Supplementary Information for “Quantifying temporal change in biodiversity:
challenges and opportunities”
This file includes a discussion of 1) sources of temporal data 2) challenges of dealing with
historical and 3) paleontological data, 4) more detailed information about the use of GAMs
for modeling biodiversity time series and 5) Figures S3, S4, and S5. Figure S3 illustrates the
decomposition of a time series into multiple cycles. Figures S4 and S5 are provided to
illustrate the point that multiple components of biodiversity can be analyzed with the same
tools. These figures are similar to Figure 2 in the main text, but using taxonomic and genetic
richness respectively.
1) Sources of temporal data
We identify four main sources of biodiversity time series: intentionally
temporal investigations, chronosequences (in which space is used as a proxy for
time), legacy or historical records, and palaeobiological assemblages
Intentionally temporal data arise from scientific projects or monitoring
programs specifically designed to generate time series. These are potentially the most
desirable data, because they are based on standardized sampling and explicit,
repeatable methodology. However, these data usually have the shortest time span.
They are often tied to grant funding cycles of less than 10 years, or limited by the
lifespan of a laboratory or the career of a scientist. Notable exceptions exist, such as
the Park Grass experiment (1), which has been running since 1856 (see more
examples in (2)). There are some ongoing efforts to promote long-term survey studies
(e.g. www.lternet.edu, www.neoninc.org).
1
In chronosequences, space-for-time substitution entails a snapshot survey
of multiple contemporary communities that differ in their age or some other feature
that varies with time. Chronosequences have been instrumental in understanding the
process of succession (3). We can compare communities that differ in their time since
a disturbance (4), or in their history of land use (5). The key advantage of the
chronosequence is that it does not require samples from the past. However, the
validity of chronosequence analyses depends critically on the assumption that spatial
variability in contemporary assemblages is an accurate proxy for temporal change,
and this has not always been supported (6).
Legacy or historical data exploit ecological records collected in the past,
such as land surveys, fishery catch data or specimen records from scientific collecting
expeditions (7). Legacy data were usually collected and preserved for reasons other
than monitoring temporal change in biodiversity, and typically allow analyses over
temporal durations on the order of decades to centuries (8). Legacy data have been
exceptionally useful in establishing ecological baselines prior to anthropogenic
changes. For example, revisiting land survey records in North America has allowed
pre-European settlement conditions to be used as targets for conservation or
restoration (9). However, the accuracy, reliability and bias of legacy data are variable,
and depend on the methods and motivation for their original collection. A suite of
approaches has been developed for addressing these limitations (see section 2).
Palaeontological data consist of samples of fossilized organisms or
evidence of their presence and geological context, and they allow the longest possible
time series, typically of thousands to millions of years (10). These data are our only
source of information about the distant past. For example, fossil records from before
the Pleistocene have shown that the large-bodied portion is largely missing from
2
contemporary communities (11). However, variation in ecological conditions and
preservation potential can distort patterns. Palaeontologists have devoted considerable
effort to understanding and quantifying biases in the fossil record (10) and recent
efforts have focused on explicitly linking palaeontological and biological data to
inform conservation decisions (12).
There are also taxonomic biases and resolution issues in many temporal
data sets. Intentionally longitudinal studies, for instance, tend to focus either on
sessile organisms (e.g. plants), or on charismatic organisms for funding or logistical
reasons (e.g. large mammals, birds). Legacy data typically focus on organisms that
can be used as indicators of environmental conditions (e.g. plants) or organisms of
economic importance (e.g. fisheries). Palaeobiological data are most often available
for organisms and environments that preserve well (e.g. hard-shelled marine molluscs,
pollen in lakes, terrestrial mammals). To the extent possible, an important goal for
future studies is to counter these biases, by conducting contemporary studies of
organisms for which we have good historical or palaeo data, but also actively
searching for creative ways to recover past information about organisms we are
studying in the present.
3
2) Characterizing temporal biodiversity change using legacy data
Over the past several centuries, land surveyors, natural resource managers,
explorers, historians, and ecologists have been making observations of particular species or
ecological communities across the globe. These human-created records include diaries, land
surveys, herbarium and museum specimens, fishing and hunting harvest records, and early
ecological studies (7). The “legacy data” found in these sources has been immensely valuable
in allowing quantification of historical biodiversity patterns in terrestrial plants, animals and
birds (13-15), as well as marine mammals and fish (16). However, most historical surveys
were not conducted for the purpose of allowing future analyses of temporal change, so the use
of legacy data presents some non-trivial challenges. Here we use examples from the literature
on biodiversity change mainly in terrestrial plant communities and fisheries to illustrate some
of these challenges, and their solutions.
The location and relocation of past surveys
Challenges: Most historical survey points or plots were not permanently marked, although
some spatial information is available (e.g., points on a map, written descriptions with roads or
topographic features as landmarks). In such cases, it is not possible to re-survey in the same
precise locations (17). In addition, the location of past survey plots was often highly nonrandom. For example, many past plant surveys were aimed at vegetation classification, and
therefore over-sampled underrepresented environmental conditions (18). A comparison with a
modern survey (based on (stratified) random sampling) could falsely attribute an observed
difference to temporal change (18).
Solutions: With imprecise spatial matching of past and present observations,
researchers should not attempt to draw strong conclusions about temporal changes in
4
individual plots. However, as long as systematic biases in contemporary plot locations (e.g.,
with respect to environmental conditions) can be avoided, valid temporal comparisons can be
made for the set of plots in aggregate (e.g., species frequencies across plots), especially if the
sample size is large (17). Understanding potential biases in the exact positions of past survey
plots, such as the tendency for vegetation classifiers to seek out “homogenous” areas, can help
contemporary researchers minimize survey location error. Multiple plots in the vicinity of the
historical survey can be surveyed, and averages used (e.g., of abundance or diversity) to
increase confidence in plot-level temporal comparisons (17). This approach can also allow
quantification of small-scale spatial variance in species composition, and therefore estimating
survey location measurement error (19).
Uncertainty about or changes in survey methods
Challenges: Knowledge of important attributes of past surveys is often
incomplete, including their intensity (e.g., how much time spent searching a plot), the
competency of the surveyors, the seasonal timing of surveys with respect to organisms’
phenology, the exact meaning of abundance estimates (e.g., visual percent cover classes), and
taxonomy. Alternatively, the method of making the observations may be known, but may
have changed at some point in a time series. For example, in fisheries records the species that
correspond to a common name often change throughout the time series, as does the location
and fishing effort (20).
Solutions: In some cases, these uncertainties can be minimized by referring to
unpublished field notes and data sheets (21), or by consulting people involved in the original
surveys (22). Faced with the inevitable uncertainties that remain, contemporary researchers
must be careful to restrict their temporal analyses to variables for which there is high
confidence in the past-to-present comparability. For example, given the strong sensitivity of
5
species richness estimates to sampling intensity (23), it would be inadvisable to compare local
species richness across surveys if the possibility of differences in sampling intensity cannot be
excluded, although a multivariate analysis of community composition based on relatively
common species might be valid. Alternatively, statistical methods can be used to account for
known differences in sampling intensity (e.g. (24) using herbarium records).
Species that are likely to have been observed only at one time period, due to
factors such as seasonal timing (e.g., spring ephemeral plants) or different taxonomic criteria,
should either be excluded from analysis or pooled with other species when appropriate (e.g.,
one observer recognized two species where the other recognized only one) (25). Given the
fluidity of taxonomic nomenclature, the use of morphospecies and ambiguous common
names, considerable effort is often needed to ensure comparability across time. Likewise, if it
is impossible to ensure comparability of local abundance estimates across time, it may be
necessary to analyze only patterns of presence-absence across plots (26).
In the case of a known shift in methods, this change can be incorporated into
models of population or community change, as has been done successfully in the case of
changing harvest methods in fisheries data (27).
Bias in survey methods
Challenges: Especially in cases in which historical surveys were conducted for
very different reasons than contemporary surveys, there may be systematic biases to confront
in the historical data. For example, in the case of land survey data in North America, which
has been widely used to characterize historical vegetation patterns, the purpose was to define
new property boundaries and to characterize the potential of the land for agriculture and other
uses (28). At regularly spaced points on the landscape, surveyors recorded the identity, size,
and distance-from-point of “witness” or “bearing” trees. An example of bias (despite
6
documented instructions to surveyors) was a tendency for surveyors to favor trees that were
neither too large nor too small (29). Other important biases to consider are potential incentives
to falsify records, as for example present in the case of fisheries logs in regulated fisheries
(30).
Solutions: Strategies for dealing with biases are case specific. As one example, for
land survey data in North America, bias in the “point” data (i.e., data taken at the points
defined by intersecting survey lines) can to some extent be assessed by comparison with “line
tree” data, for which surveyors recorded trees that intersected survey lines. Because these
trees were not used as property markers, it is thought that they should be less biased by
species (9). Because larger trees are more likely to be intersected by a line, these data are size
biased (29), but it is straightforward to correct for this bias by scaling tree occurrences by the
inverse of their diameter (9). More generally, to the extent that the magnitude of biases in
historical data can be quantified, researchers can specify a degree of past-to-present difference
that must be exceeded before allowing an inference that temporal change has occurred (29).
In addition to these recommendations, confidence in biodiversity changes
documented using legacy data can be improved by combining multiple sources of these data,
as well as biological records (e.g. palaeontological data) when available (7). For example,
(31) used multiple sources of legacy data along with fossil pollen and charcoal records to
understand vegetation change in the Indiana Dunes. In spite of the challenges, legacy data
represent a rich store of information that cannot be found anywhere else.
7
Figure S1 – Challenges and solutions in using legacy data to measure
changing biodiversity over time.
8
3) Fossils, a powerful perspective on the past and future
Paleontologists and biologists have increasingly recognized the utility of fossil
records for determining pre-anthropogenic ecological baselines and for providing examples of
ecological responses to conditions unlike those we have experienced (i.e., conservation
palaeobiology (32)). While the selection of an appropriate baseline or analogous time interval
is ultimately question specific, it is worth considering that modern ecological systems were
likely already impacted by human actions before the change of interest. For example, most
palaeobiologists would argue that the Pleistocene megafaunal extinction is strong evidence of
the impact of early humans on ecological systems (33). Palaeontological records have been
used to establish baselines in a wide variety of environments. Good examples include lakes
and rivers (34), estuaries (35), and coral reefs (36), but many other excellent studies exist.
Fossils document previous examples of rapid global change. These deeper time
examples do not have the confounding influences of anthropogenic land clearing and habitat
fragmentation, and they provide important insights into how ecological systems respond to
climate changes like those projected for the next century. One of the best such analogies for
our current climate is the Paleocene-Eocene Thermal Maximum (PETM, 55.8Ma). An
examination of leaf damage suggests that increased insect herbivory is likely to be a net effect
of warming temperatures (37). Multiple studies have documented sweeping ecological
changes associated with the rapid migration of mammals (38) and plants (39) during the same
climate transition.
Palaeontological perspectives are critical to understanding the present and
potential future state of the biosphere. However, palaeontological data need to be analyzed
9
carefully, fully considering the fundamental differences between fossil assemblages and
modern communities. Here we briefly review some of these issues.
Time period sampling bias
Challenges: Not all time periods are equally well represented in the fossil record,
and this presents a problem that is analogous to variable sampling effort through time.
Because sampling effort seriously affects biodiversity estimates it is necessary to standardize
sampling effort per time interval prior to analyzing the time series.
Solutions: Some techniques that can be used for this purpose include rarefaction,
and other forms of sub-sampling to achieve standardization (see section on measurement error
in the main text).
Habitat bias
Challenges: Habitats where sediments are being deposited are most likely to
preserve a fossil record, and wide spread environments are more likely to be preserved and
sampled than others. Marine sediments have an exceptional fossil record because it is the
largest depositional environment, and therefore many palaeobiological studies focus on
marine organisms with durable shells. While marine soft-sediment environments and molluscs
have some of the best fossil records, these environments involve only 4 of the 566
documented modern molluscan extinctions (40). This work suggests that the true number of
modern molluscan extinctions is almost double that reported on the International Union for
the Conservation of Nature's red list and that the bulk of these extinctions involve terrestrial
species on oceanic islands and fresh water species from the United States. So, our knowledge
of present day extinctions and the species most impacted by the current extinction crisis is
concentrated amongst taxa and environments that are least likely to have a good fossil record.
Solutions: To resolve this problem modern equivalents of these habitats can be sampled.
Taxa Sampling probability
10
Challenges: No sampling method is equally likely to sample all individuals or
taxa, and this is equally true of the fossil record. Another problem is that our knowledge of
modern day extinction is concentrated in taxonomic groups and environments where fossil
records tend to be poor. The passenger pigeon (Ectopistes migratorius) is an iconic symbol of
human caused extinction, but it is also a good example of the limitations of the fossil record.
Prior to European colonisation passenger pigeons numbered in the billions, but these birds are
represented by only about a dozen fossil occurrences (http://paleodb.org). Birds have
lightweight bones that are easily crushed and not typically preserved in fossil deposits, so it
would be very difficult to reconstruct the importance of this species based solely on its fossil
record. While birds are one of the best groups for modern and even historical studies, they are
amongst the most problematic for palaeontological investigations due to their low sampling
probability.
Solutions: Any model allowing for unequal sampling probabilities of individuals
or taxa (for example models dealing with different rates of detectability (41)) can be readily
adapted for use with palaeontological data. Investigating in the present, taxa with rich fossil
records can maximize long term time series.
Time resolution
Challenges: Modern ecological studies take place on timescales much finer than
typically preserved in fossil records.
Solutions:
While
some
exceptional
palaeontological
records
preserve
annual/seasonal signals most record centennial scale signals. This effect will be similar to
running a centennial run-average on the output of an ecological model capable of finer
resolution. Although this means that some fine resolution analysis are exceedingly difficult to
do with fossil data, what is lost in larger grain is made up for with a longer temporal series.
11
Alternatively it is possible to focus on those environments such as varved lake sediments,
which more often preserve high-resolution records.
Productivity, not standing crop
Challenges: Biological data are most commonly a census of organisms alive at a
particular time and place, while fossil assemblages are typically the sum of all the organisms
that died at a particular spot over a period of time whose duration depends on the type of
sedimentary deposit. Since organisms join a fossil assemblage after they die and are buried,
the fossil record is more analogous to productivity than standing crop.
Solutions: Although most ecological models focus on instantaneous abundance or
diversity dynamic, models may be adapted to provide relevant predictions by adjusting the
variables being tracked through time.
There is an unfortunate disjunction between organisms receiving the most
attention by biologists and those receiving the most attention by palaeobiologists, which make
broad scale comparisons of modern and fossil data often problematic. Increasing sampling
effort on current taxa that have good fossil records can solve this disjunction. Focusing on
long biodiversity time series is likely to contribute to increased awareness of the organisms
for which it is possible to recover the longest time series. Moreover, most ecological models
can work with the unequal sampling probabilities, productivity instead of standing crop, and
coarser temporal grain typical of fossil records. Palaeontological data will be most useful and
powerful when linked with well-defined questions in ecological systems with good fossil
records. Greater coordination between those studying the living and those studying the dead
has clear potential to reap significant rewards for both groups of investigators.
12
Figure S2 –Challenges and solutions in using fossil data to measure changing biodiversity
over time.
13
4) Using GAMs for analyzing biodiversity time series
Generalized additive models (GAMs) combine generalized linear models
with non-parametric regression models known as additive models. GAMs provide a
powefull tool to parsimoniously fit complex non-linear models. A GAM specifies a
distribution function for B(t)obs (normal, Poisson, binomial, etc.) and a link function g,
which relates μt = E(B(t)obs) to a vector of p predictors (covariates or environmental
variables)
(2)
( p)
{x (1)
t , x t ,..., x t } (such as climate variables, habitat information,
geographic information and/or their combinations) as:
(2)
(2)
(p)
.
g(mt ) = a + h(t) + f1(x (1)
t ) + f 2 (x t ) + ....+ f p (x t )
Each of h, f1, f2,…, fp can be modeled as parametric (including linear, quadratic or
polynomial models) or non-parametric (including regression splines or any smooth
functions). Variables known to contribute to measurement error, such as changes in
methods, may also be included to control for their effect.
Based on generalized linear model theory, the choice of link
function in Eq. (2) depends on the distribution of B(t)obs. For example, if the
distribution is Poisson (e.g. a model for species richness counts), then a log-link g(μt)
= log(μt) is used, with the Poisson regression model as a special case (42).
To assess a long-term linear increase or decrease in diversity over time (i.e a
global trend), a simple model h(t) = a + bt in Eq. (2) can be fitted with B(t)obs as the response
and a time variable as the predictor. The short-term fluctuations are considered noise. For
time series these noise terms are often modeled as an autoregressive process or a correlated
ARIMA series. Previous knowledge of the autocorrelation patterns of the time series helps
14
make an informed choice in the type of autocorrelation appropriate for the error term. Longterm nonlinear trends can also be considered by choosing h(t) as any type of nonlinear
function.

Models of spatio-temporal trends
The GAM framework for temporal trend (Eq. 2) can be extended to
spatio-temporal data. Assume B(t,s)obs is the diversity for time t and site s and that
(2)
( p)
there are K sites. Let μt,s = E(B(t,s)obs) and {x (1)
be the corresponding
t,s , x t,s , ..., x t,s }
predictor variables. If the K sites are categorized (e.g., as habitat types) and can be
assumed to have different site effects a1, a2, ..., aK , then a spatio-temporal GAM trend
with a specified distribution for B(t,s)obs can be expressed as
(3)
(2)
( p)
g(mt,s ) = as + h(t) + f1(x (1)
t,s ) + f 2 (x t,s ) + ....+ f p (x t,s )
As in Model (2), each of h, f1, f2,…, fp can be modeled as parametric or
nonparametric. If sites are associated with a continuous variable s (spatial gradient or
functions of coordinates, which can be univariate or multivariate), then we can
replace the term as + h(t) in (3) with a+h(t, s) where h(t, s) is a parametric or
nonparametric smooth function of t and s. Tensor product splines (a kind of multidimensional smoother) incorporating space-time “interaction” are usually constructed
to estimate smooth functions of several variables (42). As in temporal data,
autocorrelation can be incorporated by including additional predictors (neighboring
site information or previous observations) or modeling residuals. See (42, 43) for
details.
15
5) Supplementary figures
Figure S3 – This figure shows a standard decomposition of a time series into distinct components.
These data examine changes in species richness in Portal, Arizona as in Figure 2. Three separate
components are identified: seasonality, a consistent deviation due to month of the year (mid-top); a
trend, here locally smoothed, but linear trends can also be used (mid-bottom); and noise or remainder
(bottom). The sum of the three components gives the original time series (top). This example does not
further separate out nuisance variables/measurement error as the data do not support it. More
information on the methods in the documentation of the function stl() in R (44).
16
Supplementary Figures S4 and S5 are supplied to illustrate the point that the same
statistical tools can be used to analyze trait, genetic and taxonomic time series, once
appropriately standardized to minimize the effects of measurement error.
Figure S4 – Taxonomic diversity: The data are small rodents from Portal as in Figure 2 but for
all plots (including experimentally manipulated plots). A well-documented regime shift reveals the
near elimination of a species that was initially dominant as well as changes in species richness which
have been attributed to changes in precipitation patterns among other things (45, 46). We analyze this
dataset summed across all sites and treatments to illustrate different methods for analyzing temporal
changes in species richness. Top-left – a t-test comparing richness of groups years (plotted as a box
plot) with observed mean richness of 13.1 species in the earlier years and 15.9 in the later years is
significantly different at p<0.001. Top-right –a linear trend using OLS, and GLS using an AR1 model
with temporal autocorrelation of errors. The lines estimated by the two methods are very similar,
showing that richness increases by about 0.149 species per year in OLS vs. 0.156 species/year in GLS.
The r2 is 0.27 for the OLS. Bottom-left – A local regression with LOESS smoothing and a GAM spline
model of richness vs. time. Both suggest that the change in richness over time is non-linear and
steepest until about 1990. Bottom-right – Threshold regression to identify the number and location of
breakpoints. In this case BIC suggested that one threshold was optimal (although two thresholds had a
ΔBIC of 1.57). The plot shows the null model of no threshold, the preferred model of one threshold
break (occurring between 1987 and 1988 and involving a jump in richness from 13.4 to 16.3 species)
and the 2nd best model which adds a break between 1997 and 1998.
17
Figure S5- Genetic diversity: A time series of microbial OTU’s in a microbial bioreactor over a period of
24 weeks from (47) used here to illustrate different methods for analyzing temporal changes in genetic richness.
Panels illustrate the same analysis as in Figure 2 in the main text and Figure S4. Top-left – a t-test show the two
periods (with 16.01 and 13.01 OTU’s respectively) are significantly different at p<0.001. Top-right –a linear
trend using OLS, and GLS using an AR1 model with temporal autocorrelation of errors. The lines estimated by
the two methods are identical. The r2 is 0.25 for the OLS. Bottom-left – A local regression with LOESS
smoothing and a GAM spline model of richness vs. time. Both suggest that the change in richness over time is
non-linear. Bottom-right – Threshold regression to identify the number and location of breakpoints. In this case
BIC suggested that one threshold was optimal. The plot shows the null model of no threshold, the preferred
model of one threshold break and the 2nd best model with two breakpoints.
18
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