Phylogenetic niche conservatism – common pitfalls and ways forward
Münkemüller, Tamara1,2, Boucher, Florian C.1,2,3, Thuiller, Wilfried1,2, and Lavergne,
Sébastien1,2
1 Univ.
Grenoble Alpes, LECA, F-38000 Grenoble, France
LECA, F-38000 Grenoble, France
3 Institut für Systematische Botanik, Universität Zürich, Zollikerstrasse 107, CH-8008
Zürich, Switzerland
2 CNRS,
Appendix S1: Simulated data
In the simulation model we simplify the niche evolution process by assuming that
species’ niches can be represented by a single trait capturing those optimal
environmental conditions in which a species can thrive (hereafter ‘niche value’). For the
sake of this theoretical exercise, we assume one niche gradient to which adaptation is
conferred by one quantitative trait. We argue that selection in the evolutionary models
should rather act at the level of the niche, i.e. the weighted combination of those
ecological traits that determines species’ performance, than independently at the level of
each niche-relevant trait. This way synergies and trade-offs between different traits are
accounted for. We could have added on top of the evolved niche value a combination of
directly observable traits linked to the niche. However, this increased realism would
have strongly increased parameter space while only adding an observer and
interpretation error to the simulations (e.g. trait measurement errors, errors in
identifying the niche-relevant traits, errors in estimating the importance of different
traits for the niche). Assuming that these errors would only add random noise we kept
the simulation model as simple as possible and focussed on a single niche value trait.
This niche value evolves according to an Ornstein-Uhlenbeck (OU) process along
simulated phylogenies. Given that niche conservatism always results from constraints
on the emergence of niche innovations (Holt 1996; Gomulkiewicz & Houle 2009), the
OU-process, which combines a Brownian motion (BM) process with selection towards
one or several optimal values, is a ‘natural’ model for describing this process of
constrained niche evolution (Butler & King 2004). It is consistent with a range of
evolutionary interpretations and varying the parameters results in a variety of
distributions consistent with phenotypic evolution under both drift and selection
(Hansen & Martins 1996).
The OU process models the evolution of a continuous niche value as the weighted
sum of a BM component and a selection term mimicking stabilizing selection. BM
simulates a continuous-time random walk of the niche values along the branches of the
phylogenetic tree (Felsenstein 1973). Thus, under BM, the expected variance between
ancestor niche values and descendent niche values increases linearly with branch length
and is not constrained by additional factors. The selection component describes
constraints on niche evolution due to stabilizing selection towards one or several clade-
specific optimal values. When selective optima are changing across the phylogenetic
tree, the model will mimic niche diversification while one single optimum fixed across
the entire tree mimics tree-wide niche conservatism (Butler & King 2004). When the
selection strength is zero, the process equals BM. Thus the basic OU process allows
simulating a range of different evolutionary scenarios, while changing parameter values
and combinations.
In a first step, we simulated a phylogenetic tree under a Yule model (R function
birthdeath.tree in package geiger, Harmon et al. 2008). In each simulation, a tree with
100 tips was simulated with a branching rate of 0.05 lineages per time unit.
In a second step, we simulated niche values along these phylogenies following an OUmodel, where the evolution of the niche value (x) is governed by the following
differential equation: x ( t + dt ) = x (t ) + a (q (t ) - x ( t )) dt + s dte . In this equation, e ~ N ( 0,1) ,
σ is the neutral drift rate, θ the optimal value (that can depend on time), α the selection
strength, and dt is an elementary unit of time. Niche evolution was simulated
consecutively through a discretized continuous time process (R function evolve.trait in
package picante on R-forge, www.r-forge.r-project.org, α was redefined in this function
such that a value of zero describes BM and 1 describes strong selection towards niche
optima). In each simulation, niche evolution started from a root value of zero and σ was
set to 0.01.
Across simulations we varied the strength of selection towards optima, α, the number
of optima and the values of optima in order to describe contrasting processes of niche
evolution:
1. OU model with a single optimum (OU1) – In our first set of simulations all nodes and
tips in the tree shared the same optimum, which was set to zero while the selection
strength, α, was varied between simulations. If all species share one optimum and this
optimum is equal or very similar to the common ancestor’s niche (root niche value),
species tend to retain their ancestral niches. We thus suggest that this niche evolution
model can be interpreted as increasingly strong PNC for increasing α (for α equal to zero
it is a BM model). As the selective constraint that is exerted onto related taxa is external
it could, for example, be interpreted as an environmental selective constraint (Harvey &
Pagel 1991; Desdevises et al. 2003; Losos 2008).
2. OU model with evolving internal optima (OUevol) – In our second set of simulations we
set the optima of branches in the OU-model to the realized niche values of the respective
parent nodes of these branches. Thus there are as many optima as realized niche values
of inner nodes in the phylogeny. The stronger α the more similar are realized niche
values of the descendants to those of the ancestral node. Due to these conserved
ancestor’s trait values we suggest that increasing strength of α can be interpreted as
increasing strength of PNC under internal constraints, e.g. due to limits to adaptive
evolution (Holt 1996; Gomulkiewicz & Houle 2009), or to a lack of genetic variability
(Bradshaw 1991).
3. OU model with multiple external optima (OUext) – In our final set of simulations
different clades differ in their external selective optima and these optima also differ
strongly from the root value. In these simulations niches diversify quickly over a long
time during early evolution and stay more constant during the late period (see also the
‘time-dependent stochastic peak shift’ model, Revell et al. 2008). When considering the
entire phylogeny at once, niches may be interpreted as being labile because they change
more extremely than under BM and PNC. However, when considering different parts of
the phylogeny separately one may argue that a long period of labile niches is followed by
a short period of conserved niches.
To implement this model we needed to define clades with different environmental
optima. To calculate the optima for all nodes of the tree we first identified the tips
belonging to the same clade by cutting the phylogenetic tree at a certain time (we chose
times that resulted in η different clades with η=10 when not reported otherwise). All
species in each clade were assigned the same optimum. The optima were randomly
chosen from a set of η values evenly distributed (i.e. with the same distance between
them) around zero and between the boundary values -β and β. Starting from the optima
values of the tips we then calculated the optima for the nodes backwards in time along
the phylogeny such that each node's optimum was the mean of the descendants' optima.
We chose this approach to obtain gradually changing optima over time while at the same
time allowing for large differences in optima between neighboring clades (as optima
were assigned randomly to clades). This is a numeric method for parameterizing the
external optima that allows comparing different values and combinations of optima and
to study opposing cases. For the sake of simplicity we did not implement a sub-model
simulating emerging environmental niche optima over time (which would have required
to check whether emerging optima were appropriate to simulate labile niches). Under
relatively large values of β (we used 1 and thus a range of -1 to 1 for the optima if not
stated otherwise) niches were increasingly labile for increasing strength of α. We also
did not simulate niche evolution under randomly sampled optima because this model
has been shown to converge with a process of Brownian motion at least if selection
strength is not extremely strong (Hansen & Martins 1996; Revell, Harmon & Collar
2008). Overall, we would like to highlight that our aim was to use a simple model with a
small parameter space to illustrate some of the potentially emerging problems of
commonly used PNC measures. A more realistic model would be required if the aim
would be a quantitative comparison of model performance. This is because our OUext
model generates some extreme patterns, such as a very high phylogenetic signal (due to
the way optima and shifts between optima are imposed on the phylogeny) and a bias
towards identifying multi-peak OU models in a model comparison approach (due to the
overdispersed optima).
Each scenario in the three sets of simulation was repeated 100 times. Results are
presented as boxplots such that the degree of variation among these 100 repetitions is
visualized. The number of repetitions was sufficient to differentiate between scenarios
but one should note that for smaller trees a higher number of repetitions can be
required.
Appendix S2: Approaches to estimate PNC
1. Phylogenetic signal – We measured phylogenetic signal using Blomberg's K (Blomberg,
Garland & Ives 2003). Values close to zero indicate phylogenetic independence and
values of one indicate that species’ niches co-vary in direct proportion to their shared
evolutionary history as expected under Brownian motion. Higher values indicate
stronger phylogenetic signal. We chose Blomberg's K as it can take values much beyond
those expected under BM (in contrast to Pagel’s λ, Pagel 1999) and is especially suitable
for simulation models where scenarios can be repeated (Münkemüller et al. 2012).
2. Evolutionary rate – We estimated the rate of evolution using the variance of
phylogenetic independent contrasts, which assumes a Brownian motion model of
evolution (Felsenstein 1985; Cooper, Freckleton & Jetz 2011).
3. Niche retention – We estimated niche retention with Pagel’s δ (Pagel 1999), a
transformation of branch lengths that contracts or stretches branches depending on
their age.
4. Estimation of the α parameter and the stationary variance in an OU-model – We used
the motmot package (Thomas & Freckleton 2012) to fit the OU-model. Parameters were
estimated by maximum-likelihood, using the independent contrasts algorithm
(Felsenstein 1985; Freckleton 2012). The stationary variance of the OU process is σ2/2α.
5. Model comparison– In a first step, we applied the common approach and compared the
fit of a white noise, a Brownian motion and an OU model with one external optimum on
the data (Cooper, Jetz & Freckleton 2010). For clades of mammals, we also fitted OU
models with multiple optima without any a priori on the nodes where shifts between
selective regimes would occur (Ingram & Mahler 2013). All models were fitted using the
SURFACE package (Ingram & Mahler 2013) and compared using AIC (Akaike). The AIC
was calculated following Ingram and Mahler (2013) with one exception: we did not
count the placement of the ancestral regime as a free parameter because we also did not
count it for BM and WN. Maximum likelihood estimates of model parameters were
obtained using large-scale bound-constrained optimization (L-BFGS-B, Byrd et al.), with
the maximum number of iterations set to 100,000. Following the suggestion of Boettiger
et al. (2011) we finally applied a power analysis based on a phylogenetic Monte Carlo
approach, which explicitly tests whether more complex models are chosen solely
because they have more free parameters or because they better describe the process. As
we were mostly interested in whether or not simple BM assumptions were fulfilled we
simulated 100 repetitions of random drift (BM) for each clade with those parameters
that fitted the clade data best. We then tested the null hypothesis that the simulated data
were in concordance with the observed clade data. By doing this, we included in our
analysis data that were simulated under BM and tested the performance of the model
comparison approach to correctly identify BM.
Note, that we did not fit OUevol models to the data, as methods for doing so do not exist.
Appendix S3: Mammal data
In order to avoid relying exclusively on a predefined model for PNC, we also added
empirical data to the analysis. The advantage of the empirical data is that the underlying
trait evolution processes are realistic; the disadvantage is that they are unknown. In this
empirical example we apply the different measures of PNC to the single trait ‘body size’
in order to illustratively compare them. Body size is an important determinant of
species resource niches and is commonly used as a proxy for mammalian niches, since it
influences many aspects of life history including dispersal, diet, generation time, energy
budget (Gillooly et al. 2001). However, an in-depths study of PNC for these clades should
obviously include a better estimate of the niche and thus further niche relevant traits.
We studied the evolution of body mass in 17 clades of mammals. We chose those clades
for which information on both body mass and phylogeny were available for at least 20
species and 75% of species described by taxonomists in the clade. Phylogenetic trees for
clades came from the supertree of Fritz et al. (2009), except for clades of carnivores and
primates (Arnold, Matthews & Nunn 2010), Dasyuromorphia and Heteromyidae (Pigot,
Owens & Orme 2012). Adult body masses were extracted from the PanTHERIA database
(Jones et al. 2009) and were log-transformed prior to analysis.
Table S1: Results for the analyses of body mass evolution along the phylogeny.
The last column presents the power analysis in the model comparison analysis for the
mammal data based on a phylogenetic Monte Carlo approach with 100 repetitions
(Boettiger, Ralph & Coop 2011). Results show that the evolutionary process significantly
differed from Brownian motion in almost all clades (except Tamias). * marks p-values
smaller than 0.05.
Clade
N species
N shifts
N optima
α of OU
σ2 of OU
p-values
Sciuridae subf. Xerinae tribe
Protoxerini (African ground
squirrels)
28
3
2
0.22
0.14
0.04*
Afrosoricida
34
5
3
1.87
1.91
0.01*
Canidae
Musteloidea (Ailuridae,
Mephitidae, Mustelidae,
Procyonidae)
27
3
3
1.42
0.41
0.01*
66
5
4
0.06
0.07
0.01*
Ctenomys
34
3
3
0.21
0.06
0.01*
Dasyuromorphia
56
6
5
0.44
0.26
0.01*
Diprotodontia
Bovidae subf. Cephalophinae
(Duikers)
107
18
9
0.03
0.01
0.01*
24
4
3
0.04
0.02
0.01*
Feliformia
76
8
4
0.05
0.06
0.01*
Geomyidae
33
4
3
6.45
1.62
0.01*
Heteromyidae
52
5
4
0.02
0.01
0.01*
Lemuriformes
Primates parvorder
Platyrrhini (New world
monkeys)
Papionini (Cercopithecidae
tribe)
35
5
3
0.03
0.02
0.01*
57
7
6
0.10
0.01
0.01*
29
2
2
0.09
0.03
0.03*
Phyllostomidae
120
16
5
72.67
16.85
0.01*
Tamias
23
2
2
0.20
0.01
Xenarthra
29
5
3
0.31
0.23
0.06
0.02*
Figure S1: Application of PNC approaches to mammal data
Pairwise correlations between parameters estimated during the model selection
analysis of the mammal data (indices of Pagel’s δ and Blomberg’s K in addition). We
considered white noise, Brownian motion and flexible OU-models (shown are number of
optima, estimated selection strength, estimated evolutionary rate and stationary
variance for the models with the lowest AIC). The upper right triangle shows correlation
coefficients from a Spearman rank correlation, the diagonal shows the histograms of the
parameters and indices. If all parameters and indices performed well as estimates of
PNC than they should be highly correlated. In contrast, high α* values indicate PNC for
the same clades for which low K, high evolutionary rates and high values of Pagel’ δ
indicate labile niches. The number of optima and the stationary variance were not
strongly related to one of the other estimates.
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