The Molecular Phylogenetic Signature of Clades in Decline

Abstract

Molecular phylogenies have been used to study the diversification of many clades. However, current methods for inferring diversification dynamics from molecular phylogenies ignore the possibility that clades may be decreasing in diversity, despite the fact that the fossil record shows this to be the case for many groups. Here we investigate the molecular phylogenetic signature of decreasing diversity using the most widely used statistic for inferring diversity dynamics from molecular phylogenies, the γ statistic. We show that if a clade is in decline its molecular phylogeny may show evidence of the decrease in the diversification rate that occurred between its diversification and decline phases. The ability to detect the change in diversification rate depends largely on the ratio of the speciation rates of the diversification and decline phases, the higher the ratio the stronger the signal of the change in diversification rate. Consequently, molecular phylogenies of clades in relative rapid decline do not carry a signature of their decreasing diversification. Further, the signal of the change in diversification rate, if present, declines as the diversity drop. Unfortunately, the molecular signature of clades in decline is the same as the signature produced by diversity dependent diversification. Given this similarity, and the inability of current methods to detect declining diversity, it is likely that some of the extant clades that show a decrease in diversification rate, currently interpreted as evidence for diversity dependent diversification, are in fact in decline. Unless methods can be developed that can discriminate between the different modes of diversification, specifically diversity dependent diversification and declining diversity, we will need the fossil record, or data from some other source, to distinguish between these very different diversity trajectories.

Full text

The Molecular Phylogenetic Signature of Clades in
Decline
Tiago B. Quental
1
*, Charles R. Marshall
2
1Departamento de Ecologia, Universidade Estadual de Sa
˜o Paulo (USP), Sa
˜o Paulo, Sa
˜o Paulo, Brazil, 2Museum of Paleontology and Department of Integrative Biology,
University of California, Berkeley, California, United States of America
Abstract
Molecular phylogenies have been used to study the diversification of many clades. However, current methods for inferring
diversification dynamics from molecular phylogenies ignore the possibility that clades may be decreasing in diversity,
despite the fact that the fossil record shows this to be the case for many groups. Here we investigate the molecular
phylogenetic signature of decreasing diversity using the most widely used statistic for inferring diversity dynamics from
molecular phylogenies, the cstatistic. We show that if a clade is in decline its molecular phylogeny may show evidence of
the decrease in the diversification rate that occurred between its diversification and decline phases. The ability to detect the
change in diversification rate depends largely on the ratio of the speciation rates of the diversification and decline phases,
the higher the ratio the stronger the signal of the change in diversification rate. Consequently, molecular phylogenies of
clades in relative rapid decline do not carry a signature of their decreasing diversification. Further, the signal of the change
in diversification rate, if present, declines as the diversity drop. Unfortunately, the molecular signature of clades in decline is
the same as the signature produced by diversity dependent diversification. Given this similarity, and the inability of current
methods to detect declining diversity, it is likely that some of the extant clades that show a decrease in diversification rate,
currently interpreted as evidence for diversity dependent diversification, are in fact in decline. Unless methods can be
developed that can discriminate between the different modes of diversification, specifically diversity dependent
diversification and declining diversity, we will need the fossil record, or data from some other source, to distinguish
between these very different diversity trajectories.
Citation: Quental TB, Marshall CR (2011) The Molecular Phylogenetic Signature of Clades in Decline. PLoS ONE 6(10): e25780. doi:10.1371/journal.pone.0025780
Editor: Carles Lalueza-Fox, Institut de Biologia Evolutiva - Universitat Pompeu Fabra, Spain
Received May 27, 2011; Accepted September 9, 2011; Published October 4, 2011
Copyright: ß2011 Quental, Marshall. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: University of California, Berkeley and Universidade de Sa
˜o Paulo, Brazil. The funders had no role in study design, data collection and analysis, decision
to publish, or preparation of the manuscript.
Competing Interests: The authors have declared that no competing interests exist.
* E-mail: tbquental@usp.br
Introduction
Understanding the controls of biodiversity is one of the main
goals of ecology and evolutionary biology. In recent decades this
endeavor has been revitalized by the use of molecular phylogenies
to study the diversification of many clades [1–6]. Key has been the
development of analytic methods for estimating speciation and
extinction rates from molecular phylogenies, despite the absence of
extinct species [7–13], and ways of investigating the tempo of
diversification [1,12,14]. This is especially important given that
many clades do not have a fossil record of sufficient quality (or any
fossil record at all for that matter) to enable detailed diversification
studies.
Currently, these tools have been used to distinguish between
clades that are diversifying exponentially from those that might be
undergoing diversity dependent diversification, and are at or
approaching an equilibrium carrying capacity [4,5,14,15]. In some
cases the relative contributions of changes in speciation and
extinction rate to overall diversification patterns have also been
estimated [4,14,15]. Even though caution is warranted – over-
dispersed sampling commonly used by biologists [1,16] and under-
parameterization of the DNA models [17] might mask true
diversification patterns – many phylogenies show a pattern of
decreasing diversification rates, which in turn are typically
attributed to diversity dependent diversification [4,5,15].
However, molecular phylogenies, by the virtue of only
considering extant species, carry the perceptual bias of increasing
diversity [13], and most biologist, perhaps for this reason, work
with the premise of expanding diversity with time, either
unbounded (exponential growth) or with some sort of diversity
saturation. Yet, the fossil record shows that many clades have been
in decline for a significant part of their history, and, of course,
many are now extinct [18–21]. Hence it is probable that many
extant clades are also currently in decline, and have thus
experienced negative diversification rates over their recent history.
Clades for which the fossil record shows this to be true include the
Cetacea [18], perissodactyl mammals, lungfish, brachiopods,
stenolaemate bryozoans, gymnosperms, sphenophytes (the horse
tails), etc [21].
Unfortunately, none of the current methods used for deducing
diversity trajectories from molecular phylogenies incorporate this
very real possibility of negative diversification rates [18]. Hence, if
we want to understand whether molecular phylogenies are able to
properly reveal a clade’s true diversity dynamics, we need to
understand what effect declining diversity will have on the
appearance of molecular phylogenies. Here we use computer
simulation to conduct this investigation, and explore the
robustness of some of the ecological interpretations currently
drawn from the analysis of molecular phylogenies, including
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testing the hypothesis that molecular phylogenies of clades in
decline look similar to those driven by diversity-dependent
diversification [18].
Methods
Simulation scenarios
The fossil record clearly shows that clades rise and fall in
diversity [19–21] so our main goal is to use computer simulation to
investigate the consequences of declining diversity on the
diversification signature of molecular phylogenies. The rise and
fall of clades could in theory happen in many different ways. For
example, a clade could spend most of its ‘‘life’’ either in the rise
phase, or in the decline phase, or have approximately symmetric
rise and decline phases. Additionally, during either the rise or
decline phases, the rates of extinction and speciation could be
constant (i.e., exponential growth or decline) or decrease (or
increase) with respect to time or diversity. There are obviously
even more complex dynamics, but our purpose is not to explore all
the possibilities, but to focus on a few simple scenarios to explore
the first order molecular signature of clades in decline.
The specific simulation approach used here was motivated by
importance of diversity dependent diversification reported in the
literature [4,5,15], and our suspicion that exponential decline
could leave a similar signature on molecular phylogenies [18].
Thus, we choose the simplest diversification scenario that would
allow us to: 1) broadly characterize the molecular signature of
clades in decline; 2) highlight potential shortcomings in current
interpretations of the diversity dependent dynamics; and, 3)
enhance our understanding of the extent to which molecular
phylogenies can, or cannot, be used to study the diversification
process. Thus, we simulated the diversity trajectories with an
expansion of diversity at a constant rate followed by declining
diversity, also at a constant rate (Figure 1).
For each set of simulations a total of 100 replicates were run, a
sample size large enough to capture the stochastic variation in the
models used. We used the R package TreeSim [22,23] for
simulating trees and the R packages Geiger [24] and paleoPhylo
[25] to manipulate and analyze the data. TreeSim enabled us to
run simulations that conditioned both on a specific final diversity
(10 lineages) and on a specific duration for the decline (10 million
years).
Metric for comparing simulated phylogenies
Several different tools are available for using molecular
phylogenies to infer diversity dynamics [1,7–9,12,14]. However,
it is becoming apparent that the methods developed for estimating
speciation and extinction rates are unable to estimate extinction
rates when clades are in decline [18], which in turn leads to
inaccurate estimates of speciation rates as well [18]. Given the
inability of these methods to handle clades in decline, we chose to
work with a simpler method, the cstatistic [1], introduced to
simply detect changes in the diversification rate. We note,
however, that while the cstatistic cannot be used to estimate
speciation and origination rates, per se, simulation studies show
that when the cstatistic indicates a change in the diversification
rate, it must have been driven in part by a decrease in the
speciation rate [15,18,26].
The cstatistic has some other advantages. First, it is easily
understood (negative values mean the nodes are concentrated deep
in the tree). Second, it is widely used, especially in the literature on
diversity-dependent diversification [1,4–6,18]. Third, by virtue of
being a summary statistic, it allows straightforward comparison
among trees (although see below for a discussion of its dependence
on tree size).
The cstatistic does have its limitations, primarily an appreciable
type II error rate. Specifically, it has low discriminating power
between exponential growth and the early phases of diversity
dependent diversification [27], or when the diversity dependent
diversification is driven by a low initial speciation rate relative to
the equilibrium extinction rate [26], or if clades are experiencing
species turnover at an equilibrium diversity [27]. Similarly, it has
low discriminating power when one is trying to distinguish
between subtly different models of diversification [14] (although
here we are not trying to distinguish between subtly different
models of diversification). Second, as a summary statistic, it may
not handle cases where the diversification dynamics change
appreciably through the history of a clade (for example, late bursts
of speciation can mask early bursts of diversification [28].
However, it has a negligible Type I error rate – an inference of
decreasing diversification rate appears to be a reliable inference.
Clades in decline
The rise and fall of simulated clades was modeled by
exponential growth followed by exponential decline. We chose
this way of simulating the waxing and waning of diversity because
preliminary data suggested that the resulting phylogenies would
give the appearance of diversity dependence, and so we wanted to
make sure that we did not confound the interpretation of our
results by having the initial diversification process be diversity
dependent. We chose a range of realistic speciation and extinction
rates [21], although the absolute values are not relevant if one is
interested in investigating the topologies of molecular phylogenies
under different diversification scenarios [26,27]. Figure 1A–C
show the rates used. Figure 1A (fast relative rate of decline)
illustrates a scenario where the loss of diversity is fast compared
with the rate of accumulating diversity. The scenarios shown in
Figure 1B (slow relative rate of decline) and 1C (slowest relative
rate of decline) represent scenarios where the rate of loss of
diversity is progressively slower than the initial rate of accumu-
lation of diversity. For ease of comparison, in all simulations the
decline phase was modeled with the same constant extinction and
speciation rates, and the extinction rate during the initial
diversification was also held constant. We also arbitrarily chose
to condition the decline phase to a time span of 10 million years
and a final diversity of 10 species, although the specific values
chosen do not affect our main conclusions (data not shown; see
also [26]). This conditioning meant that the average peak diversity
was the same among different scenarios, but that the average time
taken to reach that diversity varied among the three decline
scenarios (see histogram in upper left of panels A, B, and C in
Figure 1).
Analyzing the simulations – time traveling
To characterize the molecular signature of the declining
diversity as it unfolds, we calculated the cstatistic at different
points in time, a procedure we term ‘‘time traveling’’ (see Figure 2
for an outline of the procedure; see also [27]). The molecular
signature of the diversification phase of our simulations is the well-
understood constant birth-death process [7–9,11], and was not
examined further here. Figure 2A shows an exemplar phylogeny,
with extant and now-extinct taxa. The pink box highlights the
decline phase. We ‘‘time traveled’’ back in time every 1 million
years (represented by the dashed lines) from the present to the time
when diversity peak was reached, 10 million years before the
present. At each point in time we calculated the number of species
extant and the cstatistic for what would have been the molecular
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Figure 1. Cartoon of the different simulation scenarios employed in this paper. Panels A, B and C represent the clades in decline scenario,
where the number of species rise (grey portion) and decline (pink portion) exponentially. Panels D, E and F represent the ‘‘stasis’’ scenario, where the
number of species grows (grey portion) in a manner similar to the clades in decline scenario (A, B, and C) but then stays fixed thereafter (pink
portion). The only difference among the simulations within each scenario is the speciation rate in the rising phase. This meant that each scenario took
a different time to reach the peak diversity. The small histograms (top left of panels A, B and C) represent the time it took to reach the peak diversity
for each scenario. Each simulation was run so that the final diversity was 10 lineages and the decline phase was set to last 10 million years. Given our
simulation scheme, each group of simulations resulted in similar average peak diversities, with a mean of 76. lrepresents the speciation rate and m
represents the extinction rate.
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phylogeny (only the extant species) at that point in time (see
Figures 2B and 2C). In some cases the cstatistic changed so fast
that additional time points were analyzed to capture its behavior as
diversity was lost.
The reason time-traveling analysis is required is that in the
absence of a good fossil record it is virtually impossible to know,
even if you knew your clade was in decline, how long ago peak
diversity was reached, and what its peak diversity was [18,27].
Thus for a given phylogeny, we don’t typically know where it is in
its ‘‘ontogeny’’ – time traveling is needed if one wants to
investigate how well molecular phylogenies store a record of their
diversification history at different points in their history.
Results
The signature of declining diversity
Our simulations show that clades in the initial phases of their
decline typically result in molecular phylogenies with the most
negative cvalues (Figure 3A–C). The strength of the signal of the
decline depends, at least in part, on the magnitude of the ratio of
the rate of speciation in the diversification (waxing) phase to the
rate of speciation in the decline (waning) phase, lwax =lwane jj . The
higher the ratio (the lower the relative rate of decline), the more
negative the cstatistic (Figure 3A–C). When the ratio is too low
(i.e., when the relative rate of decline is high), for example when
lwax=lwane jj is 2.5 (Figures 1A and 3A), the null hypothesis of a
constant diversification rate will not usually be rejected (the
resulting cvalues are only rarely ,21.645). In this case the
exponential decline would most likely be interpreted as exponen-
tial diversification, as appears to have happened in a molecular
phylogenetic analysis of the diversity dynamics of the living
cetaceans [18,29], although as we note above, the cstatistic has
low statistical power – a cvalue.21.645 could also mean the
early phases of diversity dependent growth [27]; diversity
dependent growth with low a ratio between the initial speciation
rate and equilibrium extinction rate [26]; or, species turn-over at
equilibrium diversity [27]. Given that molecular phylogenies only
directly store information of cladogenic events it is perhaps not
surprising that if the change in speciation rate is not high enough
there will not be enough power to detect the change in the
diversification rate.
When lwax=lwane jj is high (the relative rate of decline is slow),
for example 20 (Figures 1B and 3B), in most cases the negative
diversification rate is reflected in significantly negative cvalues. In
addition, the higher the ratio, the more quickly in time the cvalues
become significantly negative, and the longer the cvalue stays
significantly negative (Figure 3). For example, in our simulations
when the ratio is low (Figure 3A) the most negative values of care
only seen several million years after the onset of the decline, while
at higher ratios (Figure 3B, C) the most negative cvalues are seen
within a million years of the onset of the decline, and cstays
significantly negative until the clade is nearly extinguished.
Meaning of the negative cvalues
Negative cvalues are generally taken to mean that there was a
decreasing diversification rate, and more specifically a decrease in
the speciation rate [4,26]. Our simulations are consistent with this
observation – in each simulation there was a large and
instantaneous drop in the diversification rate as we switched
from the waxing phase to the waning phase, which we achieved
largely through a decrease in the speciation rate (see Figure 1A–
C). Thus, while negative cvalues have been traditionally used as
evidence of diversity dependent diversification [4,5,14,15], in our
simulations there is no diversity dependence. Thus, these
simulations show that there is more than one way (in an
evolutionary/ecological sense) to generate negative cvalues (see
discussion below).
Figure 2. An exemplar simulation of a clade in decline. Rates of
increase and decline used correspond to the slow relative rate of
decline from Figure 1B. A) Exemplar phylogeny. The pink portion
represents the decline in diversity phase. The dashed lines represent
points in time where the cvalue and diversity of each phylogeny was
assessed. B) The number of extant species at each point in time for
decline phase. C) The cstatistic for what would have been the
molecular phylogeny at each point in time for the decline phase.
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Why does declining diversity lead to negative cvalues?
Our basic finding is that the cvalues drop as soon as the
diversification rate becomes negative, and that the cvalues can be
surprisingly negative. However, as the diversity continues to drop,
the cvalue rises again, and can ultimately become positive again
mimicking exponential growth (among other scenarios – see
above), when in fact the clade is in exponential decline. We wished
to understand why the cvalues become negative in the first place,
and why cthen becomes more positive as the clades continue to
decline in diversity, and so we ran additional simulations to
explore these questions.
Effects of under-sampling after exponential growth
Under-sampling species will generate a predictable bias in the
diversification signature of molecular phylogenies by artificially
increasing the relative importance of early splitting events [1,16],
which will lead to more negative cvalues. Following this
observation, we [18] suggested that extinction could be viewed
as evolutionary under-sampling (the failure to sample species due
to extinction, rather simply failing to collect them in the field),
which led us to posit that clades in decline might also have
negative cvalues.
To test this supposition, we ran a set of simulations with simple
exponential growth followed by different degrees of under-
sampling after a pre-assigned fixed diversity had been achieved.
For these simulations we used the same speciation and extinction
rates used in the initial diversification phase of our clades-in-
decline simulations (Figure 1). For the under-sampling simulations
the final diversity was set to 76 (the average peak diversity of the
clades-in-decline simulations) and 760 species to explore the effect
of the absolute number of species on the signal introduced by
under-sampling of the terminal branches. The simulated trees
were progressively under-sampled until only 10 species remained,
the final diversity in our clades-in-decline simulations. Terminals
were removed at random.
While under-sampling made the cstatistic more negative than
the fully sampled tree, conly became significantly negative for the
760 species scenario (Figure 4) – under sampling via extinction is
not the primary driver of the negative cvalues found in our
simulations of clades in decline, having only a minor effect on the
cvalue.
Clades in stasis – the effects of aging
Given that the loss of terminals, per se, is not responsible for the
strongly negative cvalues seen in our simulations of clades in
decline, what could be responsible? Our second guess was based
on the realization that one way to achieve strongly negative c
values is to simply extend the lengths of the terminal branches,
without adding or subtracting branches. Thus, we ran a set of
‘‘pure-aging’’ simulations, initiated with exponential growth with
the same rates of initial diversification used in the clades-in-decline
simulations (Figure 1A–C). Then, instead of switching to
exponential decline, the branch lengths were simply extended
for 10 million years (see Figure 1D–F). Two peak diversities were
used: 10 and 76 species. These values were chosen because in our
simulations of clades in decline the average peak diversity was 76
species (see above) and because we conditioned on a final diversity
of 10.
Figure 3. The cstatistic and number of species through time for all simulated trees for the decline phase (last 10 MY) for the clades
in decline simulations (Figure 1A–C). Note that while the diversity declines are effectively the same for all three simulations (bottom row), the
different diversification phases result in different cvalues (upper row). The green line represents the average cstatistic or average number of species.
The red line represents the 5% cutoff point for rejecting the null hypothesis of constant diversification (c=21.645).
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As expected, the clades in stasis produce highly negative c
values (the green lines in Figure 5A–C). As time passes the cvalue
continues to decline, and after an infinite amount of time the c
value will reach the maximum possible negative value given the
number of species in the phylogeny (the ‘‘star phylogeny’’ scenario
described by McPeek [6]; Figure 5D). For the simulations with
relatively rapid diversification phases (Figure 1B,C) after 10 Myr
the cvalues of our simulated trees under the stasis scenario are
indeed very close to this most negative potential value
(Figure 5B,C).
However, Figure 5 shows that the simulated data for clades in
decline never produce cvalues as negative as seen in the pure
aging scenarios. There are two reasons for this. The first and most
important is that the maximum cvalue is a function of the number
of terminal branches ([6]; Figure 5D). In the clades in decline
simulations, while on average the simulations start with 76 species,
that number steadily drops as the extinction proceeds to a final
diversity of 10 lineages. Thus we expect the cvalue to become less
negative as the extinction proceeds. However, if this were the only
factor at play, then the simulations of clades in decline should have
cvalues that lie between the pure-aging scenarios for a diversity of
76 terminals and 10 terminals. However, the cvalues continue to
rise beyond the values expected for a star phylogeny of 10 species
(see Figure 5). The reason is that in our simulations while there is a
net loss in diversity, we employed a positive speciation rate, and so
new nodes are also being added, making the cvalues more
Figure 4. The effects of under-sampling on the cstatistic. The phylogenies were generated using the same three exponential rates of increase
used in the clades-in-decline simulations (grey portion of Figures 1A–C). Two final diversities were used, 76 species (left column) and 760 species
(right column). The green line represents the average cstatistic. The red line represents the 5% cutoff point for rejecting the null hypothesis of
constant diversification (c=21.645). Under-sampling has a surprisingly small effect on the cvalue – the reason for the highly negative cvalues seen
in our simulations has little to do with extinction mimicking the effects of under-sampling.
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positive. The validity of this reasoning was confirmed when we re-
ran the simulations for the ‘‘stasis-after-fast-diversification’’
scenario (Figure 1E), with no speciation during the decline phase
– the cvalues lie, as expected, between the pure-aging scenarios
with the diversities of 76 terminals and 10 terminals (see
Supplemental Figure S1).
Discussion
The molecular signature of declining diversity
Our results clearly show that molecular phylogenies of clades
experiencing a decline in diversity will present a molecular
signature of the decreasing diversification rate, the switch from the
waxing phase to the waning phase. Consistent with previous
studies that show that changes in speciation rate are more
important than changes in extinction rate on the appearance of
molecular phylogenies [4,18], we find that the ratio of the rate of
initial speciation to the rate of speciation during the decline plays a
major role in determining whether the molecular phylogeny will
exhibit the signature of the switch in diversification rate (Figure 3).
As noted above, given that molecular phylogenies only directly
store information of (some) cladogenic events, and not the
extinction events, it is perhaps not surprising that if there is
insufficient change in the speciation rate between the waxing and
waning phases that there will not be enough power to detect the
changes in the diversification rates. There are other factors, such
as the time spent in each phase (which is determined by the
diversification rates in each phase) and the ratio of the extinction
rates in the two phases that influence the exact signature of
decreasing diversification as well. However, unlike diversity
dependent diversification where a simple metric (the LiMe ratio
of Quental and Marshall [26], the ratio of the initial speciation
Figure 5. A–C) The evolution of the cstatistic (green line) for all simulated trees in the pure aging scenario after initial exponential
growth. A) Stasis after a slow diversification. B) Stasis after a fast diversification. C) Stasis after an abrupt diversification. The asterisk at time= ‘
represents the most negative value possible for the cstatistic for a given phylogeny with 10 or 76 species, which corresponds to a phylogeny after an
infinitely long aging phase (i.e., a star phylogeny). The blue line represents the average cstatistic for the clades in decline simulations (data from Figure 3).
The red line represents the 5% cutoff point for rejecting the null hypothesis of constant diversification (c=21.645). D) The expected most negative value
for the cstatistic for given phylogeny as a function of the number of species (based on [6]); this represents a phylogeny with a star topology.
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rate to equilibrium extinct rate) controls the molecular signature of
the diversification scenario, we have been unable to find a simple
metric that fully captures the behavior of the cstatistic for clades in
decline.
Our initial hypothesis that the elevated extinction rate acts as
the evolutionary equivalent of under-sampling [18], while
technically true, is not the primary reason declining diversity
leads to strongly negative cvalues. The primary reason for the
strongly negative cvalues is the drop in the speciation rate that
results in the relative absence of new nodes, coupled with the
passage of time that extends all the branches that have so far
escaped extinction – once the diversification rate becomes negative
the aging of the surviving lineages results in the vast majority of
nodes becoming concentrated deeper and deeper in the tree. And
then, as the diversity continues to drop, the cvalues begin to rise,
largely due to the fact that cis a function of total diversity of the
phylogeny (Figure 5D), but also because the low levels of
speciation in the decline phase continue to add some young nodes
to the phylogeny. In some cases, the effect of decline-phase
speciation can cause the cvalues to become positive again,
especially when the decline has persisted for long enough that most
of the original speciation events have been lost to the molecular
phylogeny due to the ongoing extinctions.
The dependency of con the number of taxa, also noted by
McPeek [6], can be alleviated by normalizing all gamma values
by the maximum possible value for the number of taxa present,
but we do not pursue this further here. However, we note that
when using the cstatistic to test against the null hypothesis of a
constant birth-death process, the original intention of the c
statistic [1], the critical value for rejecting the null hypothesis is
not dependent on the number of species. The distribution of
gamma values will always be centered on zero and with a 5%
cutoff at 21.645 for a pure birth process regardless of the total
diversity (because exponential growth is self-similar), or shifted
towards more positive values when extinction is present, which
simply increases the type II error [1]. Thus, the dependency of c
on the number of taxa seen in our simulations does not
undermine its original use as a simple and effective way of
testing the null hypothesis of constant rates of diversification, but
it does indicate, as noted above, that it has lower power if used to
discriminate between a wide variety of diversification processes
(see also [18]).
The meaning of a decrease in diversification rate
Analyses of a large number of molecular phylogenies have
repeatedly suggested the prevalence of decreases in diversification
rates [4,5,14,15]. Apart from the potential artifacts – non-random
sampling [1,16] and under-parameterization of DNA models [17]
these results have been traditionally interpreted as evidence for
diversity dependent diversification [4,5,14,15]. Even though the
field has seen some promising methodological advances [14], we
suspect that this conclusion is premature given the limitation of the
methods used [18,27,30] and the fact that none of them
incorporate the possibility of declining diversity (but see [9]). In
this context, our results show that a clade in decline can produce a
molecular phylogeny with a signature of decrease in diversification
rate (when viewed through the cstatistic), but that the decrease in
diversification rate results from the switch from exponential
growth to exponential decline, rather than due to diversity
saturation, the standard interpretation.
Given our results, and the frequency with which declining
diversity is found in the fossil record [19–21], we suspect that
the high frequency of molecular phylogenies that show
decreasing diversification rates [5,6] is due to some of these
clades being in decline, rather than because they are all
undergoing diversity dependent diversification, a conclusion
supported by a recent analysis of a snake molecular phylogeny
[31]. In fact, the eroding effect of extinction, and the
observation that diversity-dependent diversification with low
initial speciation rates may frequently escape detection [4,27],
led Quental and Marshall [18] to suggest that there is in fact too
much evidence of diversity dependent diversification, and thus
that there are probably other mechanism(s) responsible for the
large number of phylogenies that show decreasing diversifica-
tion rates. Our results here confirm that suspicion, and provide
an alternative diversification model that will lead to molecular
phylogenies that might be interpreted as supporting diversity-
dependent diversification. Indeed, while the observation that a
molecular phylogeny has a decreasing rate of diversification,
once made, appears robust, it also appears that many different
diversification processes can produce very similar molecular
phylogenies, making it almost impossible to determine the true
process of diversification without the help of independent
evidence, such as the fossil record (see also [18]). Given current
methodological limitations and the absence of sufficient fossils
for many clades to make inferences about past diversity
trajectories, one of our highest priorities must be the
development of methods for discriminating between all the
possible mechanisms that can lead to decreasing rates of
diversification in molecular phylogenies, including the likelihood
of declining diversity.
Supporting Information
Figure S1 The cstatistic through time for a decline diversity
scenario without any speciation in the decline phase (last 10 MY).
Rates of speciation and extinction used here were chosen to
produce the same diversification rates in the rise (speciation =2.0;
extinction = 0.1; r = 1. 9) and declin e (speciation = 0. 0; extinc-
tion = 0.2; r = 20.2) phases as used in the scenario shown in
figure 1B. The blue line represents the average cstatistic. The red
line represents the 5% cutoff point for rejecting the null
hypothesis of constant diversification (c=21.645). The green
lines represent the average cstatistic for simulated trees in the
pure aging scenario after initial exponential growth for a peak
diversity of 10 and 76 species (same as in figure 5B). The asterisk
at time = ‘represents the most negative value possible for the c
statistic for a given phylogeny with 10 or 76 species, which
corresponds to a phylogeny after an infinitely long aging phase
(i.e., a star phylogeny). Note that the cstatistic through time for
the decline diversity scenario without any speciation in the
decline phase falls in between the average values for the pure
aging scenarios.
(TIF)
Acknowledgments
We are grateful to Nathalie Nagalingum, Helene Morlon and Santiago
Ramirez for discussion, Tanja Stadler for help with the R package
TreeSim, and the reviewers of this manuscript for their helpful evaluations.
Author Contributions
Conceived and designed the experiments: TBQ CRM. Performed the
experiments: TBQ. Analyzed the data: TBQ CRM. Wrote the paper:
TBQ CRM.
Molecular Signature of Clades in Decline
PLoS ONE | www.plosone.org 8 October 2011 | Volume 6 | Issue 10 | e25780

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PLoS ONE | www.plosone.org 9 October 2011 | Volume 6 | Issue 10 | e25780