCl]
Sal [M NaCl]
1.2
SMax
[M
NaCl]
S[M
[M
NaCl]
SMax
NaCl]
Max
A
T T T
M M M
S aSx aSx ax
M M M
M aMx aMx ax
Ho Ho Ho
t t t
A 1.6
A 1.6
A 1.4
1.6
38
38
38
40
40
40
uate their significance. Even after accounting for the phylogeny, the observed trends
remained statistically significant: TM ax and SM ax had a correlation of 0.86 (p-value
7.2e-4); TM ax and Mhot had a correlation of -0.62 (p-value 2.7e-2); SM ax and Mhot
1.0
0.95
0.9
0.85
0.75
0.7
0.65
0.6
TMax [˚C]
V.chOP4A
V.chN16961
V.psOP3H
V.psOP6B
L.anguill
V.harveyi
V.parahaem
V.fischeri
1.0
1.0
0.95
1.0
0.95
0.9
0.95
0.9
0.85
0.9
0.85
0.8
0.85
0.8
0.75
0.8
0.75
0.7
0.75
0.7
0.65
0.7
0.65
0.6
0.65
0.6
0.6
MHot
MHot
MHot
Evolution of the fundamental niche
Comparison of niche shape across 17 strains provides a clear answer to the question
of whether the majority of variation in niche shape occurs within or between species.
Inspection of Figure 3C shows that niche shapes tend to be more similar between
closely related strains, with very limited or no qualitative niche morphology changes
occurring within species. For example, the cluster of V. splendidus isolates shows low
tolerance to high temperatures and salinities, and almost rectangular niche shapes
(high M ), while the V. cholerae/metecus isolates display high temperature and salinity tolerances and nearly diagonal niche shapes (low M ). The average difference
in niche parameters measured between these groups exceeds the within-population
variation by a factor of 2.5 (for SM ax ) to 5 (for TM ax ).
Discussion
The fundamental niche captures the range of environmental conditions in which a
species can persist in isolation. However, since natural communities typically comprise
numerous interacting species, the extent to which the fundamental niche is relevant to
the ecology of natural communities is unclear and warrants further investigation. In
this study, we show that all studied strains could tolerate salinities that are unlikely
to be ecologically relevant, indicating that, in this dimension, their fundamental niche
is far broader than their ecological range. In addition, Randa et al. [27] found that
V. vulnificus usually occurs in low salinity environments, but, as the temperature
increases, it can expand its range into higher salinity environments. In light of our
results, the fact that V. vulnificus is rare at saline, low temperature environments is
likely a consequence of biotic interactions, such as competitive exclusion or predation,
rather than an inherent inability to thrive at these conditions. Thus, V. vulnificus
realized ecological range is a limited section of its fundamental niche.
Temperature and salinity tolerances are positively correlated across all strains in
the study despite the fact that these factors are negatively correlated in some of the
environments the strains were isolated from (e.g., V. metecus strains from a warm,
28
low salinity environment in contrast to V. splendidus strains from a colder, saline
marine environment.). These results indicate that salinity and temperature tolerance mechanisms may be coupled at the molecular level, consistent with the findings
of previous studies demonstrating that pre-exposure to osmotic stress increased the
tolerance to heat stress in Vibrio vulnicus [46]. Such coupling may result from temperature and salinity responses using common molecular pathways such as the SOS
response pathway, the heat-shock response pathway, and the general stress response
pathway [47, 48]. However, Rosche et al. have demonstarted that the cross-protection
between osmolarity and heat in Vibrio vulnicus is independent of rpoS, the master
regulator of the general stress response mechanism, and were unable to elucidate the
origin of this cross-protection [46].
An alternative potential mechanism for coupling between stress responses is partitioning of cellular resources between different stress response pathways. In the
simplest (linear) model, a cells tolerance would be a function of the sum of the two
stress levels, leading to diagonal niche shapes (M ∼ 0.5). Remarkably, we observe
an inverse correlation between stress tolerance and M values that remains significant
even after controlling for phylogeny. Together with the unexpected positive correlation between the two stress tolerances, this correlation suggests a model in which
the temperature and salinity response pathways are coupled, and moreover, that they
compete for common cellular resources (e.g., ATP).
Temperature adaptation may explain the incongruence between salinity tolerance
and environmental salinity. Since maximal temperatures are consistent with conditions at environments strains typically occur in, and strains can tolerate a much
wider range of salinities than is ecologically relevant, it is possible that heat tolerance is under much stronger selection than salinity tolerance. Under this hypothesis,
heat tolerance is set by the environmental conditions, which in turn affects salinity
tolerance, which is mechanistically coupled to it. Thus, like heat tolerance, salinity
tolerance is predicted to be correlated with environmental temperature, rather than
environmental salinity. This is indeed the case in our data.
The potential for coupling between stressors cautions against making inferences
29
based on individual stress tolerance phenotypes, as the results could be at odds with
ecology. In fact, we cannot rule out coupling along other unmeasured dimensions
(e.g., nutrient levels, pH), nor can we rule out that these factors (rather than temperature) may be driving salinity and/or temperature tolerance levels. Nonetheless,
these results indicate that meaningful work linking physiological, ecological, and evolutionary aspects of niche theory will require an appreciation of the nuances of a
multi-dimensional and potentially highly coupled niche space.
30
Concave
Super-Convex
Synergistic
Antagonistic
Additive
Diagonal
Convex
Type of interaction
Non-interacting
Niche shape
Rectangular
The combined stress incurred
by a combination of the two
factors is more severe than the
stress incurred by only one factor at the equivalent level.
The combined stress incurred
by a combination of two
factors is less severe than the
stress incurred by only one
factor at the equivalent level.
Growth rate is determined by
a linear combination of the
stresses.
Description
Growth rate is determined by
the more severe of the two
stresses and is completely unaffected by the other stress. As
noted by Hutchinson the corresponding niche shape is rectangular (G.E. Hutchinson, 1957).
Multiple
forms.
compatible
functional
Concentrations of relevant cellular components under either
stress alone are disparate.
Concentrations of
relevant cellular
components under
either stress alone are
similar.
For each unit of either stress
a common cellular resource is
dedicated to alleviate stress effects. The cellular resource
may be ATP, a mineral, specific proteins (e.g. chaperons),
etc.
g(S1, S2) = f (a1 ∗ S1 + a2 ∗ S2),
where f (a1 ∗ S1 + a2 ∗ S2) is any
arbitrary function of its argument,
and a1, a2 are the amount of common resource required to cope with
stresses S1 and S2, correspondingly.
Multiple compatible functional
forms.
Mechanism/example
The cellular mechanisms related to the two stresses,
and/or the limiting cellular resources used to alleviate their
influence are distinct.
Functional form
g(S1, S2) = min{f 1(S1), f 2(S2)}.
Note that f 1(S1) and f 2(S2) can
be any two arbitrary functions.
M < 0.5
M >1
0.5 < M < 1
M = 0.5
M
M =1
Table 1.2: Basic classes of fundamental niche shapes, and corresponding stress interactions
31
Chapter 2
Population Genomics of Early
Events in the Ecological
Differentiation of Bacteria
B. Jesse Shapiro, Jonathan Friedman, Otto X. Cordero, Sarah P.
Preheim, Sonia C. Timberlake, Gitta Szab, Martin F. Polz, Eric J. Alm
This chapter is presented as it originally appeared in Science 336, 48 (2012).
Chapter 2
Population Genomics of Early
Events in the Ecological
Differentiation of Bacteria
Genetic exchange is common among bacteria, but its effect on population diversity during ecological differentiation remains controversial. A
fundamental question is whether advantageous mutations lead to selection
of clonal genomes or, as in sexual eukaryotes, sweep through populations
on their own. Here we show that in two recently diverged populations
of ocean bacteria, ecological differentiation has occurred akin to a sexual
mechanism: a few genome regions have swept through subpopulations in a
habitat specific manner, accompanied by gradual separation of gene pools
as evidenced by increased habitat-specificity of the most recent recombinations. These findings reconcile previous, seemingly contradictory empirical
observations of the genetic structure of bacterial populations, and point to
a more unified process of differentiation in bacteria and sexual eukaryotes
than previously imagined.
33
How adaptive mutations spread through bacterial populations and trigger ecological differentiation has remained controversial. While it is agreed that the key
factor is the balance between recombination and positive selection, theory and observations remain seemingly at odds. On the one hand, evidence for genes spreading
through populations independently via recombination (gene-specific sweeps) is found
in observations of environment-specific genes [49] and alleles [50], and reduced diversity at single loci amidst high genomewide polymorphism [51, 52]. On the other
hand, mathematical modeling suggests that empirically observed rates of homologous recombination should not be high enough to unlink a gene, which is under even
moderate selection, from the rest of the genome [8, 53]. Importantly, this recombination/selection balance, expressed most saliently by the ecotype theory, leads to a
prediction that is actually observed but at odds with gene-specific sweeps: bacterial
diversity is organized into ecologically differentiated clusters [21, 34, 54]. The proposed mechanism involves cycles of neutral diversification punctuated by genomewide
selective sweeps [53]. While the observations of environment-specific genes and locusspecific reduced diversity conflict with the ecotype model of selected clonal genomes,
they do not explain why its prediction of coincident genetic and ecological clusters
hold true, nor provide insights into the early genomic events accompanying adaptation. How to reconcile these different empirical observations, so seemingly at odds
with each other, therefore remains an open question.
Here, we test whether recombination is strong enough relative to selection to allow
gene-specific rather than genomewide selective sweeps in natural microbial populations and explore the effect on population-level diversity. Using whole-genome sequences from two recently diverged Vibrio populations with clearly delineated habitat
associations, we show that genome regions rather than whole genomes sweep through
populations, triggering gradual, genomewide differentiation. Our proposed evolutionary scenario is based on three lines of evidence. First, most of the genetic divergence
between ecological populations is restricted to a few genomic loci with low diversity
within one or both of the populations, suggesting recent sweeps of confined regions
of the genome. Second, we show that only one of the two chromosomes compris34
ing the genome has swept through part of one population. Third, the most recent
recombination events tend to be population specific but older events are not, reinforcing the notion that these populations are on independent evolutionary trajectories,
which may ultimately lead to the formation of genotypic clusters with different ecology. Although such clusters have been interpreted as evidence for the ecotype model,
our results suggest that they can arise even in populations that do not experience
genomewide selective sweeps.
In a previous study, we noticed an instance of very recent ecological differentiation
among two populations of Vibrio cyclitrophicus by their divergence in fast-evolving
protein-coding genes and differential occurrence in the large (L) and small (S) size
fractions of filtered seawater, suggesting association with different zoo- and phytoplankton or suspended organic particle types [21]. This population structure was
reproduced across independent samples taken in 2006 and 2009. We sequenced whole
genomes from both populations (13 L and 7 S isolates, all obtained in 2006). As in
other Vibrionaceae, these genomes consist of two chromosomes, each with a flexible
and core component, defined as blocks of DNA not universally present in all isolates
or shared by all, respectively. To estimate the extent and patterns of recombination
among the isolates, we subdivided the core genome into blocks of DNA on the basis of
their supporting different phylogenetic relationships among the 20 isolates (see Materials and Methods). Overall, the ecological populations described here are among
the most closely related (identical 16S and ¿99% average amino acid identity) studied
with genomewide sequence data, making them an ideal test case for observing the
early events involved in ecological differentiation.
Genes, not genomes, sweep populations
Our first line of evidence favoring gene-specific rather than genomewide selective
sweeps is that most of the differentiation between populations is restricted to just a
few small patches of the core genome. Ecological differentiation (separate phylogenetic grouping of S vs. L) is supported by 725 ecoSNPs, which cluster in a few discrete
patches of the genome (11 in total, 3 of which contain ¿80% of ecoSNPs), whereas
35
the rest of the genome is dominated by 28,744 SNPs rejecting the ecological partition
(Fig. 3.1; S1, S2). Any signal of clonal ancestry has been thoroughly obscured by
homologous recombination (affecting equally genes of all functions, therefore likely
not driven by selection; fig. S3, Materials and Methods), such that no single bifurcating tree relating the 20 strains adequately describes the evolution of more than
1% of the core genome (Fig. 3.1C). Such a pattern could have been produced either
by an ancient genomewide selective sweep in one or both populations, followed by
recombination between populations eroding the clonal frame down to a few regions,
or by recent gene-specific selective sweeps centered on these few regions. The latter
explanation is favored because most major ecoSNP clusters (three out of the four
peaks in Fig. 3.1B) have significantly lower within-habitat diversity (in one or both
habitats) than the chromosome-wide average. The exception is the highly diverse
RTX/RpoS locus, which may be under diversifying selection both within and between habitats. The low within-habitat diversity in the other three regions, which
account for the majority of ecoSNPs, suggests they arrived recently by recombination
(likely from a distantly related population, see Materials and Methods) and swept
through a population before accumulating much polymorphism.
Our second line of evidence shows that genomic fragments can sweep through
populations in an ecology-specific manner without purging genomewide variation. In
particular, a large fraction of chromosome II has swept through a subset of the S population, without impacting the diversity of chromosome I. As evidence for this, each
chromosome has a distinct core phylogeny, with five of the seven S strains grouping
together on chromosome II, but not chromosome I (Fig. 3.1). This 5-S clade (grouping together strains 1F97, 1F111, 1F273, FF274 and FF160; blue branch in Fig. 3.1A
and blue points in Fig. 3.1B) is supported by 796 SNPs: 790 on chromosome II and
six on chromosome I an over 200-fold imbalance after normalizing by the 1.45X more
SNPs/site on chromosome II. Chromosome II also strongly supports one phylogeny
within the 5-S strains; SNPs inconsistent with this phylogeny are restricted almost
entirely to chromosome I (fig. S4, S5). The degree of support for the 5-S group on
chromosome II suggest that a variant of this chromosome swept through these five
36
S strains, independently of chromosome I. The sweep likely occurred recently, before
the clear phylogenetic signal within the 5-S strains was disrupted by recombination.
This signature of a long stretch of DNA (in this case, a chromosome) largely uninterrupted by recombination is a hallmark of recent positive selection in sexual eukaryotes
[55], suggesting a selective sweep of chromosome II independently of the rest of the
genome (chromosome I). The mobilization of genomic fragments on the size scale
of chromosomes may also explain the hybrid genomes observed in novel pathogenic
variants of Vibrio vulnificus [56].
Emergent habitat-specific recombination
Our third line of evidence shows how, despite the lack of genomewide selective sweeps,
tight genotypic clusters may eventually emerge as a result of preferential recombination within, rather than between, habitats. This is evident from quantification of
recent recombination in the core genome, using three very recently diverged pairs
of sister strains, 1F175-1F53, 1F111-1F273 and ZF30-ZF207, that group together at
nearly all SNPs in the genome (Fig. 3.1A). The grouping of such young sister pairs
should only be broken by the most recent recombination events identifiable in our
sample, involving one of the sister strains as a donor or acceptor. We quantified
such events by counting core genome blocks inconsistent with phylogenetic pairing
of sister strains (see Materials and Methods). Out of 93 such blocks (Fig. 3.2A),
76 resulted from one sister strain pairing with another strain from the same habitat. This is significantly more within-habitat recombination than expected under a
model with random recombination across habitats (p ¡ 1e-5; (Materials and Methods)). The excess within-habitat recombination was detectable in both S (p = 0.03)
and L (p < 1e−5) populations considered separately, and is robust to variation in our
assumptions about the relative S:L population sizes (see Materials and Methods). In
contrast, the pairing of more anciently diverged S strains, FF160-FF274, is more often
broken up by recombination with L (222 blocks) than S strains (8 blocks)(p < 1e−5),
perhaps owing to the higher abundance of L strains in the past (e.g., if the ancestral,
undifferentiated population was L-associated). This suggests that the trend toward
37
A
m
p
ep
e o e
e o e L
ECO p
B
h omo ome
h omo ome
m
G
m Xm
n ECO p
n ECO p
# NP
5S p
X
m
m
# NP
upp
# SNPs
m
po
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m
C
●
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M
genome position (Mbp)
%
m
%
%
%
%
%
%
Figure 2.1: Phylogeny follows ecology at just a few habitat-specific loci. (A)
Maximum-likelihood (ML) V. cyc itrophicus phylogenies rooted by V. sp endidus 12B01,
based on core genome nucleotide sequence for chromosome I (left) and II (right). Scale is
substitutions per site; all nodes have 100% bootstrap support unless indicated. (B) Genome
regions with uninterrupted support for (black bars) or against (gray bars; note different
scale) the ecological split of strains into distinct habitats (S/L). Bar height indicates the
number of in- formative SNPs in each region. ECO-sup regions 1 to 11 are described in table
S2; ML trees for four major regions are shown, rooted with 12B01; polyL/polyS indicates
regions with significantly higher (up arrows) or lower (down arrows) nucleotide diversity and
density of segregating polymorphic sites within the L (red) or S (green) habitat, relative to
the chromosome-wide average. Tracks below x axis are as follows. ECO: locations of ECOsupporting (black points) and -rejecting (gray) SNPs. 5-S: SNPs supporting (blue points)
or rejecting (gray) the 5-S branch. Breaks: number of inferred recombination breakpoints
per kb. (C) Tree topologies accounting for most genome length. Top four ranked unrooted
topologies are shown for chromosome I, top 2 for chromosome II, and the percentage of the
core genome accounted for (see Materials & Methods).
the habitat-specific gene flow we identified has emerged relatively recently.
The preference for within-habitat recombination is also apparent in the flexible
genome. This component of the genome changes so rapidly that even the two most
closely-related genomes in our study (1F175-1F53), differing by only 66 substitutions
in 3.54 Mb of core genome, each contain about 4,500 bp of unique DNA (fig. S6).
38
A
CORE GENOME
B
recombination of one sister strain
with S strains
FLEXIBLE GENOME
S strains
0.1
with L strains
FF75
ZF99 ZF99
1F289
ZF28 ZF28
ZF30
ZF65 ZF65
within L
8
ZF207ZF207
4
2
ZF30 ZF30
6
5
9 11
992
8
6
2
sisters
6
ZF207
8
similarity in flexible genome content
between
ZF264ZF264
ZF99
3
ZF270
FF75 FF75
ZF65
ZF255ZF255
ZF205
ZF14 ZF14
ZF28
613
ZF170ZF170
within S
ZF270ZF270
1
1F53 1F53
ZF170
between
ZF264
1F1751F175
FF274
552
580
sisters
FF160
FF160FF160
998
FF274FF274
within S
1F97 1F97
1F2731F273
1F1111F111
1.00
ZF255
1F2891F289
0.001
L strains
ZF14
ZF205ZF205
4
sisters
3
1F175
1000
1F53
between
1
2
1F97
1
1
1
1F111
991
1000
1
1F273
0.1
ZF14
ZF255
Figure 2.2: Recent recombination is more common within than between habitats. (A) Genomewide ML phylogeny based on 3.54 Mb of aligned core genome, with
sister strains highlighted in red or green. All nodes have 79 to 100 bootstrap support. Bar
graphs show events (number of core genome blocks) that split up sisters by recombination
between (gray bars) or within habitats (S, green; L, red). (B) Relative amount of shared
flexible genomic blocks between strains. The neighbor-joining (NJ) tree (left) is a consensus
across 1000 bootstrap resamplings of the flexible blocks. Only nodes with support > 500
are shown. Scale bar: Bray-Curtis distance used to construct the NJ tree (see Materials &
Methods).
FF75
1F289
ZF30
ZF207
ZF99
ZF270
ZF65
ZF205
ZF28
ZF170
ZF264
FF274
FF160
1F175
1F53
1F97
1F111
1F273
The flexible genome tree also has a different topology to that of the core (Fig. 3.2),
suggesting that the flexible genome is shaped largely by horizontal transfer (integrasemediated and illegitimate recombination), with limited clonal descent. The separate
grouping of S and L strains (Fig. 3.2B; 99.8% bootstrap support) when clustered
by the proportion of shared flexible DNA (Fig. 3.2B) indicates preferential recombination occurs within habitats. Compared with a model of random recombination
among habitats, there is significantly more habitat-specific sharing of flexible blocks
than expected by chance (p < 5.5x10 − 58; Materials and Methods; Table S1). Interestingly, all seven S strains not just the 5-S strains hypothesized to have undergone a
selective sweep on chromosome II share significant amounts of flexible DNA on this
chromosome (fig. S7). Therefore flexible genome turnover is sufficiently rapid that
flexible DNA does not hitchhike with selective sweeps for very long. Rather, high
turnover, with a clear bias toward within-habitat sharing of DNA, maintains distinct
but dynamic and habitat-specific gene pools.
39
Functions of ecologically differentiated genes
The revelation that there is a suite of habitat-specific genes and alleles has shed light
on the selective pressures associated with specialization to different microhabitats in
the ocean (Table S1, S2; Materials and Methods). The RTX locus and syp operon
exhibit both allelic variation (core) and gene content variation (flexible). Several syp
genes, present in all L but absent from S genomes, and their upstream regulator
sypG, present in different allelic variants between habitats, are involved in biofilm
formation and host colonization [57]. RTX proteins are important virulence factors
in pathogens [58] and may play a role in interactions with different hosts. The stressresponse sigma factor RpoS, in the core genome nearby the RTX locus, has been
shown to mediate a tradeoff between stress tolerance and nutritional specialization
in environmental Escherichia coli isolates [59]. Finally, MSHA biosynthesis genes,
many of which are unique to L flexible genomes, promote adherence to chitin [60] and
zooplankton exoskeletons [61]. Together, these suggest that ecological specialization,
possibly through differential host association, can be achieved by fine-tuning genes in
a few key functional pathways.
A model for ecological differentiation in bacteria
Our observations can be generalized with a model predicting independent evolutionary trajectories for nascent populations triggered by gene-specific sweeps (Fig. 3.3).
The mosaic genomes we observed, with different genome blocks supporting different
phylogenies suggest a frequently recombining, ecologically uniform ancestral population (Fig. 3.3B, early time points). The recent acquisition of habitat-specific flexible
genes and core alleles likely initiated specialization to different hosts or habitats leading to decreased gene flow between populations. The populations we studied are in
a very early stage of ecological specialization, with little genetic divergence between
them. However, if the trend towards greater within-population recombination can
be extrapolated into the future (as might indeed be expected given that recombination drops loglinearly with sequence divergence [62–66]), they will eventually form
40
distinct genetic clusters, potentially indistinguishable from those predicted by (and
often taken as evidence for) the ecotype model (Fig. 3.3A). Genetic isolation by preferential recombination has been suggested previously [67], and this trend might be
enhanced if homologous recombination between populations is reduced in the vicinity
of acquired habitat-specific genes [68]. Thus, a mechanism of gene-centered sweeps
may eventually lead to a pattern characteristic of genomewide sweeps. In this way,
our study of the very early stages of ecological specialization has provided a simple
resolution to seemingly conflicting empirical observations.
Outlook
Our findings of ecological differentiation driven by gene-specific rather than genomewide
selective sweeps, followed by gradual emergence of barriers to gene flow, leave open
three major questions for future investigation: what mechanisms (aside from unrealistically high recombination rates) are responsible for preventing genomewide selective sweeps (e.g., negative frequency dependent selection by viruses and protozoa),
how often and by what mechanism are entire chromosomes mobilized, and what are
the barriers to gene flow between sympatric ecological populations (e.g., reduced encounter rates or some form of assortative mating)? No matter how marked the decline
in gene flow between ecological populations, they will always remain open to uptake of
DNA from other populations, thus remaining fundamentally different from biological
species of sexual eukaryotes [50]. Yet strikingly, the process of ecological differentiation we have inferred for these ocean bacteria is similar to models of sympatric
speciation by habitat-specific allelic sweeps in sexual eukaryotes [69, 70]. Despite
differences in how adaptive alleles are acquired, our results suggest that how they
spread within populations may follow a more uniform process in both prokaryotes
and eukaryotes than previously imagined.
41
A
neutral marker genes sampled
0.1
1
0.1
sample t2
(A)
B
sample t1
ancestral
gene
flow
population dynamics
(C)
restricted gene
flow between
habitats?
(B)
time (t)
Time
habitat - specific
alleles arrive
Figure 2.3: Ecological differentiation in recombining microbial populations. (A)
Example genealogy of neutral marker genes sampled from the population(s) at different
times. (B) Underlying model of ecological differentiation. Thin gray or black arrows represent recombination within or between ecologically associated populations. Thick colored
arrows represent acquisition of adaptive alleles for red or green habitats.
42
Chapter 3
Sympatric speciation: when is it
possible in bacteria?
Jonathan Friedman, Eric J. Alm, B. Jesse Shapiro
This chapter is presented as it originally appeared in PLoS ONE 336, 48 (2012).
Chapter 3
Sympatric speciation: when is it
possible in bacteria?
According to theory, sympatric speciation in sexual eukaryotes is favored
when relatively few loci in the genome are sufficient for reproductive isolation and adaptation to different niches. Here we show a similar result for
clonally reproducing bacteria, but which comes about for different reasons.
In simulated microbial populations, there is an evolutionary tradeoff between early and late stages of niche adaptation, which is resolved when relatively few loci are required for adaptation. At early stages, recombination
accelerates adaptation to new niches (ecological speciation) by combining
multiple adaptive alleles into a single genome. Later on, without assortative mating or other barriers to gene flow, recombination generates unfit
intermediate genotypes and homogenizes incipient species. The solution
to this tradeoff may be simply to reduce the number of loci required for
speciation, or to reduce recombination between species over time. Both
solutions appear to be relevant in natural microbial populations, allowing
them to diverge into ecological species under similar constraints as sexual
eukaryotes, despite differences in their life histories.
44
Author Summary
It has been theorized for some time that sexual animal populations diverge more
readily into new species when a small number of genes are sufficient to initiate and
complete the speciation process. Some of these genes may promote sexual isolation
between species (important in ’sympatric’ speciation, where there are no physical
barriers to mating) and others may confer adaptation to different ecological niches.
Bacteria, like sexual organisms, adapt to diverse ecological niches. Yet they reproduce
clonally, exchanging genes occasionally by recombination, potentially with distant
relatives, such that sexual isolation between species is never complete. Despite these
differences from sexual organisms, we show that bacteria are also more likely to form
new species when just a few genes are involved in niche adaptation. The reason
for this is an evolutionary tradeoff: frequent genetic exchange (recombination) is
required to generate optimal combinations of multiple adaptive alleles, but without
mechanisms for sexual isolation these optimally adapted species tend to merge back
together rather than diverging into separate species. This tradeoff imposes a simple
constraint on the speciation process in bacteria, and may explain certain aspects of
bacterial biology such as the clustering of genes into operons (effectively reducing the
number of genes involved in speciation) and variable recombination rates over time.
45
Introduction
Microbes have adapted to nearly every ecological niche imaginable on earth, yet the
evolutionary mechanisms of the specialization process and their constraints remain
poorly understood. In our recent study of ecological differentiation between two marine Vibrio populations [71], we were surprised to observe relatively few regions of the
genome underlying differentiation: up to 11 (but as few as 3) in the ’core’ genome,
with different alleles fixed between large (L) and small (S) particle associated strains,
and up to 19 in the ’flexible’ genome (horizontally transferred tracts of DNA exclusively present in genomes from one habitat but absent in the other). Habitat specific
genes and alleles likely arrived in S and L populations by recombination with other
more distantly related population, suggesting that recombination rather than mutation is the dominant source of genetic variation. Aside from these few habitat-specific
regions, most of the genome showed a history of rampant recombination within and
between populations, consistent with a relatively large influence of recombination
on Vibrio genomes [72]. At face value, this observation seemed to be satisfactorily
explained by modeling work predicting that speciation by habitat shift should not
involve many loci [73–77]. However, these were models of sexual eukaryotes, which
unlike bacteria necessarily undergo homologous recombination every generation and
form species by assortative mating and sexual isolation. In their 1986 paper, ”Sympatric speciation: when is it possible?”, Kondrashov and Mina [78] conclude that for
sexual populations ”sympatric speciation is possible when essential differences (including isolating mechanisms) between the formed species depend on up to 10 loci”.
Here, we reformulate these classic models in order to ask the same question for bacteria: when, and with how many loci involved, is sympatric ecological differentiation
likely to occur?
While many different speciation scenarios are possible for bacteria, here we limit
ourselves to one scenario that we hypothesize to be most relevant for Vibrio and other
frequently recombining bacteria, where populations differentiate in sympatry, with
relatively high rates of recombination among all individuals. For simplicity, we take
46
sympatry to mean that all individuals recombine with equal probability, regardless
of their niche or species affiliation. This is, intentionally, a rather extreme version of
sympatry, in which there is no opportunity for establishment of new species in physical
isolation. Although extreme, such a model is consistent with the suspected transience
of marine Vibrio microhabitats: vibrios disperse rapidly among invertebrate hosts
[79], and particle habitats may have short half-lives. Rapid turnover of microhabitats
would allow very little opportunity for recombination within habitats (environmental
assortative mating, as termed by J. Mallet, personal communication). If turnover is
less rapid, a model of mosaic sympatry [80] may be more appropriate for bacteria with
preferences for different microhabitats (e.g. large zooplankton or copepods vs. small
organic particles), but with frequent mixing among microhabitats. We do not aim
to describe bacteria that speciate due to strong barriers to recombination (allopatry,
e.g. [81]), or in which recombination is weak relative to mutation, selection and drift
[82–84]; such ’effectively clonal’ populations are already well described by various
versions of the stable ecotype model, involving periodic selection and genomewide
selective sweeps [82, 85].
Sympatric speciation is is increasingly being observed in plants and animals [77,
86]. In all domains of life, the likelihood of sympatric speciation depends on the
balance between the homogenizing force of recombination (inhibiting speciation) and
disruptive selection, favoring speciation by adaptation to different niches [87]. This
balance essentially a restatement of Haldane’s isolation theory [88] can be applied
to individual genes, such that some parts of the genome (i.e. those under disruptive
selection) can be strongly differentiated, while others (neutral loci) are not. Here
we are interested in the early stages of speciation, in which populations become
differentiated at selected loci, but not necessarily at neutral loci [89]. This amounts
to an ecological species concept, in which species are defined as genotypes optimally
adapted to different niches through acquisition of selectively favored alleles at one
or more loci [90]. Speciation is therefore driven by selection on adaptive loci, and
does not require differentiation in neutral loci, or any form of assortative mating. For
the purposes of this study, we define speciation in this ecological sense: directional
47
selection favors different alleles in different niches. As a result, incipient species are
defined as having the optimal combination of alleles in their respective niches.
Following Kondrashov [73, 74, 78], sympatric speciation can be conceptually divided into early stages, where recombination helps generate optimally adapted genotypes, and late stages, where recombination homogenizes incipient species unless barriers to gene flow emerge. At early stages, the rate of adaptation to new niches may
be increased dramatically in recombining (as opposed to strictly clonal) populations
by bringing multiple adaptive alleles into a common genomic background [91], and
unlinking them from deleterious mutations [92]. When fitness in a new niche is controlled by adaptive mutations that can fix in any order, recombining populations are
favored by selection [93], but when fitness depends on the order of fixation, recombining populations adapt more slowly than clonal populations [94]. Sex may also come
with a cost (e.g. reduced rate of cell division), in which case switching between sexual
and clonal phenotypes provides an optimal strategy [95].
Although recombination speeds up adaptation within a single population (at least
when fitness is additive), it can be a powerful hindrance to the later stages of sympatric speciation. In the absence of barriers to gene flow between emerging species,
recombination may homogenize their gene pools, effectively preventing speciation.
Under the biological species concept [96], assortative mating is generally required for
sympatric speciation, and this is borne out in modeling work [75, 97]. In these and
earlier models [74, 78], sympatric speciation was delayed by increasing the number
of loci contributing to assortative mating, such that speciation is very unlikely when
more than ∼ 10 loci are involved.
In support of this theoretical prediction, recent surveys of genomic variation in
sympatric pairs of sexual eukaryotic species have identified just a few (< 10) genomic islands of high divergence between mosquito species [69], although divergence
was subsequently shown to encompass larger stretches of the genome than initially
thought [98–100]. These islands could contain genes responsible for ecological specialization, assortative mating, or both. Sequence divergence in islands may locally
inhibit recombination between incipient species, extending the islands into ’conti48
nents’ of divergence in a process termed ’divergence hitchhiking’ [101]. Similarly, in
stickleback fish, a small number of alleles (∼ 1 − 5) involved in pelvic morphology
[102] and armor plate patterning [103] are sufficient for significant ecological differentiation. Although these alleles may have contributed to early divergence of marine
and freshwater stickleback species 2 million year ago, many more adaptive changes
(in ∼ 90 − 215 loci) have occurred since that time [104].
With or without assortative mating, it seems plausible that speciation will proceed
more readily when fewer loci are required to confer ecologically different phenotypes
to each nascent species. This concept is explained eloquently by Kondrashov [74]:
“In a panmictic equilibrium population the phenotype variance [and the variance in
relative fitness, if this phenotype is related to fitness] decreases with the growth of the
number of loci controlling any character. It leads to the weakening of the effects of
selection [...]”. Under an additive fitness model where each locus contributes equally
to niche adaptation, as more loci are involved in adaptation, the fitness landscape
becomes smoother and the competitive advantage of the optimal genotypes becomes
relatively weaker, such that intermediate genotypes are maintained and speciation is
impeded.
Regardless of what type of fitness model is used, as more loci are necessary to
achieve an optimal genotype (ecological species), more recombination will be needed
to collect all the optimal alleles into a single genome. However, high recombination
rates come at a cost: once an optimal genotype is generated for a new niche, there
is nothing to prevent it from recombining with individuals from the ancestral niche,
thus delaying or preventing speciation. We investigate the importance of this apparent
tradeoff in a microbial context, where recombination can occur, but not necessarily
every generation. We strove for the simplest possible model that could account for
our empirical findings that few adaptive loci could drive ecological differentiation in
highly recombining bacterial populations [71]. Like Kondrashov’s models, ours is a
deliberate abstraction aimed at capturing major qualitative features of speciation. We
follow the conceptual framework of Kondrashov [78], changing details as necessary to
suit bacterial populations. Unlike models of sexual eukaryotes, we use a model with49
out assortative mating, which we assume to be negligible among very closely-related
bacteria in the very early stages of speciation. Although forms of assortative mating
cannot be ruled out, studies of highly recombining bacteria such as Streptococcus
pneumoniae have failed to find evidence for assortativeness [105]. However, because
recombination drops loglinearly with sequence divergence [52, 62, 63, 65], barriers to
gene flow should eventually emerge between more distantly-related bacteria, and even
very closely related sympatric bacterial populations show signs of emerging barriers
to gene flow [71, 106]. We chose not to model assortativeness or any barriers to gene
flow for two reasons. First, such models have already been explored [75, 78, 97].
Second, we are interested in the early stages of speciation, which are necessary for,
yet do not guarantee the establishment of long-lived species. These early stages are
driven by directional selection, and may or may not be followed by a reduction of
gene flow between incipient species.
Model
Our sympatric speciation simulation (symsim, implemented in MatLab and available
at http://almlab.mit.edu/star/symsim/) models a microbial population growing in an
environment composed of two distinct niches, one ancestral (niche 0) and one derived
(niche 1). Niches are deliberately abstract, but could consist of different carbon
sources, optimal growth temperature, host or particle association, etc. Genotypes
consist of L unlinked adaptive loci, each with two allelic states, 0 or 1, conferring
adaptation to niche 0 or 1, respectively, and one representative background locus
with two allelic states both neutral to fitness.
We considered two models of fitness: one additive and the second a ’step’ function
[78]. In both models, fitness is a function of fi,j , the fraction of adaptive loci in genotype i that contain alleles adapted to niche j. Optimally adapted genotypes (defined
here as ecological species) have fi,j = 1. In the additive model, microbes compete and
reproduce exclusively in the niche to which their genotype is best adapted, (Figure
3.1A). Fitness is an additive function of fi,j . For example, with L = 5, the genotype
50
11100 would compete in niche 1 with f11100,1 = 3/5. Genotypes always reproduce in
the niche for which fi,j > 0.5; if fi,j = 0.5, a niche is chosen at random. This constitutes a strong tradeoff in niche adaptation: each strain can only have one niche. As
a result, until a strain acquires at least L/2 niche-1 adaptive alleles, it will compete
in niche 0, with any niche-1 alleles incurring a fitness disadvantage. The step fitness
model relaxes this strong tradeoff: strains with fi,j < 1 may shuttle between niches,
acquiring their full complement of resources from a combination of both niches (Figure 3.1B). However, the disruptive selection necessary for speciation is maintained
because all intermediate genotypes must pay a fitness cost for the time and energy
spent switching between niches. This cost (in the form of a selective coefficient, s) is
uniform for all fi,j < 1. Thus, all intermediates pay an identical fitness cost relative
to the specialized, optimally niche-adapted genotypes.
Both fitness models, while simple, are reasonable starting points for describing
natural bacterial populations with different metabolic or microhabitat specializations.
In natural marine Vibrio populations, for example, ecological differentiation is likely
driven by genes involved in host or particle attachment (mshA and syp genes) and
transcriptional regulators (sypG, rpoS) [71]. Additive fitness effects would result
if there were an incremental advantage to encoding and expressing each additional
adaptive gene or allele. Alternatively, intermediate genotypes could gather resources
from two different hosts or particle types, but with a penalty for time spent switching
between the two, as in the step model. Similar fitness landscapes can be imagined
for populations that rely on different metabolic or successional strategies to achieve
ecological differentiation [52].
Symsim is a discrete generations model with varying population size, required
for investigating the colonization of a new, initially empty niche. Each generation
consists of resource competition, population growth and recombination, as follows:
I. Competition
At each generation, each niche has an amount of resource R for which individuals
compete. In each niche, the resource is partitioned among individuals according
51
Figure 3.1: Schematic of the symsimmodel. (A) Additive fitness. The steps of the
simulation are (i) growth/selection according to relative additive fitness within each niche,
(ii) small probability of recombination (r) by gene conversion of homologous loci (diagonal
lines) in a sympatric, mixed pool of genotypes from both niches, and (iii) individuals return
to the niche to which their genotype is best adapted (e.g. in this 3-locus example, genotypes
000 and 010 go to niche 0, while 111 and 011 go to niche 1). Steps (i), (ii) and (iii) are
iterated for a set number of generations or until any of the derived alleles go extinct. (B)
Step fitness. The steps of the simulations are the same as for additive fitness, except that
individuals can grow and be selected in both niches. Optimally adapted genotypes (111 and
000) compete in just one niche. Intermediates compete in both niches, but pay a fitness
cost s for niche switching. In the example shown, an individual of genotype 010 obtains
2/3 of its resources in niche 0 (and adds a count of 2/3 of an individual to the population
size of niche 0), and 1/3 from niche 1 (and adds a count of 1/3 of an individual to niche 1).
to their competitive fitness. In the additive model:
s
wi,j = 1 + fi,j
.
52
(3.1)
And in the step model:
wi,j =


1
fi,j = 1

1 − s
otherwise,
(3.2)
where s is a tunable parameter controlling the strength of selection. We ran
simulations using s = 0.1 and s = 0.01, representing the range of selective coefficients measured for single fixed beneficial mutations in experimentally evolved
E. coli populations [107]. Instead of selection on a single locus, in our model
s stands for disruptive selection (Equation 3.1) or negative selection (Equation
5.2) on multiple loci. The average amount of resource allocated to each individual of genotype i in niche j scales with their relative fitness:
wi.j
,
i wi,j Ni,j,t
Ri,j = R P
(3.3)
where Ni,j,t is the number of cells with genotype i in niche j at time t. Under
additive fitness, genotypes only obtain resources in the niche to which they are
best adapted (for which fi,j ≥ 0.5, as described above). Under step fitness, each
individual can obtain resources from both niches, and also counts toward the
number of cells in in both niches, proportionally to its genotype. For example,
genotypes with fi,j = 0 obtains resources only from niche 0, fi,j = 1 only from
niche 1, and fi,j = 0.5 obtains half its resources from each niche and contributes
half a count to each population size.
II. Clonal Reproduction
At each generation, the average expected number of offspring of each individual
of genotype i in niche j is:
Ei = 1 + bi − a,
(3.4)
where d is the death rate and bi , the birth rate, is a saturating Michaelis-Menton
53
function of the resources allocated to it:
bi = bmax
Ri,j
,
R0 + Ri,j
(3.5)
where bmax is the maximal birth rate per cell and R0 is the half-saturation
constant of the birth function. Therefore, the number of individuals (N ) of
genotype i in the next generation is drawn from a Poisson distribution:
Ni,j,t+1 = Poisson(Ei Ni,j,t ).
(3.6)
The carrying capacity (K) of each niche (the steady-state population size) is
related to the amount of resource available and the birth and death parameters
by:
R
K=
R0
bmax
−1 .
d
(3.7)
In all simulations, we set R = 1, bmax = 10, d = 0.1, and K = 106 in each niche.
We investigated two different selective coefficients: s = 0.1 and s = 0.01.
III. Recombination
After population growth and selection, all microbes enter a common sympatric
pool and recombine with one another at random, independently of their genotype (Figure 3.1), with rate r per individual per locus. The total number of
recombination events per generation is therefore rN (B + L), where N is the
total number of individuals in both niches, L is the number of adaptive loci, and
B is the number of neutral background loci (set at B = 1 in all simulations). In
each event, a donor/acceptor pair of microbes is chosen at random, and one of
the B + L genomic loci is chosen to be recombined, also at random. Recombination between homologous loci is non-reciprocal, and occurs by gene conversion
resulting in allelic replacement of the acceptor by the donor allele.
Cycles of growth and recombination continue for a set number of generations,
or until any of the adaptive alleles go extinct (meaning that speciation fails
to occur). Mutation is not included in our model because we are particularly
54
interested in the case where recombination rates are much higher than mutation rates, and where adaptive alleles are highly divergent, containing multiple
nucleotide differences. We also point out that symsim is model as one of homologous recombination by gene conversion, although extending it to include
non-homologous recombination (horizontal gene transfer) would be straightforward.
Result
We aimed to answer two questions: (1) How long does it take the derived (niche-1
optimized) species to appear, and what is the likelihood that it appears at all? (2)
Given that the derived species does appear, what is its equilibrium frequency relative
to intermediate (sub-optimal) genotypes? In other words, what is the completeness
of the ecological speciation process?
Recombination expedites the appearance of new ecological
species
To address the first question, we initiated the symsim model with niche-1 empty
(the novel niche having just appeared) and niche-0 (the ancestral niche) occupied by
95% optimal genotypes. The remaining 5% of the population contained a niche-1
allele at a single locus (distributed uniformly across the L loci), with all other loci
containing niche-0 alleles. We varied the model of selection (additive or step), the
selection coefficient (s), the number of loci involved in niche adaptation (L) and
the recombination rate (r), and allowed the simulation to proceed until the niche-1
optimal genotype (defined as the derived species) was generated by recombination,
or until any of the niche-1-adapted alleles went extinct, rendering the niche-1 optimal
genotype unattainable. We performed 100 replicate simulations for each parameter
combination and obtained qualitatively similar results for both additive (Figure 3.2)
and step (Figure 3.3) models of selection, with both strong and weak selection. We
55
will therefore focus first on the results of the additive model with weak selection
(s = 0.01) because they are also representative of the qualitative features of the other
models.
How does the number of loci contributing to adaptation affect the likelihood that
the derived species is generated by recombination? With only two adaptive loci,
the derived optimal genotype is always generated by recombination (Figure 3.2A),
even when the recombination rate is relatively low (r = 10−6 , resulting in only ∼ 2
recombination events per locus per generation in the pooled population), but not
when it approaches zero expected recombination events per generation (r = 10−7 ).
As the number of adaptive loci is increased to L = 3, the derived species still almost
always appears, but takes longer to do so. With L = 5, a higher recombination rate
(r = 10−4 ) is required for even a 48% chance of appearance before extinction, and
with L = 7 appearance is only likely at very high recombination rates (r = 10−2 ).
The exact values of L and r required for appearance of niche-1 optimal genotypes
depend on the selection model, strength of selection and population size (which influences the likelihood of stochastic extinctions, not investigated here). With more
than 2 adaptive loci, the appearance of derived optimal genotypes is less likely under
the step fitness model (Figure 3.3), likely due to strong and uniform selection against
intermediate genotypes. To a lesser extent, increasing the strength of selection also
hinders slightly the appearance of derived optimal genotypes (compare panels A and
D in Figures 2 and 3); the effect is only slight because fitness is relative to other competitors in the population (Equation 3.3). In general, the simulations all support a
major qualitative conclusion: higher recombination rates are necessary for ecological
speciation when more adaptive loci are involved. For many adaptive loci and low
recombination rates (area below the red line in Figures 2 and 3), ecological speciation
is very unlikely to be initiated
Recombination hinders the later stages of speciation
To investigate any potential tradeoffs between the early and late stages of speciation
(appearance of the new species, and disappearance of sub-optimal intermediate geno56
types, respectively), we fast-forwarded the simulation to a point in time when the
derived species (niche-1 optimal genotype) had reached 1% of the pooled population
(having thus escaped extinction by drift), the ancestral (niche-0) species constituted
95%, and the intermediate genotypes were distributed uniformly to make up the
remaining 4%. From these starting conditions, and we ran symsim for 100,000 generations for each combination of L and r. In each replicate simulation, we recorded the
maximum mean frequency of optimal genotypes (averaged over both niches) observed
any time after 25,000 generations. Based on visual inspection, genotype frequencies
always reached an equilibrium by this point, so the maximum frequency of optimal
genotypes proved to be a reasonable measure of the ’completeness’ of speciation.
We found that the high recombination rates necessary to generate the derived
species tended to hinder the completion of speciation later on. For example, under
additive fitness and s = 0.01, with L = 5 adaptive loci, a minimum of r ≈ 10−4
is required for the derived species to appear and survive (Figure 3.2A,B), yet this
amount of recombination also generates many intermediate genotypes, resulting in a
low equilibrium frequency (0.21) of optimally adapted species (Figure 3.2C, 4B). The
incompleteness of speciation at high recombination rates is less pronounced with fewer
adaptive loci, for example when L = 2 (Figure 3.2C, 4A). When the recombination
rate is kept low (r = 10−6 ), speciation proceeds essentially to completion, with nearly
the entire populations of both niches occupied by optimally adapted genotypes (Figure
3.2C, 4C,D). Of course, such low recombination rates would be unlikely to produce
optimally adapted genotypes in the first place (falling below the red line in Figures
2), resulting in a serious impediment to sympatric speciation as increasing numbers
of adaptive loci are involved.
The same tradeoff between early and late stages of speciation is also observed in
the step fitness model. Although speciation is generally more complete under step
than additive fitness (for the same values of r and L), the combinations of r and L
most likely to maintain complete speciation are unlikely to have generated optimally
adapted derived genotypes at earlier stages (Figure 3.3). Thus, even under a step
fitness model, in which the variance in fitness does not decrease with L (and there is
57
no weakening of selection with L, as in the additive fitness model), we still observe a
tradeoff between early and late stages of speciation.
Figure 3.2: Results of symsimmodel under additive fitness. (A, B, C) Weak
selection. (D, E, F) Strong selection. (A, D) Probability of appearance (p) of the derived
(niche 1) optimal genotype in 100 replicate simulations for each combination of the number
of loci involved in niche adaptation, L and the recombination rate, r. High probabilities
(p = 1) are shown in white, low probabilities in black, and intermediate probabilities in grey
scale. The space under the red line indicates extinction of the niche-1 optimal genotype
in all 100 replicates (p,0.01). (B, E) Time to appearance of the niche 1 optimal genotype
(mean over 100 replicate simulations). The red line is the same as in (A); n.d. refers to
appearance time not determined, or effectively infinite, because extinction of niche-1 alleles
occurred before the optimal genotype could appear. Shorter times are shown in white,
effectively infinite times in black, and intermediate times in grey scale. (C, F) Completeness
of speciation. The mean fraction of the pooled populations (niche 0 and 1) occupied by
optimally-adapted genotypes is based on 10 replicate simulations for every combination of L
and r. Complete speciation (optimal genotype fraction near 1) shown in white, incomplete
in black, and intermediate completeness in grey scale. Magenta letters in C refer to the
same simulations depicted in panels (A, B, C, D) of Figure 3.4.
58
A practical note on our ability to recognize adaptive loci
Sympatric species of bacteria are difficult to recognize in the wild because the niches
to which they adapt are often difficult to observe, and their adaptive genomic changes
indistinguishable from neutral changes. In practice, sympatric ecological species can
be identified when different alleles have been fixed between populations by directional
selection [8, 108]. In a perfectly clonal scenario (r = 0), selectively neutral background
alleles would also become differentially fixed between species, making them hard to
distinguish from the adaptive alleles driving speciation. Our simulations included
a representative neutral background locus, and we asked under what circumstances
it could be mistaken for an adaptive locus. Selection acts to fix a different allele
in each niche at adaptive loci, but not background loci. However, when recombination rates are low, background alleles may hitchhike with adaptive alleles, resulting
in the fixation of background alleles between habitats. Given sufficient recombination, background alleles will eventually become randomly distributed across niches
(’mixed’), making them unlikely to be confused for adaptive loci. We defined a population as mixed when background alleles were randomly distributed across niches (e.g.
background allele 1 at frequency 0.5 in both niches). We also defined t(mix) as the
time, in generations, when mixing is achieved in a simulation initiated as described
in section (ii) above, with the derived species at an initial frequency of 1%, and background alleles in perfect association with niches (allele 0 in niche 0 only; allele 1 in
niche 1 only). As expected, t(mix) was highly dependent on the recombination rate.
Under additive fitness and s = 0.01, as the recombination rate increased, less time
was required to achieve mixing: the mean t(mix) across replicate simulations was
always over 100,000 generations with r = 10−5 , 7,999 generations (s.d. = 2420) with
r = 10−4 , and only 62 generations (s.d. = 2.2) with r = 10−2 . This suggests that
at high recombination rates, adaptive loci should be easily discernible from neutral
loci very soon after the initiation of speciation, but at low to moderate recombination
rates neutral loci may hitchhike for thousands of generations, making them easy to
confuse with adaptive loci using many standard population genetic tests for positive
59
selection Shapiro:2009hp.
Figure 3.3: Results of symsim model under step fitness. (A, B, C) Weak selection.
(D, E, F) Strong selection. See Figure 3.2 legend.
Discussion
Our simulations identified a major tradeoff between early- and late-stage recombination, predicting that the initiation of sympatric speciation is much more likely when
the number of loci required to adapt to a new niche is small. The same qualitative result is obtained using different selection models and selection coefficients. As
the number of loci increases, the tradeoff becomes more restrictive: high recombination rates are required to generate multi-locus optimal genotypes at early stages,
but such high recombination rates eventually homogenize gene pools and prevent the
maintenance of ecologically adapted species at late stages.
Have we described a realistic model of bacterial sympatric speciation? It is cer60
Figure 3.4: Higher recombination rates maintain intermediate genotypes and
reduce the completeness of speciation. Panels A, B, C and D show dynamics of a single
simulation under different combinations of L (number of adaptive loci) and r (recombination
rate), corresponding to magenta letters in Figure 3.2C. The y-axis shows the frequency of
optimal genotypes in a given niche (ancestral or derived).
tainly not a model of biological species because biological speciation is impossible
without barriers to recombination, which are not included in our model. It is more a
model of early niche invasion and evolution of optimal genotypes. We argue that this
is an important early step toward speciation, and one that is increasingly observed
in diverging natural microbial sympatric populations, which mix by recombination at
all but a few adaptive loci [52, 71]. Because the fitness landscapes of these diverging
populations are unknown, we have used two very different fitness models, one additive
and one ’step’, which can be considered an extreme version of epistasis. Other fitness
models are also plausible, so long as they include some degree of disruptive selection
61
[77], but a thorough investigation of other models is beyond the scope of this study.
Despite being a deliberate abstraction of real fitness landscapes, our model describes
one simple (but not exclusive) mechanism that generates data consistent with the
observation that relatively few adaptive loci tend to drive early stages of sympatric
speciation, in microbes just as in many sexual eukaryotes [69, 103, 109, 110].
Another limitation of our model is that extinction occurs when any of the adaptive alleles disappears. In real bacterial populations, alleles may be replenished by
recombination from other populations, giving speciation another chance to occur.
Therefore, our model probably overestimates the likelihood of extinction preventing
speciation. Due to this and other limitations and assumptions, we do not claim that
there is a single ’magic number’ of adaptive loci that provides the easiest path to
sympatric ecological speciation. The exact number will always depend on the recombination rate, selection strength, population size and niche complexity, but smaller
numbers will always tend to facilitate speciation.
Given the tradeoff predicted by our simple model, how do pairs of well-adapted
sympatric bacterial species emerge? Perhaps they do not, or only rarely. Ecological
species may be transient, and rapidly merge back in to a homogenous parent population. In cases where a new species does evolve, the effective number of adaptive
loci could be kept low by combining suites of genes into operons, allowing complex
phenotypes to be acquired in a single recombination event. Our model could thus
provide an example of how linking coadapted genes together into operons, in addition
to providing a selective advantage for the genes themselves as in the selfish operon
hypothesis [111] could also provide an advantage in facilitating ecological speciation.
Despite such ’strategies’ to keep L low, it is possible that many opportunities for speciation are missed because new niches are too complex to be exploited by genotypes
with just a few adaptive alleles. However, there is mounting evidence from natural
microbial communities that surprisingly few adaptive genes or alleles may be sufficient
for adaptation to fairly complex niches, including different hosts or nutrient utilization strategies [49, 52, 71, 112]. In other cases, large continents of divergence have
been observed, containing many genes [106]. Such continents may not fit the model
62
described here, or may come about at later time points in the speciation process,
perhaps once gene flow has become more restricted.
What if many ( 10) adaptive loci are required to exploit a new niche? Perhaps
speciation could still be achieved if recombination rates varied over time, such that
the stress experienced in a new habitat would trigger periods of hyper-recombination,
promoting the rapid generation of genotypes with the optimal combination of adaptive
alleles. In order for new species to be maintained on the long term (rather than being
eroded by recombination with the ancestral species), recombination would have to
revert to a low rate. This could occur if barriers to gene exchange between niches, or
forms of assortative mating, emerged over time.
It is known that sex (recombination) can slow the rate of adaptation within a population when the fitness landscape is such that alleles must be acquired in a particular
order to be adaptive [94]. Here we have shown another intuitive, yet to our knowledge
unrecognized, disadvantage of sex that arises even in simple, additive or step fitness
landscapes without assortative mating. Recombination, although advantageous in the
early stages of speciation, erodes ecological specialization later on, resulting in less fit
populations. As a result, recombining microbial populations, like sexual eukaryotic
populations, are predicted to form new species using only a few loci. Although this
limitation is common to microbes and sexual eukaryotes, it comes about for different
reasons. In simulated populations of sexual eukaryotes, recombination is uniformly
high (occurring before every mating), and some form of assortative mating is usually
required for speciation (e.g. [87]). In the earlier models of Kondrashov [73–75, 78] and
Felsenstein [87], it was shown how the reduced efficacy of selection with increasing
number of loci (involved in adaptation, assortative mating, or both) is important in
preventing the initiation of sympatric speciation, and also how recombination later
erodes ecological specialization. Here, we have presented an updated model, specifically for microbial populations with clonal reproduction, variable recombination rates,
and without assortative mating. In microbes, although the efficacy of selection is still
important, the recombination rate is the key factor: for ecological traits controlled by
many adaptive loci, high recombination rates are necessary to generate a new species,
63
but this also produces many intermediate genotypes and reduces the completeness of
speciation at later stages. A simple, although not exclusive, solution to this tradeoff is
to require adaptation at just a few loci to initiate and maintain ecological speciation.
The generality of this solution will be put to the test as more data become available
from population genomic studies of ecologically diverse, recombining wild microbial
populations.
64
Chapter 4
Inferring Correlation Networks
from Genomic Survey Data
Jonathan Friedman, Eric J. Alm
This chapter is presented as it originally appeared in PLoS Computational Biology
320, 1081 (2008). Corresponding Supplementary Material is appended.
Chapter 4
Inferring Correlation Networks
from Genomic Survey Data
High-throughput sequencing based techniques, such as 16S rRNA gene
profiling, have the potential to elucidate the complex inner workings of
natural microbial communities - be they from the world’s oceans or the
human gut. A key step in exploring such data is the identification of dependencies between members of these communities, which is commonly
achieved by correlation analysis. However, it has been known since the
days of Karl Pearson that the analysis of the type of data generated by
such techniques (referred to as compositional data) can produce unreliable
results since the observed data take the form of relative fractions of genes
or species, rather than their absolute abundances. Using simulated and
real data from the Human Microbiome Project, we show that such compositional effects can be widespread and severe: in some real data sets many
of the correlations among taxa can be artifactual, and true correlations
may even appear with opposite sign. Additionally, we show that community diversity is the key factor that modulates the acuteness of such compositional effects, and develop a new approach, called SparCC (available
at https://bitbucket.org/yonatanf/sparcc), which is capable of estimating correlation values from compositional data. To illustrate a potential
66
application of SparCC, we infer a rich ecological network connecting hundreds of interacting species across 18 sites on the human body. Using the
SparCC network as a reference, we estimated that the standard approach
yields 3 spurious species-species interactions for each true interaction and
misses 60% of the true interactions in the human microbiome data, and,
as predicted, most of the erroneous links are found in the samples with
the lowest diversity.
67
Author Summary
Genomic survey data, such as those obtained from 16S rRNA gene sequencing, are sub
ject to underap- preciated mathematical di?culties that can undermine standard data
analysis techniques. We show that these e?ects can lead to erroneous correlations
among taxa within the human microbiome despite the statistical signicance of the
associations. To overcome these di?culties, we developed SparCC; a novel procedure,
tailored to the properties of genomic survey data, that allow inference of correlations
between genes or species. We use SparCC to elucidate networks of interaction among
microbial species living in or on the human body.
68
Introduction
The study of natural communities using high throughput genomic surveys, such as 16S
rRNA gene profiling, has become routine [2], yet the development of appropriate, well
validated analysis methods is still ongoing. The first challenge is obtaining reliable
and informative counts from 16S rRNA gene sequences by filtering spurious reads
and grouping the remaining reads in a meaningful way [113], [114], [115]. Once such
counts have been obtained, analysis techniques which are appropriate for discrete
survey data need to be applied [116], [117] [118].
A common goal of genomic surveys is to identify correlations between taxa within
ecological communities. Correlation analysis provides a well trodden path to achieving this goal, but we show that it is not valid when applied to genomic survey data
(GSD), and may produce misleading results. The challanges associated with GSD
stem from the fact that they are a relative, rather than absolute, measure of abundances of community components. The counts comprising these data (e.g., 16S rRNA
gene reads) are set by the amount of genetic material extracted from the community
or the sequencing depth, and analysis typically begins by normalizing the observed
counts by the total number of counts. The resulting fractions fall into a class of data
termed closed or compositional, and poses its particular geometrical and statistical
properties [119], [118]. Specifically, standard methods for computing correlations from
GSD are theoretically invalid. Correlation estimates are biased by the fact that, since
they must sum to 1, fractions are not independent and tend to have a negative correlation regardless of the true correlation between the underlying absolute abundances
(termed the basis abundances) [120]. Thus, correlations estimates often reflect the
compositional nature of the data, and are not indicative of the underlying biological
processes [121]. In fact, in 1897 Karl Pearson warned against “attempts to interpret
correlations between ratios whose numerators and denominators contain common
parts” [122], and since that time it has been shown that many other standard analysis techniques are invalid when applied to such compositional data, and that their
interpretation is unreliable and often misleading [121], [123], [124]. Nonetheless, these
69
methods remain the primary tools used in studies of microbial ecology.
Although approaches to compositional data analysis have been developed (e.g.
[124], [125]), the basic task of inferring dependencies between components remains an
outstanding challenge. A widely used method is Aitchison’s test for complete subcompositional independence [126], which tests whether any dependencies are present,
but does not indicate which components are correlated, nor the magnitude of the
correlation. Filzmoser and Hron [127] recently developed a method for inferring correlations in compositional data after an appropriate mathematical transformation,
but their method does not provide a mapping relating the correlations of the transformed variables to those of the underlying genes or species.
In this paper, we first use simulations and real-world data from the Human Microbiome Project (HMP) to demonstrate that GSD can be severely biased by “compositional” effects, and then identify the factors the modulate their severity. Finally,
we present a novel method, called SparCC, and show that it can infer correlations
with high accuracy even in the most challenging data sets.
Results
Standard correlation inference techniques perform poorly on
GSD
To what extent do compositional artifacts affect real-world GSD? We applied standard
statistical methods to 16S rRNA gene survey data from the Human Microbiome
Project (HMP) [128], which measure the compositions of microbial communities found
in different body sites of ∼ 200 individuals. The composition of each community is
described in terms of operational taxonomic units (OTUs). Because only relative
abundances for each OTU are available, these data qualify as compositional and are
thus subject to potential biases as described above.
Networks inferred from Standard Pearson correlation display distinct patterns
within different body sites, suggestive of biological structure (Fig. 4.1, left column.
70
See Fig. S1 for all 18 HMP body sites). Specifically, a prominent feature of the midvagina, retroauricular crease, and buccal mucosa networks is the presence of an OTU
that is negatively correlated with multiple other OTUs. Despite the temptation to
attribute biological significance to these observations, correlation networks inferred
from randomly shuffled data with similar taxon abundances, but lacking any correlations between OTUs (see Materials and Methods), reproduce this feature (Fig. 4.1,
middle column) indicating that it may arise from the closure (normalization) process.
The mechanism behind these spurious correlations is straightforward. The pattern
observed in the mid-vagina network results from the dominance of OTU 3, a Lactobacillus. This OTU has a median abundance of 97%, so fluctuations in its relative
abundance have a strong effect on the abundance of the rest of the community simply due to the requirement that the relative abundances of all OTUs sum to 100%:
when the abundance of Lactobacillus varies, all other OTUs’ relative abundances
vary in unison in the opposite direction creating artificial negative correlations with
Lactobacillus, and artificial positive correlations with each other.
Diversity and correlation density control the severity of compositional effects
Compositional effects are severe in some datasets, but mild in others. We found
that diversity of the samples in the dataset (often referred to as alpha diversity),
is a good predictor of the strength of compositional effects, which diminish with
increased diversity. Intuitively, the fewer OTUs comprise the community, the worse
the compositional effects are, with the extreme case of a community composed of only
two OTUs, which will always appear to be perfectly negatively correlated. Moreover,
compositional effects can be significant even in communities comprised of multiple
OTUs, if only a few OTUs dominate the community. This notion of diversity can be
quantified using the Shannon effective number of OTUs,(nef f ) [129], which quantifies
both the number of OTUs and the dominance in a community. nef f ranges from 1,
when the community is completely dominated by a single OTU, to the number of
71
OTUs in the community (richness), when all OTUs are equally abundant.
Simulated networks of varying nef f (see Material and Methods) with known correlations illustrate the effect of diversity on compositional artifacts. True correlations
(Fig. 4.2A-C) are only recovered when the community is diverse (Fig. 4.2F). In
networks of similar diversity to the HMP samples, inferred connections are often
dominated by negative correlations to the dominant OTU, which leads to positive
correlations among the remaining OTUs (Fig. 4.2D,E). This effect is so strong that it
eliminates the negative correlation between OTU 4 and OTUs 3 and 5, and positive
correlation between OTUs 1 and 2 (Fig. 4.2E). Worse yet, as diversity decreases
further, the negative correlation between OTU 4 and OTUs 3 and 5 is turned into an
apparently positive one (Fig. 4.2D). It is important to note that these compositional
effects are not limited to Pearson correlation, and are also present in non-parametric
correlations, such as Spearman correlations (Fig. S2).
If the underlying network has true positive correlations, then compositional effects
can be even more pronounced than expected based on the community diversity. This
happens because strong correlations between components lowers the effective diversity
of the sample (i.e., two OTUs that are perfectly correlated behave as a single OTU).
This effect can confound naive efforts to correct for compositional effects by comparing
observed correlations against shuffled networks. When the data are shuffled, as in the
middle column of Fig. 4.1, few spurious connections may arise relative to the structure
observed for the unshuffled data (as observed for the buccal mucosa samples), creating
false confidence in the observed network. Thus, randomization is not sufficent to
establish significance of observed correlations, nor is it possible to identify correlations
by comparing against (or “subtracting out”) a randomized network.
SparCC: a novel procedure for inferring correlations from GSD
Here, we describe a new technique for inferring correlations from compositional data
called SparCC (Sparse Correlations for Compositional data). SparCC estimates the
linear Pearson correlations between the log-transformed components. Since these
correlations cannot be computed exactly (as described below), SparCC utilizes an
72
approximation which is based on the assumptions that: (i) the number of different
components (e.g., OTUs or genes) is large, and (ii) the true correlation network is
’sparse’ (i.e., most components are not strongly correlated with each other). Later,
we show that SparCC is surprisingly robust to violations of the sparsity assumption.
SparCC does not rely on any particular distribution of the basis variables, i.e. the
true abundances in the community can follow any distribution, and the choice of
the log-normal distribution in subsequent examples is motivated solely by ease of
implementation and empirical fit. For clarity, we present the method in the context of
16S rRNA gene data, where the components are OTUs and the basis variables are their
true abundances in a community, but SparCC can be applied to any compositional
data for which its approximation is valid.
Like most compositional data analysis techniques, SparCC is based on the logratio transformation:
yij = log
xi
= log xi − log xj ,
xj
(4.1)
where xi is the fraction of OTU i. This transformation carries several advantages:
First, the new variables yij contain information regarding the true abundances of
OTUs, as the ratio of fractions is equal to the ratio of the true abundances. Second,
unlike the fractions themselves, the ratio of the fractions of two OTUs is independent
of which other OTUs are included in the analysis, a property termed subcompositional coherence. Third, this transformation is mathematically convenient, as the
new variables yij are no longer limited to the simplex, but are free to assume any real
value. Taking the logarithm removed the positivity constraint, and induces (anti)
symmetry in the treatment of the variables.
To describe the dependencies in a compositional dataset, Aitchison suggested using
the quantity
xi
tij ≡ Var log
= Var [yij ] ,
xj
(4.2)
where the variance is taken across all samples [123]. When OTUs are perfectly cor73
related, their ratio is constant, therefore tij = 0, whereas the ratio of uncorrelated
OTUs varies and the corresponding tij is large. Though tij contains information regarding the dependence between the OTUs, it is hard to interpret as it lacks a scale.
That is, it is unclear what constitutes a large or small value of tij (does a value of
0.1 indicate strong dependence, weak dependence, or no dependence?). This can be
further appreciated by relating tij to our quantity of interest, the correlation between
the true abundances of the OTUs. The relation is given by
tij = ωi2 + ωj2 − 2ρij ωi ωj ,
(4.3)
where ωi2 and ωj2 are the variances of the log-transformed basis abundances of OTUs
i and j, and ρij is the correlation between them. It is now evident that tij can only
be interpreted in relation to the basis abundance’s variances: tij < ωi2 + ωj2 indicates
a positive correlation, and tij > ωi2 + ωj2 indicates a negative correlation. Ideally, we
would like to solve the set of eqs. 4.3 for all OTU pairs and simultaneously infer
both the basis variances and correlations. However, because there are more unknown
variables than equations, this is not generally possible. Nonetheless, it is possible to
obtain a good approximation of the variances if, on average, OTUs are uncorrelated.
Once we obtain estimates of the basis variances, these can be plugged into eqs. 4.3 to
infer the correlations between each OTU pair, which, unlike the average correlations,
needn’t be small.
More accurate estimation can be achieved by iterating the above procedure. At
each iteration the strongest correlated OTU pair identified in the previous iteration
is excluded from the basis variance estimation. This reinforces sparsity among the
remaining pairs and yields better variance and correlation estimates.
OTU fractions need to be estimated from the observed counts to apply SparCC.
Normalizing each OTU by the total counts in the sample (the maximum-likelihood
estimate) is unreliable for rare OTU because it overestimates the number of zero
fractions [130]. This can give rise to artifacts that are driven by variations in the
sequencing depth. These artifacts have motivated some authors to downsample their
74
data such that all samples have the same total counts, however downsampling does
nothing to alleviate compositional effects, and requires discarding a substantial portion of the available data. Therefore, we employed a Bayesian approach to estimate
component fractions (see Materials and Methods), which allows the assessment of the
robustness of downstream analysis and the assignment of confidence values.
SparCC is highly accurate on simulated data
We used the previously described simulated datasets to demonstrate the accuracy
of SparCC at inferring correlations, even in highly problematic compositional data
dominated by a single OTU (Fig. 4.2G-I). A more systematic evaluation of SparCC
was performed by creating multiple simulated datasets of varying diversity and density. We measure density as the average Pearson correlation between OTUs, such
that denser datasets have more strongly correlated OTUs, challenging the sparsity
assumption used by SparCC. For each combination of density and diversity, multiple true correlation networks were assigned, and corresponding data was sampled.
Networks inferred by SparCC or standard correlations were evaluated using the rootmean-square error (RMSE) (Fig. 4.3). Standard techniques only gave reasonable
estimates for very diverse, sparse networks (Pearson RMSE ∼ 0.02), whereas for
networks with diversity comparable to those observed in the HMP set, the Pearson RMSE was unacceptably high, reaching ∼ 0.5 for communities with diversity
similar to the mid-vagina. Spearman correlations performed only marginally better
(Fig. S3A). By contrast, the performance of SparCC was independent of diversity,
and gave improved results for all parameter values, even for dense networks in which
the sparsity assumption is violated. In fact, the worst accuracy achieved by SparCC
(∼ 0.02, for unrealistically dense networks), was comparable to the best accuracy
achieved using standard correlations on highly diverse samples. Moreover, though
stronger correlation can be estimated more reliably, using standard methods, attention needs to be restricted to exceptionally strong correlations before the accuracy
improves significantly, and the resulting accuracy is at best comparable to SparCC’s
accuracy (Fig. S5).
75
SparCC identifies phylogenetically structured correlations in
HMP data
We used SparCC to infer the taxon-taxon interaction networks from the HMP data
sets (Fig. 4.1, right column, Fig. 4.4), and from their corresponding shuffled datasets
(in which all OTUs are uncorrelated). In contrast to the naive approach shown in
Fig. 4.1, SparCC found no significant correlations in the shuffled dataset (Dataset
S1). For the real data, however, numerous correlations are found, which differed
significantly from the standard Pearson correlations. SparCC inference indicated
that on average ∼ 3/4 of the correlated OTU pairs identified using Pearson were
false, and that ∼ 2/3 of the correlated OTU pairs were missed using Pearson (see
Table S1 for breakdown by body site.). Of particular note, we observe a positive
correlation between OTU 3 and OTU 148, both belonging to the Lactobacillus genus,
which was absent from the Pearson network, likely because of the bias of the highly
abundant OTU 3 toward making negative correlations. Intriguingly, using SparCC we
observe a higher likelihood of positive correlations between phylogenetically related
taxa (Table S2), a finding that on its surface seems to support a role for neutral
community dynamics as related organisms are likely to inhabit similar niches, but do
not seem to dominate by competitive exclusion (although more complicated scenarios
are certainly possible). We anticipate that techniques such as SparCC will play a
major role in analyzing these data to address this and other basic ecological questions.
Discussion
In this study we have focused on an outstanding challenge of compositional data
analysis – inference of correlations. We have demonstrated that compositional effects
are pronounced in 16S rRNA gene surveys of the human microbiome, and, motivated by the properties of this data, have developed a novel procedure for estimating
correlations.
We found that diversity of species and density of interactions are the two key
76
factors that influence the severity of compositional effects on correlation estimates,
with low diversity, high density data being the most challenging to infer correlation
from using standard methods. SparCC does not rely on high diversity, rather it only
requires sparsity of correlations, but in practice is robust even when the sparsity assumption is strongly violated (%30 of all component pairs are strongly correlated).
Therefore, we recommend that SparCC be used on any GSD that has low diversity:
as a rule of thumb we recommend an effective number of components of at least 50
for standard techniques (with the potential caveat that if strong positive correlations
are present among many OTUs, the effective diversity may be much lower than estimated). We emphasize that simply having many components is not sufficient to
avoid compositional effects. For example, 16S rRNA gene surveys from the HMP include hundreds to thousands of distinct OTUs, yet have have a relatively low effective
number of species, with a small number of species dominating most samples.
An important subclass of GSD are genome-wide surveys conducted using techniques such as DNA microarrays, RNA-seq and ChIP-seq. These genome-wide data
are also subject to compositional effects, however, as these data tend to have high
diversity, they are likely to be much less severe or negligible. For example, the average effective number of genes in microarray experiments available through the M 3D
database [131] was 2200 for S. cerevisiae and 1800 for E. coli. This may explain
why to date comparatively less attention has been paid to compositional effects in
the biological sciences than in other disciplines.
The preponderance of zero values are another area of concern with GSD. These
zeros can represent either components that are truly absent from the community,
or rare components that, by chance, were not present in the sample drawn from
the community. Without additional knowledge, these options are indistinguishable,
and, depending on goal of the analysis, the researcher must decide how to interpret
them, and choose analysis methods accordingly. We emphasize that the treatment
of zero values is a challenge that is in no way unique to compositional data, but is
merely highlighted by the log-ratio transformations employed to analyze these data
[132]. In this study, we eliminate zero fractions by adding small pseudocounts, as
77
detailed in the Materials and Methods. Complementary approaches, where zeros are
treated differently than non-zero values, are substantially more challenging, and are
the subject of ongoing research [133].
Though the method presented in this paper allows detection of correlation within
communities, many challenges still remain. First, SparCC relies on having reliable
component counts, which as noted in the introduction, is not trivial. Second, the
correlations estimated by SparCC measure the linear relationship between log transformed abundances. Compositional methods for inferring more general dependencies between components, equivalent to rank correlations and mutual information for
non-compositional data, have not yet been developed. Third, relating the patterns
detected within a community to external factors (e.g. relating the composition of a
human gut microbial community to human health status), and detecting temporal
patterns within and between communities requires non-standard, compositional approaches. While some such methods exist [124], [123], [134] they are rarely employed
in the context of GSD, and are not tailored for its particular properties. Finally, GSD
is often associated with phylogenetic information (relatedness of species or genes),
which ideally would be included in the analysis (e.g. the weighted UniFrac distance,
which attempts to capture differences in both abundance and phylogenetic composition of communities.). We believe that developing systematic, statistically-sound
methods for such analyses of compositional GSD is a necessary step on the road to
understanding the structure of biological communities, the processes by which they
evolve, and the forces that shape them, and thus represents an important direction
for future research.
Materials and Methods
HMP 16S rRNA gene data
HMP OTU counts and their taxonomic classification were obtained from the HMPOC
dataset, build 1.0, available at http://hmpdacc.org/ [135]. The dataset corresponding
78
to high-quality reads from the v3-5 region was used. Only samples from the May 1st
production study were included in the analysis. Additionally, if multiple samples were
obtained from the same body site of an individual, only the first sample collected was
included in the analysis. For each body site, the data was further filtered by removing
samples for which less than 500 reads were collected and OTUs that were, on average,
represented by less than 2 reads per sample .
Shuffled HMP datasets
Shuffled datasets are created by assigning each OTU in each sample a number of
counts that is randomly sampled from the OTU’s observed counts across all samples,
with replacement. This procedure ensures that the resulting marginal distributions
of counts of each OTU alone are the same as in the real data, and that there are no
correlations between the OTUs in the simulated data.
Simulated basis datasets for basis correlations estimation
Simulated communities were generated by sampling the joint abundances of 50 OTUs
from a log-normal distribution with a given mean and covariance matrix. The mean
abundances were equal for all OTUs except OTU 1, whose abundance was set such
that the community will have a given effective number of OTUs (nef f ), on average.
The variance was set to .01 for all OTUs, and random covariance matrices were
generated by assigning each OTU pair a probability p of being perfectly correlated,
with positive or negative correlations being equally probable. The resulting random
symmetric matrix was then converted to the nearest positive-definite matrix to ensure
it is a valid covariance matrix. 500 individuals were randomly sampled from each of
these communities to give counts data similar to the one contained in GSD.
For each combination of the parameters nef f and p, 50 such random communities
were simulated, and the correlation inference accuracy was quantified using the root-
79
mean-squared error averaged over all OTU pairs, given by:
RM SE =
X
1
|ρ̂ij − ρij |
D(D − 1) i>j
(4.4)
The final inference error is given by averaging the inference error of all 50 runs.
Effective number of species
The entropy effective number of species of a community, is defined as
nef f = eH ,
where H = −
P
i
(4.5)
xi logxi is the entropy of the community [129]. Sample entropies were
computed according to the method descried by Chao and Shen [136], as implemented
in the R ’entropy’ package [137]. For each body-site, the effective number of species
reported in the main text is the average of the effective number of species of all
samples corresponding to that body-site.
Estimation of component fractions
We adopt a bayesian framework for estimating the true fractions from the observed
counts. Assuming unbiased sampling in the sequencing procedure, and a uniform
prior, the posterior joint fractions distribution is the Dirichlet distribution [138]:
p(x | N ) = Dir(N + 1),
(4.6)
where x and N are vectors of the components’ true fractions and observed counts,
respectively. Unlike Maximum-Likelihood estimation, the bayesian approach results
in the full joint distribution of fractions, rather than their point estimates.
Point estimates of fraction values, if desired, can be given by the the mean of the
posterior distribution:
N +1
x̂M AP = PD
.
i=1 (Ni + 1)
80
(4.7)
, which is equivalent to adding a pseudocount of 1 to all count values, and normalize
by the total number of counts in each sample. However, we prefer setting the estimator of true fractions to be a random sample from this posterior distribution. This
randomness avoids the detection of spurious correlations between rare components,
which arrises since the fractions resulting from adding a fixed value pseudocount mirror the sampling depth. Additionally, repeating downstream analysis using many
such randomly drawn estimators allows the quantification of the effects of sampling
noise on the analysis (one can attempt to model the noise analytically, but this often
challenging in practice).
It is important to note that in SparCC, like in any method employing log transformations, some pre-processing is required to eliminate zero values. As described
above, SparCC employes a variation of the well-known pseudocounts method which
assigns a small fraction to OTUs that were not detected in a sample. This approach
implicitly assumes that all components are in fact present in the sample, and that
all zero value result from finite detection resolution [130]. For very rare OTUs who
are only present at a few samples, this may not be a reasonable assumption. Even if
this assumption holds, typically there is not enough information to reliably estimate
correlations involving such components, and such components should not be included
in the correlation analysis.
Basic SparCC
As noted in the main text, the quantity
xi
tij ≡ Var log
,
xj
81
(4.8)
contains information about the dependence between components i and j, and can be
related to the basis correlations. The relation is obtained
wi
xi
= Var log
= Var [log wi − log wj ]
tij ≡ Var log
xj
wj
= Var [log wi ] + Var [log wj ] − 2Cov [log wi , log wj ]
(4.9)
≡ ωi2 + ωj2 − 2ρij ωi ωj ,
where ωi2 and ωj2 are the variances of the log-transformed basis variables i and j,
and ρij is the correlation between them [121]. Our aim is to exploit relation 5.1
to infer the unobserved covariance matrix of the log transformed basis variables Ω,
from Aitchison’s variation matrix T, whose elements are tij . Unfortunately, this
is impossible for the most general case, since the basis variances are unknown a
priori, and the system of equations for all pairs of components is underdetermined,
as it involves D(D − 1)/2 equations and D(D + 1)/2 variables (D variances and
D(D − 1)/2 correlations). In fact, even the D variance variables alone, with all
correlations set to zero, allow solving eq. 5.1 for up to three components. Therefore, at
least four components are required to detect deviations from complete independence
between all components (this is related to the fact that Aitchison’s test for complete
subcompositional independence is only effective when at least four components are
analyzed [139]).
Since an exact solution cannot be found, we SparCC utilizes an approximation,
which is valid when there are many components which are only sparsely correlated.
Eq. 5.1 can be rearranged to give the following expression for the correlation:
ωi2 + ωj2 − tij
ρij =
,
2ωi ωj
(4.10)
which, given the basis variances can be solved to give the basis correlations. Therefore,
we employ the following approximation procedure to estimate the basis variances:
82
First, define the variation of component i as
ti ≡
D
X
tij = dωi2 +
j=1
X
ωj2 − 2
j6=i
"
X
ρij ωi ωj
j6=i
X ωj2
ωi2
j6=i
1 X ωj
1
−2
ρij
=
1+
d
d j6=i
ωi
"
#
2
ω
ω
j
j
≡ dωi2 1 + h
ii − 2hρij ii ,
ωi
ωi
dωi2
#
(4.11)
where d ≡ D − 1, and h·ii represents averaging over all pairs involving component i.
Next, assume that the correlation terms in eq. 4.11 are small, i.e.
2
ωj
ωj
1+h
ii 2hρij ii ,
ωi
ωi
(4.12)
and neglect them, yielding the approximate set of equations:
ti ' dωi2 +
X
ωj2
, i = 1, 2, . . . D.
(4.13)
j6=i
Finally, solve eq. 4.13 to obtain the approximated basis variances to be plugged into
eq. 4.10, yielding values of the basis correlations.
To elucidate the nature of this approximation, consider the case where all the
basis variables have the same variance ω. The assumption made in eq. 4.12 simplifies
to:
1 hρij ii ,
(4.14)
i.e., we assume that the average correlations are small, rather than requiring that any
particular correlation be small.
Using the above approximation, the basic inference procedure is the following:
1. Estimate the component fractions in all the samples as outlined above, to obtain
the fractions matrix X.
2. Compute the variation matrix T.
83
3. Compute the component variations {ti }.
4. Solve eqs. 4.13 to get an approximate value for all basis variances {ωi }.
5. Plug the estimated log-basis variances into eqs. 5.1 to obtain the basis correlations {ρij }.
Iterative SparCC
The basic inference procedure can be improved upon by employing the following
iterative refinement scheme (Fig. 4.5):
1. Estimate correlations using the basic procedure described above.
2. Identify the most strongly correlated pair of components that was not previously excluded. If the magnitude of this strongest correlation exceeds a given
threshold, add this pair to the set of excluded pairs. Otherwise, terminate the
estimation procedure.
3. Identify components that form only excluded pairs and completely exclude them
from the analysis. Since the assumptions of our method are not met by such
components, it is unable to infer their correlations. If all components but three
are excluded, terminate the estimation procedure, as the sparsity assumption
is violated for the whole system.
4. If any components were excluded, re-estimate the fractions of the remaining
components. Note that the new fractions are relative to the new subset of
components.
(n)
5. Calculate the component variations ti , excluding all strongly correlated pairs.
(n)
That is, if ci
is the set of indices of components identified to be strongly
correlated with component i at the previous, nth , iteration, then
(n+1)
ti
=
X
(n)
j ∈c
/ i
84
tij .
(4.15)
6. Use the newly computed component variations to compute the basis correlations, as in steps 4 and 5 of the basic inference procedure.
7. Repeat steps 2 through 6 for a given number of iterations, or until no new
strongly correlated pairs are identified.
Note that the iterative procedure can result in correlations whose magnitude is greater
than 1, indicating that too many pairs were excluded. Setting a higher exclusion
threshold, or a lower iteration number will remedy this fallacy, though the resulting
approximation is likely to be of poor accuracy.
Basis correlation can also be inferred using transformed variables (see Text S1).
However, the iterative exclusion detailed above improves the quality of the approximation, making SparCC superior to these alternatives (Fig. S1)
To account for the sampling noise, the inference procedure is repeated multiple
times, each time with fraction values drawn randomly from their posterior distribution, generating a distribution of each pairwise correlation. The median value of
each pairwise correlation distribution is taken as its estimated value. In this work, a
threshold of 0.1 and a maximal number of 20 iterations were chosen, and the iterative
procedure was repeated 100 times.
Comparison of HMP networks inferred using Pearson and
SparCC
For each body site, pairwise correlations between all OTUs were inferred using both
Pearson and SparCC as described above. Interaction networks were subsequently
build by connecting all OTU pairs that had a correlation magnitude greater than a
given threshold. Results reported in the main text were obtained using a threshold
value of 0.3. Comparison between corresponding Pearson and SparCC networks was
done by treating the SparCC network as the true one, and computing the number
of true-positives (TP), false-positives (FP), true-negatives (TN) and false-negatives
(FN) detected in the Pearson network. The above quantities were calculated as
following:
85
TP = number of edges that have the same sign in both networks,
TN = number of edges are missing from both networks,
1
FP = number of edges that appear only in the Pearson network + number of edges
2
that have different signs,
1
FN = number of edges that appear only in the SparCC network + number of edges
2
that have different signs.
Assessing statistical significance
The statistical significance of the inferred correlations can be assessed using a bootstrap procedure. First, a large number of simulated datasets, where all components
are uncorrelated, are generated as described in Material and Methods. Next, correlations are inferred from each simulated dataset using SparCC with the same parameter
setting as is used for the original data. Finally, for each component pair, pseudo pvalues are assigned to be proportion of simulated data sets for which a correlation
value at least as extreme as the one computed for the original data was obtained.
Computer implementation
All analysis and procedures were implemented in Python, utilizing the Numpy [140]
and Networkx [141] modules. Plotting was done using the Matplotlib [142] module.
86
Pearson Shuffled
Pearson
3
SparCC
3
3
Mid-vagina
neff = 1.7
148
148
148
Retroauricular
Crease
neff = 2.8
Buccal
Mucosa
neff = 7.1
Gut
neff = 11.9
Supragingival
Plaque
neff = 18.4
Figure 4.1: Similar correlation networks are observed for real world vs. randomly shuffled bacterial abundance data. Correlation networks based on 16S rRNA
gene survey data collected as part of the Human Microbiome Project (HMP), inferred using
Pearson correlations (left column), and SparCC (right column). Additionally, Pearson correlation networks were inferred from shuffled HMP data (middle column), where all OTUs
are independent. The Pearson networks inferred from shuffled data show patterns similar
to the ones seen in the Pearson networks of the real data, especially for low diversity body
sites. This indicates that the observed Pearson network structure may be due to biases inherent in compositional data rather than a real biological signal. In contrast, no significant
correlation were inferred from the shuffled data using SparCC (data not shown). Nodes
represent OTUs, with size reflecting the OTU’s average fraction in the community. Edges
between nodes represent correlations between the nodes they connect, with edge width and
shade indicating the correlation magnitude, and green and red colors indicating positive
and negative correlations, respectively. For clarity, only edges corresponding to correlations
whose magnitude is greater than 0.3 are drawn. See Fig. S1 for all 18 HMP body sites.
87
<neff>
A
Basis
3
D
2
5 4
1
10
B
15
5
6
3
2
3
G
2
1
4
E
1
4
Pearson
5
6
3
2
3
2
1
4
H
1
4
SparCC
5
6
3
2
1
4
20
25
C
5
6
3
2
30 4
F
1
5
6
5
6
3
2
I
1
4
5
6
5
6
3
2
1
4
5
6
Figure 4.2: Pearson correlations inference quality deteriorates with decreasing
diversity. Basis data was simulated with a known correlation structure. OTU counts were
generated by randomly drawing from the basis , and were subsequently subject to both
correlation inference procedures. (A-C) True basis correlation network. (D-F) Networks
inferred using standard procedure. (G-I) Networks inferred using SparCC. The average
community diversities, as given by the Shannon entropy effective number of components
nef f , used in the simulations and observed in the HMP data are indicated on left indicates.
As in Fig. 4.1 , nodes represent OTUs, with size reflecting the OTU’s average fraction in
the community. Nodes represent OTUs, with size reflecting the OTU’s average fraction
in the community. Edges between nodes represent correlations between the nodes they
connect, with edge width and shade indicating the correlation magnitude, and green and
red colors indicating positive and negative correlations, respectively. For clarity, only edges
corresponding to correlations whose magnitude is greater than 0.3 are drawn.
88
Midvagina
Pearson
A
SparCC
B
2D
Midvagina
2G
Gut
Gut
2E
2H
2F
2I
Figure 4.3: SparCC outperforms standard inference. Root-mean-square error
(RMSE) of both Pearson (A) and SparCC (B) inferred correlations, as a function of the
density of the underlying correlation network, as given by the probability that any pair of
components be strongly correlated p, and community diversity, as given by the Shannon entropy effective number of components nef f . SparCC errors are smaller than Pearson errors
for all parameter values. For the maximal diversity plotted, 50 effective OTU, the inference
error obtained using Pearson correlations is greatly decreased. Therefore, it is likely that
Pearson correlations perform well on gene expression data, where the effective number of
genes is typically in the hundreds or thousands. For each combination of density and diversity, multiple basis correlation networks were randomly generated, and corresponding data
was sampled and used for correlation estimation. Dots labeled mid-vagina and gut indicate
the average diversity observed in the mid-vagina and gut communities, and the density of
their estimated correlation networks. Dots labeled 4.2D-I indicate the diversity and density
used to generate the communities analyzed in Fig. 4.2.
89
Mid-vagina
neff = 1.7
Retroauricular
Crease
neff = 2.8
Actinobacteria
Bacteroidetes
Cyanobacteria
Firmicutes
Buccal
Mucosa
neff = 7.1
Fusobacteria
Proteobacteria
Spirochaetes
Tenericutes
Verrucomicrobia
Other
Gut
neff = 11.9
Supragingival
Plaque
neff = 18.4
Figure 4.4: HMP correlation networks inferred using SparCC. Networks inferred
using SparCC from the same data as in Fig. 4.1 (see Fig. S2 for SparCC networks of
all HMP body sites). No correlations with magnitude greater than the 0.3 cutoff were
inferred from the shuffled data (not shown). Nodes represent OTUs, with size reflecting
the OTU’s average fraction in the community, and color corresponding to the phylum to
which the OTU belongs. Edges between nodes represent correlations between the nodes
they connect, with edge width and shade indicating the correlation magnitude, and green
and red colors indicating positive and negative correlations, respectively. For clarity, only
edges corresponding to correlations whose magnitude is greater than 0.3 are drawn, and
unconnected nodes are omitted. See Fig. S6 for all 18 HMP body sites.
90
abort
counts matrix
no
yes
fractions matrix
>3 components
remain?
variation matrix
yes
no
component variations
new excluded
components?
basis variances
basis correlations
yes
max iterations?
no
new excluded pairs?
yes
no
end
Figure 4.5: Flow chart of iterative basis correlation inference procedure.
91
Chapter 5
Inferring Strain Diversity from
Metagenomic Data
Jonathan Friedman, Katherine Huang, Dirk Gevers, and Eric J. Alm
Chapter 5
Inferring Strain Diversity from
Metagenomic Data
16S rRNA gene profiling enables the taxonomic characterization of entire
natural microbial communities. However, this technique offers only limited phylogenetic resolution: multiple related strains are typically lumped
together to form a single “Operational Taxonomical Unit” (OTU). Strainlevel community composition information, which is currently largely unexplored, is crucial for detecting migration between environments, and, potentially, paths of disease transmission. Moreover, strain-level resolution
provides a unique opportunity for testing existing community-assembly
theories, and gleaning insight into the dynamics of natural communities and the forces that shape them, as closely related strains tend to
be mostly functionally similar, with significant differences occurring in
ecologically-relevant traits. In this work we present a novel procedure,
termed StrainFinder, which is capable of inferring within-OTU diversity
from metagenomic shotgun sequencing data, and is applicable to the myriad of published metagenomic datasets. Using simulated data, we quantify StrainFinder’s accuracy and show that sequencing depth and strain
diversity are the key parameters affecting the inference accuracy. When
sufficient data is available, StrainFinder’s estimates are highly accurate.
93
For diverse assemblages, or when little sequence data is available, less
abundant strains remain unresolved, and StrainFinder provides a lower
bound on the true strain diversity. To illustrate a potential application
of StrainFinder, we have inferred the strain composition of 6 OTUs sampled from human cheeck and feces, and show that these OTUs are rarely
composed of a single dominant strain.
94
Introduction
16S rRNA gene profiling is commonly employed to achieve a taxonomic characterization of natural microbial communities [2]. Nonetheless, as this technique is focused
on partial sequences of a single marker gene, it inevitably provides limited phylogenetic resolution [4]. Typically, multiple related strains are indistinguishable based on
their 16S sequences and thus are all lumped together to form a single “Operational
Taxonomical Unit” (OTU) [143].
Obtaining higher resolution data regarding the individual strains that make up
these aggregate OTUs would facilitate investigation pertaining to both practical and
theoretical aspects of microbial communities. Some of the basic questions in ecology revolve around the speciation process, coexistence of similar species, and the
assembly of communities [144, 145]. Data at the strain level may provide insight into
such questions, as closely related strains tend to be mostly functionally similar, with
significant differences occurring in ecologically-relevant traits [146, 147]. Moreover,
individually resolved strains may be used to detect migration between environments,
and elucidate the role of the migration process in shaping natural communities. One
potential application of detecting migration events is the identification of the paths by
which pathogens are transmitted between humans and their environment and within
human communities.
To date, strain-level phylogenetic resolution has been achieved mainly by targeted sequencing of genetic markers specific to the taxonomic group of interest, or by
whole-genome sequencing of multiple isolates of the group of interest (e.g. [30, 148]).
Notable exceptions are recent works by Morowitz et al. [149] and Schloissnig et al.
[150] in which strain-level information has been inferred from metagenomic shotgun
sequencing data. Morowitz et al. have leveraged their ability to detect correlated
SNPs in a time-series, along with manual intervention to obtain high quality assemblies of closely related strains that colonize the infant gut. Schloissnig et al. broadly
analyzed the within-OTU genetic diversity in the human gut, without any assembly.
In this work, we develop a procedure, called StrainFinder, capable of inferring
95
within-OTU genetic diversity and abundance distribution. Importantly, our procedure does not require time-series data, nor manual intervention. Thus, it can be
straightforwardly applied to the myriad of published metagenomic datasets. Next,
we use simulated data to investigate the impact of the amount of available sequence
data, the within-OTU genetic diversity, and abundance distribution on the inference
accuracy. Finally, we illustrate a potential application of StrainFinderby applying
it to 6 OTUs from 2 sites on the human body.
Results
Metagenomic shotgun sequencing has the potential to offer higher phylogenetic resolution than 16S profiling, as it does not focus on a single genetic marker [6]. The main
caveat is that this technique provides short reads (∼100 bp), randomly sampled from
all the genomes in the community. The randomness of the sampling results in a variable sequencing depth within a genome, and renders each strain’s average sequencing
depth proportional to the strain’s abundance in the community, making it challenging
to achieve good coverage of rare strains. Moreover, short reads provide little genetic
linkage information, typically rendering genome assembly unfeasible. The following
section outlines a procedure for extracting strain level information from metagenomic
shotgun data despite the aforementioned challenges.
A prerequisite to a within-OTU-level analysis is the identification of reads sampled from strains comprising the OTU of interest. As reads are too short to enable
assembly, the desired reads are recruited by aligning all individual reads against an
available reference genome of a strain belonging to the focal OTU (Fig. 5.1, Materials and Methods). This step results in the identification of polymorphic genomic
positions, and the proportions of the alleles found in these positions. This approach
has been employed by Schloissnig et al. [150] to study the overall genomic variation
within an OTU. However, utilizing such data to identify specific strains and their
relative abundances has remained elusive, as most polymorphic positions are located
too far apart for a single read to span multiple polymorphic sites.
96
Strain
Propor6on
Genome
Fragment
Strain
1
0.3
A
A
C
G
G
A
Strain
2
0.7
A
A
T
G
G
T
Strain
1
0.1
C
A
T
G
G
A
Strain
2
0.3
A
A
C
G
G
A
Strain
3
0.6
A
A
T
G
G
T
Figure 5.1: Allele frequencies reflect combinations of strain proportions. Strain
proportions can be inferred from the allele proportions, which can be readily inferred when
deep sequencing data is available (middle column). With lower sequencing depth, sampling
noise obscures the true allele proportions (right column). Data were simulated as detailed
in Materials and Methods, with the denoted strain proportions and sequencing depths. For
clarity, only allele proportions > 0.05 from polymorphic sites are shown.
Progress can be made by noting that alleles found in the same set of genomes
should be present in the community at identical proportions. To illustrate the utility
of this fact, consider first a simple case in which an OTU is comprised of 2 strains
whose relative abundances are {0.7, 0.3} (Fig. 5.1, top row). In this scenario, in
addition to monomorphic genomic positions, there is only one type of polymorphic
position, in which the 2 strains have different base pairs. Therefore, all alleles found
at a 0.3 proportion at different polymorphic positions can be assigned to the same
genome, and there is no need to assemble large regions spanning all polymorphic
positions. When more than 2 strains are present, more types of polymorphic positions
exist, corresponding to different combinations of strains sharing the same allele. For
example, if there are 3 strains whose relative abundances are {0.6, 0.3, 0.1}, there
may be alleles found at proportions of 0.9, 0.7, 0.6, 0.4, 0.3, and 0.1 (Fig. 5.1,
bottom row). In this case, the strains’ relative abundances can be determined by
finding the minimal set of strain abundances whose combinations correspond to the
allele proportions. Once strain abundances have been inferred alleles can be readily
97
Ppoly =
0.01
Ppoly =
0.005
Inferred Proportions Inferred Proportions Inferred Proportions
Ppoly =
0.05
1
Nreads = 50
Nreads = 100
nef f
Nreads = 500
7
0.5
0
5
1
0.5
0
3
1
0.5
0
0
0.5
True Proportions
1
0
0.5
True Proportions
1
0
0.5
True Proportions
1
1
Figure 5.2: Accuracy of strain proportion inference. StrainFinder’s strain proportion estimates are highly accurate for abundant strains. For rare strains, inference accuracy
decreases in more diverse communities, though reliable estimates are obtained in lower diversity communities. Each dot indicates the true and inferred proportions of a single strain,
and colors indicate the diversity of the community to which the strain belongs. Strain
proportions were inferred from simulated data with varying number of strains, proportion
of polymorphic positions (rows), and sequencing depth (columns), and correspond to the
community diversities shown in Fig. 5.3.
assigned.
The simple procedure outlined above requires precise values of allele proportions,
which are typically not available due to the sampling noise (Fig. 5.1, right column).
Since metagenomic shotgun sequencing consists of sampling random DNA fragments
from an entire community, it is hard to achieve good coverage of a specific OTU, and
coverage varies along genomes. This coverage-dependent sampling noise obscures the
true allele proportions, except when extremely high coverage is obtained, thus limiting
the practical utility of the aforementioned procedure. In the presence of significant
sampling noise, a probabilistic framework is required in order to take advantage of
the insight that alleles found in a common set of genomes have equal proportions.
In the next section we present such a probabilistic approach, which builds upon the
same intuition presented above.
98
StrainFinder: an algorithm for inferring correlations from GSD
StrainFinder formalizes the fact that allele proportions reflect combinations of strain
proportions, and incorporates the sampling procedure to form a likelihood function
that can be maximized to find the most likely set of strains. To derive the likelihood
function, we first express the allele proportions Π in terms of the strains’ relative
abundances p = {p1 , p2 , ..., pn }:
Πi (j) =
n
X
pk Iki (j),
(5.1)
k=1
where Πi (j) is the proportion of allele j at position i, and Iki (j) captures the strains
genomes:
Iki (j) =


1
strain k has allele j in position i

0
otherwise.
(5.2)
Next, sequencing errors are accounted for by modifying the allele proportions to form
the “effective allele proportions”:
0
Πi (j) = Πi (j) [1 − ] + [1 − Πi (j)] ,
3
(5.3)
where is the probability that any sequencing error occurs. Note that the above
represents a simple error model in which all sequencing errors are equally likely, but
more detailed alternatives may be modeled in an analogous manner. Finally, the
sampling procedure is assumed to be unbiased, thus the observed counts at each
position follow a multinomial distribution. Therefore, the log-likelihood function of
the observed counts is given by:
ll(p, , I; C) ∝
L
X
X
i
j∈{A,C,T,G}
99
0
cij log Πij ,
(5.4)
where cij is the observed counts of allele j at position i, and L is the number of positions. Optimization of this likelihood function yields maximum-likelihood estimates
of the error rate and proportions of a predefined number of strains. To infer the
optimal number of strains, the above likelihood function is maximized with a sequentially increasing number of strains until no significant improvement in the optimized
likelihood is obtained (see Materials and Methods).
StrainFinder is highly accurate on simulated data
Ppoly =
0.05
Inferred nef f
7
Nreads = 50
Nreads = 100
Nreads = 500
5
3
1
Ppoly =
0.01
Inferred nef f
7
n=1
n=2
n=3
n=4
n=5
n=6
n=7
5
3
1
Ppoly =
0.005
Inferred nef f
7
5
3
1
1
3
True nef f
5
7
1
3
True nef f
5
7
1
3
True nef f
5
7
Figure 5.3: Accuracy of strain diversity inference. StrainFinder’s strain diversity
estimates are highly accurate up to a diversity threshold that depends of the amount of
available data. For very diverse communities, StrainFinder is unable to resolve all strains
and thus the inferred diversity provides a low bound on the true diversity. Strain diversities
where inferred from simulated data with varying number of strains (colors), proportion of
polymorphic positions (rows), and sequencing depth (columns). Each dot indicates the
true and inferred diversities of a single community, as quantified by the Shannon entropy
effective number of strains.
We have used simulated datasets in order to evaluate StrainFinder’s accuracy
and identify data properties that affect the inference accuracy. Simulated datasets
were generated by creating a set of random genomes with a given proportion of polymorphic positions, assigning random relative abundances to genomes, and sampling
reads from the resulting community at the desired coverage level. Multiple datasets
100
were generated for varying number of strains, proportion of polymorphic positions,
and sequencing depth. StrainFinder was applied to each of the simulated datasets,
and inferred parameters were compared to the true values used to generate the data.
StrainFinder’s strain proportion estimates are highly accurate for abundant
strains, with strain diversity and the sequencing depth being the key factors affecting the inference accuracy (Fig. 5.2). For rare strains, inference accuracy decreases
in more diverse communities, though reliable estimates are obtained in lower diversity communities. For diverse communities, or in the presence of very rare strains,
StrainFinder may be unable to resolve all strains (Fig. 5.2). Consequentially, the
inferred number of strains may be unreliable (Fig. S1). However, the Shannon entropy effective number of strains, which accounts for both the number of strains and
their proportions, can be inferred much more reliably (Fig. 5.3). StrainFinder’s
estimates of this diversity measure are highly accurate up to a diversity threshold
that depends of the sequencing depth. Beyond this threshold StrainFinder underestimates the strain diversity, due to the presence of strains with similar proportions
that cannot be resolved. Thus the inferred diversity provides a low bound on the true
diversity.
StrainFinder identifies strain-level patterns in the Human Microbiome
OTU number
53
196
1025
585
809
1638
Assigned taxonomy
Body site
Alistipes
Stool
Bacteroides vulgatus
Stool
Ruminococcus torques
Stool
Gemella haemolysans
cheek
Neisseria sicca
cheek
Streptococcus mitis B6
cheek
# Samples
123
137
11
44
6
101
Median Nreads
125
211
72
60
61
97
Median Npoly
1568
118
883
82
284
419
Table 5.1: HMP reference genomes used for strain analysis.
We used StrainFinder to infer the strain composition of 6 of the most abundant
OTUs found in the cheeck and feces (Table 5.1). We find that these OTUs are
101
typically comprised of several strains, rather than a single dominant strain (Fig. 5.4).
In addition, there is consistent variation in strain diversity between OTUs across
individuals, which appears to be independent of body site (Fig. 5.4).
Discussion
While the method presented in this paper enables extracting strain-level information
from metagenomic shotgun sequencing data, several challenges remain. Since, with
current read lengths, reads spanning multiple polymorphic positions are rare and little
linkage information is available, StrainFinder does not incorporate this information.
However, linkage information may greatly improve the inference accuracy when longer
reads are available, or in cases where a high density of polymorphic positions exists.
Like all maximum-likelihood methods, StrainFinder yields point estimates of
parameter values, whereas a Bayesian approach would yield much richer posterior
distribution of model parameters. Such an approach would require choosing an ap-
Stool
Saliva
Figure 5.4: Strain diversity in the human microbiome. OTUs identified in the
Human Microbiome Project (HMP) are typically composed of several strains. Consistent
differences in strain diversity exist between OTUs, however no relation between body-site
and strain diversity is detected. Thick lines, boxes and wishkers represent mdeians, interquartile ranges (IQR), and most extreme data within 1.5 × IQR, correspondingly.
102
propriate process for the generating the number of strains, and prior distributions for
model parameters. Additionally, implementing Bayesian approaches often requires
computationally-expensive simulations, which may render such approaches unfeasible for ever-expanding metagenomic datasets that comprise of hundreds of samples
and OTUs.
StrainFinder analyzes each sample individually, and thus can be applied to the
myriad of published metagenomic datasets. However, a better inference may be possible when several samples containing the same strains are available. For an individual
sample StrainFinder is based the fact that alleles found in a common set of strains
have similar proportions within a sample. It is possible to extend this approach by
noting that the proportions of alleles found in a common set of strains should be
correlated across samples in which these strains are present. Indeed, Morowitz et al.
[149] have used the later insight to study the microbial colonization of the infant gut
looking at metagenomic time-series data. We believe that StrainFinder sets the
path for the development of an automated, probabilistic tool capable of inferring the
distribution of individual strains across samples and over time, and, with the rapid
increase in the amount of available metagenomic data, would become an integral part
of the toolbox used by both microbial ecologists and epidemiologists.
Materials and Methods
Simulated datasets
Each dataset was generated in 3 steps:
1. n genomes of 10000 positions each are constructed. A fraction ppoly of the
positions are polymorphic, and the rest are monomorphic. At polymorphic positions, each genome is assigned a randomly selected allele (alleles are uniformly
distributed).
2. Strain proportions are sampled from an n-dimensional Dirichlet distribution
with concentration 1. This distribution is uniform over all n-strain community
103
compositions.
3. “Observed” allele counts are simulating for each position by drawing from the
appropriate multinomial distribution:
0
Csim ∼ Multi(Nreads , Π ),
(5.5)
0
where Π is the effective probability of observing each allele, as defined in the
Results section, and Nreads is the sequencing depth. A sequencing error rate
= 0.005 was used to generate all datasets.
All combinations of ppoly ∈ {0.005, 0.01, 0.05}, Nreads ∈ {50, 100, 500}, n ∈ {1 − 7}
were used. Multiple datasets were generated for each parameter combination. Since
communities composed of more strains have more possible compositions, the number
of datasets generated was set to 7n.
Effective number of species
The Shannon entropy effective number of strains in an OTU is defined as
nef f = eH ,
where H = −
P
k
(5.6)
pk log pk is the entropy of strain proportions [129]. The effective
number of species reported in the main text is computed using the either the known
or maximum-likelihood strain proportions for the corresponding OTU.
Accounting for sequencing errors
In this subsection we derive a rather general framework for incorporating sequencing errors to the StrainFinder framework. First, we define the error matrix E,
whose elements eij give the probability of observing allele i when the true allele is j.
The relation between the vector of true allele frequencies Πand the expected allele
104
0
frequencies Π is given by:
0
Π = EΠ.
(5.7)
In this manuscript, we employed the parsimonious assumption that all errors are
equally likely, and that that total error rate is . This assumption can be equivalently
stated as:
eij =




|A| − 1


1 − i 6= j
(5.8)
otherwise,
where |A| is the number of possible alleles. With 4 alleles, plugging equation 5.8 in
the general relation given in 5.7 recovers the simple expression given in Eq. 5.3 of the
Results section.
Optimization procedure
Since only polymorphic positions are informative regarding the strain composition,
we perform the optimization using only positions for which the null assumption of
monomorphism can be rejected. More precisely, the null assumption is that the most
abundant allele in a position is the sole true allele in that position, and that other
observed alleles resulted from sequencing errors. This assumption can be tested using
a one-sided binomial test with a specified error rate. In this work, we use and error
rate of 0.01 and a p-value threshold of 0.01.
The log-likelihood function given in Eq. 5.4 is maximized by searching through values of the sequencing error rate and strain proportions, and, at each iteration, setting
the genomes to the value that maximizes the log-likelihood function given the iteration’s sequencing error rate and strain proportions. As different genomic positions
are conditionally independent given the strain proportions, this approach enables optimizing each genomic position separately and greatly reduces the search space. With
a limited number of strains, it is feasible to exhaustively evaluate the likelihood of all
possible genomes, and this is the approach implemented in StrainFinder.
105
The optimal number of strain is assigned to be the one that minimizes Akaike’s
Information Criterion (AIC) [151]. Searching over the strain number is done by
starting with a single strain and sequentially adding strains until the AIC increases.
The number of model parameters used in calculating the AIC is given by:
m = |{z}
1 +
error rate
n
− 1}
| {z
strain proportions
+ |{z}
nL .
(5.9)
genomes
HMP data processing
Metagenomic reads from the stool and cheeck samples collected as part of the HMP
were aligned to reference genomes of 3 of the most abundant OTUs in each of these
sites (Table 5.1), as identified in the HMP [128]. To minimize the confounding effect
of horizontally-transfered flexible genes, only genes that mapped to one of the phylogenetic marker genes identified in the AMPHORA pipeline [152] were included in
the analysis. Additionally, reads and base-pairs with a quality score [153] < 20 were
excluded.
Computer implementation
StrainFinder was implemented in the Python programming language, utilizing the
Numpy (1.6.2) [154] and openopt (0.38) [155] packages. Optimization is conducted
using the ’ralg’ solver implemented in openopt. Simulations and analysis were also
implemented in Python, and plotting was done using the Matplotlib (1.0.1) [156]
package.
106
Part III
Conclusion
107
In this thesis, I have described algorithms and analysis that promote our understanding of microbial adaptation, differentiation, and community structure. Nonetheless, we are still far from a unified understanding of the complex interplay between
microbial ecology and evolution [144]. This last section discusses possible extensions
of the methods presented in this work, and future research directions.
In Chapter 1, we studied the fundamental temperature-salinity niche species can
occupy in isolation. Surprising, not only did we not detect a trade-off between temperature tolerance and salinity tolerance, the two were in fact positively correlated.
A trade-off could very well exist in some unmeasured parameter, like growth rates
or low temperature/salinity range, but this finding highlights the need for a better
understanding of the process by which niches evolve, and the forces that drives them.
Notably, the only niche shapes observed in this study are the ones corresponding to
additive, antagonistic, or no interactions between temperature and salinity stresses.
This is in contrast to interactions between antibiotic combinations, which are often
synergistic [42]. These findings may be indicative of selection favoring certain interactions, however the niches of many more organisms, across different environmental
conditions need to be mapped before general conclusion can be drawn.
In Chapter 2, we provided evidence indicating that only a handful of loci are responsible for ecological differentiation of two closely related Vibrio splendidus populations which are found in distinct habitats. Rampant recombination partially explains
the breakage of linkage between the adaptive loci and the rest of the genome. However,
recombination is not likely to be the sole cause, as this would require unrealistically
high rates of recombination [8]. Studying similar occasions of recent differentiation
in species that do not recombine frequently may provide clues as to the other mechanisms that hinder selective sweeps, and is necessary to assess their prevalence. In
addition, We have detected restricted gene flow between the two ecological populations. A reduced cross-habitat encounter rate may account for this observation, yet
the exact mechanism remains to be determined. Finally, we proposed that gene flow
may diminish further with time, resulting in two populations that are mostly genetically isolated. Further monitoring the gene flow across the habitats will reveal the
108
dynamics and extent of genetic isolation following a differentiation in a recombining populations, and will provide an opportunity to elucidate the mechanisms that
increase genetic isolation.
Our simulation results presented in Chapter 3 indicate that time-varying recombination rates may be advantageous in some scenarios. For mutations, such transient
periods of elevated evolutionary rates have been both modeled and observed in bacteria [157, 158]. For recombination, we have considered one relatively simple scenario,
however the general conditions under which periods of ‘hyper-recombination’ would
emerge need to be elucidated. Specifically, the distribution of fitness effects of alleles
acquired by HGT, and the ability to affect that distribution via mate selection are
likely to play a key role in determining the optimal recombination rate.
The algorithm SparCC, described in Chapter 4, allows detection of inter-taxa correlation from 16S survey data. In human-associated communities, we have detected a
tendency for more closely related taxa to be more strongly correlated, despite the fact
that for such taxa resource competition is expected to result in negative correlations.
A potential explanation is that more similar taxa are more likely to share a niche,
and that positive correlations are induced by fluctuations in niche size. If true, this
hypothesis predicts that abundance should be correlated with functional similarity, a
prediction that could be tested using datasets for which both 16S profiling and fully
sequenced genomes are available, such as the Human Microbiome Project. A key
limitation of SparCC is that it specifically infers linear correlations. However, realworld ecological interactions are unlikely to manifest as simple linear correlations,
and their detection will require the development of analogous methods for detecting
more complex, non-linear dependencies, and for the analysis of time-series data.
Lastly, in Chapter 5, we introduced the algorithm StrainFinder, which can infer
within-OTU strain diversity. Since strains comprising a single OTU are likely to be
(mostly) functionally equivalent, their dynamics are expected to resemble the predictions of neutral theory [159], and deviations from this expectation can be used as
indicators for the presence of additional forces. For example, a prolonged persistence
of individual-specific strains is consistent with the action of immune-system selection.
109
In addition, in the previous paragraph we proposed that fluctuations in shared-niche
size are responsible for the elevated correlations between related OTUs. This hypothesis can be tested using StrainFinder, as it infers relative strain proportions within
an OTU, and thus eliminates niche-size effects. Extensions that will increase StrainFinder’s accuracy, and broaden its applicability include the incorporation of linkage
information regarding alleles found on the same read and the joint analysis of several
samples expected to contain shared strains, such as samples comprising a metagenomic time-series.
110
Part IV
Bibliography
111
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