The tree balance signature of mass extinction is erased by continued evolution in clades of constrained size with trait-dependent speciation

Abstract

The kind and duration of phylogenetic topological " signatures " left in the wake of macroevo-lutionary events remain poorly understood. To this end, we examined a broad range of simulated phylogenies generated using trait-biased, heritable speciation probabilities and mass extinction that could be either random or selective on trait value, but also using background extinction and diversity-dependence to constrain clade sizes. In keeping with prior results, random mass extinction increased imbalance of clades that recovered to pre-extinction size, but was a relatively weak effect. Mass extinction that was selective on trait values tended to produce clades of similar or greater balance compared to random extinction or controls. Allowing evolution to continue past the point of clade-size recovery resulted in erosion and eventual erasure of this signal, with all treatments converging on similar values of imbalance, except for very intense extinction regimes targeted at taxa with high speciation rates. Return to a more balanced state with extended post-extinction evolution was also associated with loss of the previous phylogenetic root in most treatments. These results further demonstrate that while a mass extinction event can produce a recognizable phyloge-netic signal, its effects become increasingly obscured the further an evolving clade gets from that event, with any sharp imbalance due to unrelated evolutionary factors.

Full text

RESEARCH ARTICLE
The tree balance signature of mass extinction
is erased by continued evolution in clades of
constrained size with trait-dependent
speciation
Guan-Dong Yang
1¤
, Paul-Michael Agapow
2
, Gabriel Yedid
1
*
1Department of Zoology, College of Life Sciences, Nanjing Agricultural University, Nanjing, Jiangsu, China,
2Data Science Institute, William Penney Laboratory, Imperial College, South Kensington, London, United
Kingdom
¤Current address: Department of Biostatistics and Bioinformatics, Rollins School of Public Health, Emory
University, Atlanta, Georgia, United States of America
*gyedid02@gmail.com
Abstract
The kind and duration of phylogenetic topological “signatures” left in the wake of macroevo-
lutionary events remain poorly understood. To this end, we examined a broad range of simu-
lated phylogenies generated using trait-biased, heritable speciation probabilities and mass
extinction that could be either random or selective on trait value, but also using background
extinction and diversity-dependence to constrain clade sizes. In keeping with prior results,
random mass extinction increased imbalance of clades that recovered to pre-extinction
size, but was a relatively weak effect. Mass extinction that was selective on trait values
tended to produce clades of similar or greater balance compared to random extinction or
controls. Allowing evolution to continue past the point of clade-size recovery resulted in ero-
sion and eventual erasure of this signal, with all treatments converging on similar values of
imbalance, except for very intense extinction regimes targeted at taxa with high speciation
rates. Return to a more balanced state with extended post-extinction evolution was also
associated with loss of the previous phylogenetic root in most treatments. These results fur-
ther demonstrate that while a mass extinction event can produce a recognizable phyloge-
netic signal, its effects become increasingly obscured the further an evolving clade gets
from that event, with any sharp imbalance due to unrelated evolutionary factors.
Introduction
How the interplay of speciation and extinction has shaped the Tree of Life remains one of the
chief unsolved mysteries of evolutionary biology. Processes of origination of new taxa are
countered by a steady, low rate of species deaths (background extinction), as well as infrequent
but highly destructive episodes of mass extinction. Ideally, tree shape should encode the
evolutionary history of the described clade. Metrics of phylogenetic tree shape such as tree
PLOS ONE | https://doi.org/10.1371/journal.pone.0179553 June 23, 2017 1 / 26
a1111111111
a1111111111
a1111111111
a1111111111
a1111111111
OPEN ACCESS
Citation: Yang G-D, Agapow P-M, Yedid G (2017)
The tree balance signature of mass extinction is
erased by continued evolution in clades of
constrained size with trait-dependent speciation.
PLoS ONE 12(6): e0179553. https://doi.org/
10.1371/journal.pone.0179553
Editor: Art F. Y. Poon, Western University,
CANADA
Received: December 31, 2016
Accepted: May 30, 2017
Published: June 23, 2017
Copyright: ©2017 Yang et al. 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.
Data Availability Statement: All data files are
available from Dryad (doi:10.5061/dryad.sm379).
Funding: This study was supported by research
grants #KYRC201301 from Chinese Ministry of
Education (http://www.moe.edu.cn) and
#680600529 from National Natural Science
Foundation of China (http://www.nsfc.gov.cn) to
GY. The funders had no role in study design, data
collection and analysis, decision to publish, or
preparation of the manuscript.

“stemminess” (the relative lengths of branches closer to vs. farther from the root) and balance
(the degree to which sibling lineages subtend the same number of descendant taxa), might cap-
ture lasting “signatures” of past macro-evolutionary processes that affect speciation and extinc-
tion [1–3]. However, enthusiasm for this approach should be tempered by the consideration
that the same evolutionary processes that produce particular tree shape characteristics can
later obscure and eventually erase them [4–6], particularly if the clade is prevented from grow-
ing indefinitely [7–11].
Balance has been one of the most studied tree shape metrics [12,13], usually quantified by a
balance index (examples in [14–17]), which depends only on tree topology. These indices have
been used as tools to both test stochastic models of evolution and departures from them [18–
24], and to assess the degree of imbalance of real phylogenies [9,10,19,25–28]. It has been
previously asserted that many extant clades (and perhaps the Tree of Life as a whole) are sub-
stantially more imbalanced than expected from simple-but-plausible models of diversification
[19,29–39]. Identifying possible causes of high or low clade diversity is therefore important, as
well as for the potential to affect other aspects of tree inference [40–42]. In particular, the idea
that major macroevolutionary events, especially mass extinctions, can produce long-lasting
changes in tree shape has been seductive. While such ideas are quite amenable to exploration
with modeling, they have proven difficult to validate due to the relative lack of paleontological
data sets with sufficiently high temporal resolution [2,43,44]. The most direct demonstration
(at least in modeling terms) was shown by Heard and Mooers [45], in the context of clades
where speciation rates were controlled by the value of a heritable quantitative trait. Mass
extinction that was random produced trees that were more imbalanced compared to their pre-
extinction state, as opposed to extinction that was selective on high or low values of the trait,
which resulted in more balanced trees vs. the pre-extinction state. This result has become
embedded in the literature, having already been used as a conceptual framework for at least
one examination using real paleontological data [2]. However, the extent to which a given
tree shape property (including balance) will preserve a record of a major evolutionary event
depends on a number of factors, including thoroughness of taxon sampling, external con-
straints on clade size, and how background processes of trait evolution, speciation and extinc-
tion have proceeded and affected the clade since the event.
The present study was motivated by previous work [6] highlighting several of the aforemen-
tioned issues. We investigated the effects of random and selective mass extinctions on tree
stemminess using digital evolution, an individual-based model system very different from the
branching process (or birth-death) models usually employed to investigate macroevolution-
related questions. With branching process models, the phylogeny itself, and parameters that
affect its properties, are the objects of concern. Digital evolution, by contrast, focuses on evolv-
ing populations of simulated individual organisms. Each system has particular strengths and
drawbacks. Branching process models still provide the most direct way of addressing issues
where detailed manipulation of tree properties is needed, but fail to address ecology and inter-
actions among individuals and clades. Digital evolution permits detailed manipulation of indi-
viduals, populations, and even ecology. However, the traits that influence probabilities of
speciation and extinction are not modeled explicitly as in a branching process and so cannot
be manipulated directly, rendering the phylogeny an epiphenomenon of the evolving popula-
tion. In our previous model [6], mass extinction could be triggered either by instantaneous
random culls of a population (pulse extinctions) or by massive environmental changes (press
extinctions), and to different degrees of intensity (strong vs. weak). We found that depending
on the metric used, different signatures of mass extinction might be retained over the short,
but not long term of the recovery, irrespective of treatment. That study did not include results
on tree balance: while investigated, the findings failed to confirm the results of Heard and
Erasure of tree balance signature by continued evolution
PLOS ONE | https://doi.org/10.1371/journal.pone.0179553 June 23, 2017 2 / 26
Competing interests: The authors have declared
that no competing interests exist.

Mooers [45]. Rather, as with one metric of tree stemminess, tree balance showed short-term,
but not long-term, differences between different mass extinction treatments (Fig 1), regardless
of type or intensity. In particular, tree balance was often indistinguishable from the expectation
of a Yule or Equal-Rate Markov (ERM) process (the most common null model of stochastic
evolutionary tree growth [32,46,47]), with all treatments eventually converging on ERM-like
values and only occasional occurrence of significantly imbalanced trees either before or after
mass extinction.
However, we do not believe these results show that digital evolution is inappropriate for
macroevolution-related questions. Rather, we think they highlight several shortcomings of the
Heard-Mooers model that limit considerably the scope of its application to evolving clades:
1. The simulation is size-based as opposed to time-based. Tree growth and trait evolution
occur only until the tree reaches a specified size, a mass extinction event occurs, and recov-
ery proceeds only until the tree has recovered its pre-extinction size. In real clades and
Fig 1. Change in tree balance at select time points after mass extinction episode in communities of avida digital organisms. Data
previously unpublished from Yedid et al. (2012). Mass extinction treatments were applied randomly and instantaneously (pulse) or by
massive environmental change over a period of time (press), at strong and weak intensities. The y-axis is Aldous’ β[β
A
, 16], a measure of
tree balance applicable to non-dichotomous trees; a Yule expectation is around zero, while more negative values indicate trees more
imbalanced than this expectation. Data points are averages of 100 replicates ±2 standard errors. Solid traces are maximum likelihood
estimates of β
A
, dashed traces are 95% confidence intervals around the calculated β
A
estimates. β
A
values (with confidence intervals) were
determined using a customized version of the maxlik.betasplit function in the R package apTreeshape (courtesy M. Blum).
https://doi.org/10.1371/journal.pone.0179553.g001
Erasure of tree balance signature by continued evolution
PLOS ONE | https://doi.org/10.1371/journal.pone.0179553 June 23, 2017 3 / 26

population-based simulations (such as digital evolution), trait evolution and turnover of
taxa can continue well after the tree has reached an equilibrium size (with or without mass
extinction) with additional consequences for tree shape descriptors [6,11,44].
2. The definition of recovery is not one often employed by paleontologists, who usually define
“recovery” through criteria completely external to clade size [48], such as morphospace
occupation [49,50], ecological breadth and niche occupancy [51], or levels of geochemical
proxies for productivity [52]; digital evolution has analogous criteria [6,53].
3. The Heard-Mooers model is “pure birth” both before and after the mass extinction event.
Background extinction is an omnipresent feature in both real clades [37] and in digital evo-
lution, where it results from limits on population size, ecology, resource availability, and
user-defined limits on the age of individual organisms.
4. Heard and Mooers [45] only considered what changes occurred in the tree relative to its
pre-extinction state. This is certainly relevant for real paleontological contexts, as pre- and
post-extinction states are the only information available. Given that their modeled traits
could conceivably continue to affect tree growth and shape dynamics, it is worth consider-
ing how evolution would have proceeded in the absence of the mass extinction event, and
how tree shape would have differed as a result.
In this paper, we revisit the question posed by Heard and Mooers [45], but incorporating
considerations from Yedid et al [6] that are also likely to have bearing on real-world situations.
Specifically, we investigate the effect of mass extinction and recovery on model clades that
have heritable rates of speciation and extinction, but where clade size is constrained by diver-
sity-dependence, and where the evolution of traits—and associated speciation rates—contin-
ues past the point of clade-size recovery. Since digital evolution has potential drawbacks
concerning manipulation of tree properties, we approach the problem more conventionally,
using branching process models.
Methods
Tree simulations
We simulated tree growth with a birth-death process incorporating speciation, extinction, and
constrained clade size using MeSA v.1.12 (www.agapow.net/software/mesa; [13,27].
Basic tree growth. Each tree grew from a root node object containing a single continu-
ous-valued trait with a starting value of 10.0. Evolutionary change in this trait was simulated in
a “punctuated and Brownian” manner: at speciation, one daughter taxon simply inherited the
parental trait value, while the other received a trait value taken from a normal distribution
around the parental value (standard deviation of 0.3 for the simulations described here). The
first speciation event was forced in order to ensure that trees did not die at the root node. Only
terminal taxa that had not yet gone extinct could speciate.
Speciation, extinction, and tree size constraint. A base speciation probability of 0.1 per
extant taxon per time unit was set as the default for all terminal taxa. Speciation probabilities
were influenced by a taxon’s trait value such that the smaller the value, the higher the probabil-
ity of speciation would be, using they the formula ax
b
+ c, where c is the base speciation proba-
bility, x is the taxon’s trait value, and a and b are constants. While such a model may not
describe the evolution of many biological traits very well, we chose it for ease of implementa-
tion within MeSA and because it conforms to the assumption of linear change along a tree
branch (compare [36]). In order to make the trait-based term the same order of magnitude as
the base speciation probability, we used a = 5 and b = -2; for example a trait value of 10.0
Erasure of tree balance signature by continued evolution
PLOS ONE | https://doi.org/10.1371/journal.pone.0179553 June 23, 2017 4 / 26

would produce a speciation probability of 0.15. Trait values were bounded by a lower limit of
2.0 and an upper limit of 15.0 in order to prevent speciation from becoming too infrequent
when the tree was not near its maximum size (see below). Background extinction occurred
with a constant probability (again, see [36]) of 0.05 per time unit for all terminal taxa; values
lower than this made speciation events and trait evolution too infrequent when combined with
diversity-dependence (see below).
In order to avoid unbounded tree growth, but also allow evolution to continue, speciation
probabilities were further modified in a diversity-dependent manner, as several previous stud-
ies have found evidence for diversity-dependence in speciation rates [9,11,54,55], although
this pattern may depend on ecological and geographic scale [56]. A logistic model was chosen
for the form of diversity-dependence, as this has been employed in previous modeling
approaches [5,36,56,57]. Since the trees in the motivating study [6] were fairly large (1200
tips), we set a maximum size (768) for the number of extant terminal taxa in the tree at any
given time. With diversity-dependence, speciation probabilities for all extant terminal taxa
would decline the closer the number of such taxa came to this limit. Thus, tree size would fluc-
tuate around a long-term equilibrium as there were times when the number of taxa lost to
background extinction would exceed those generated by new speciation events.
Mass extinction events. Mass extinction was implemented as an instantaneous “pulse”
event: at a particular point in the simulation, a user-specified fraction of terminal taxa were
culled from the tree. Four treatments were employed, three of which follow Heard and Mooers
[45]:
1. a control treatment, in which no mass extinction occurred and evolution simply continued
uninterrupted;
2. Random extinction (“Random”), where taxa were culled without regard to trait value or
phylogenetic position;
3. Selective-on-diversifiers (SOD), where those taxa with the lowest trait values, and conse-
quently highest speciation rates, were culled preferentially, starting from the lowest-valued
taxon present;
4. Selective-on-relicts (SOR), where those taxa with the highest trait values, and consequently
lowest speciation rates, were culled preferentially, starting from the highest-valued taxon
present.
Each of the mass extinction events occurred at intensities (denoted μ
M
) of 90% (0.9), 75%
(0.75), and 50% (0.5) of all extant taxa in the tree. Following mass extinction, trees recovered
and continued evolving according to the same rules that had been in effect prior to the extinc-
tion event.
We further define recovery from mass extinction to have two distinct phases: clade-size
recovery, (CSR), covering the time where the tree either recovers to its pre-extinction size or
settles on a new equilibrium value, and post-CSR, the time after CSR to the end of the simula-
tion. Clade-size recovery is not defined for the control treatment as there is no mass extinction
from which to recover.
Time course. Simulation time was measured in a series of arbitrarily-valued “ticks” (prob-
abilities for speciation, extinction, etc. are per tick). During each tick, the rules for trait evolu-
tion, speciation, and extinction were applied to the terminal taxa of the tree. Rule parameter
values could be changed at any given time, although in practice nearly every tick had the same
rules applied with the same parameter values. The only ticks for which rules differed were
the first, where the initial speciation was forced (see above), and the one in which the mass
Erasure of tree balance signature by continued evolution
PLOS ONE | https://doi.org/10.1371/journal.pone.0179553 June 23, 2017 5 / 26

extinction treatment was applied (t = 300). Every five ticks, the state of the tree (containing the
complete tree structure (both extinct and extant taxa) and trait values) was saved in a NEXUS-
format file. Tree states were saved both immediately before and after the mass extinction
event.
For each combination of mass extinction type (4 types including control), and mass extinc-
tion strength (3 levels), we ran a series of 100 replicates, for a total of 1200 runs. By default,
mass extinction events were set to occur at 300 ticks of the simulation, regardless of the state of
the tree. The total length of each simulation was 600 ticks.
Tree analysis
The NEXUS files produced by MeSA were manipulated and analyzed using functions in the
APE [58], phytools [59], and apTreeshape [23] packages in R. For each file, the entire tree
structure containing both extinct and extant taxa was extracted, and all extinct taxa removed,
leaving only extant taxa for a given time point [43,44,60]. For each tree in a time series, bal-
ance was then determined using the colless function from apTreeshape, which calculates the
well-known Colless index of imbalance ([15], here abbreviated I
C
) using the normalization of
Blum et al [21]. With this normalized metric, a Yule tree has an average score of zero; trees
more balanced than Yule have negative values, while those less balanced than Yule have posi-
tive values.
Determination of Yule tree balance limits. For assessing the degree of (im)balance of a
particular tree from our simulations, the limits for balance in Yule trees of sizes similar to
those we generated were assessed using functions from apTreeshape. The rtreeshape function
was used to generate 25,000 random Yule trees with 400, 500, 600, 700, and 800 tips (the maxi-
mum size that could be attained in the simulations was 768), and a distribution of balance
scores for each tree was determined with the colless function. For each of these distributions,
we determined the upper and lower quartiles, as well as the lower 2.5% and upper 97.5% tails.
We refer to the range of values bounded by the latter pair of values as the outer Yule zone;
trees with a balance score that fall within this zone are not significantly different from trees of
that size that can be generated by a Yule process. The upper and lower quartiles define the
boundaries of the inner Yule zone; trees with balance scores within these inner bounds are
around the average expectation for a Yule process. We make this distinction because we show
examples of both full trajectories of single trees, and samples of trees at particular times of
interest. While these boundaries make clear the degree of (im)balance of a single tree, a sample
of trees may contain a substantial number of non-Yule trees and yet be not significantly differ-
ent from Yule overall (i.e. the sample’s error bars overlap the boundaries).
Data partitioning and analysis
We first examined the average change in tree balance (as measured by I
C
) at pre-extinction,
CSR, and end-simulation time points, as well as the one-quarter, midpoint, and three-quarter
points between CSR and end-simulation (hereafter called the CSR/end-simulation interval
times). The pre-extinction and end-simulation points were fixed with respect to time (at
t = 300 and t = 600 respectively), while the other time points varied considerably among repli-
cates and among treatments. For this reason and for data visualization, the times at which
these events occurred were treated as categories rather than as a continuous variable. For
example, “CSR” denotes when a recovering tree either regained its pre-extinction size or con-
verged on a new equilibrium size, regardless of the actual time during the simulation that
event actually occurred. The actual values of these times were not used in statistical analysis
Erasure of tree balance signature by continued evolution
PLOS ONE | https://doi.org/10.1371/journal.pone.0179553 June 23, 2017 6 / 26

involving comparisons of balance, but were used for comparisons of times of the given events
(see below).
Generation of significant imbalance. For control treatments, where mass extinction did
not occur, we first noted in the data when the balance score “broke out” of the Yule zone (see
S1 Data). We define a Yule zone breakout as the first of a sequence of at least five consecutive
sampling times with a normalized I
C
greater than the Yule zone’s upper boundary. We define
the breakout in this way because empirically, a trajectory was unlikely to wander back within
the upper Yule zone boundary once it had escaped for at least 25 ticks (five recordings of five
ticks each).
Determination of root age. Following Yedid et al [6], we wished to determine the identity
and age of the root of the tree through time, in order to see if changes in (im)balance over time
were being measured according to a common reference point. As MeSA does not label internal
nodes in the NEXUS-format files it produces, we could not determine root identity directly.
We instead determined root age and identity indirectly using the branching.times function in
APE. This function returns the distances between every tip and internal node, the maximum
of which is the distance between the youngest extant tip and the root. The difference between
this maximum value and the current time of sampling yields the age of the root. Assuming
that the tree is lengthening at an approximately constant rate once it has attained an equilib-
rium size, we reason that as long as that difference remains approximately constant, the tree
maintains the same root. A change in this difference indicates loss of the previous root through
extinction of a basal clade and replacement by a younger, shallower root. Using this methodol-
ogy, we recorded for each simulation the times of root replacement and the inferred age of the
root at those times.
Among-extinction-treatment comparisons. For tree balance at CSR, the post-CSR inter-
val times, and end-simulation times, we first analyzed the treatments involving a combination
of extinction type and intensity (Random, SOD, SOR) with two-way ANOVA with Tukey-cor-
rected multiple comparison testing, in order to see whether there were any significant treat-
ment-by-intensity interactions. Different treatment intensities were treated as non-numerical
factors, and a family-wise confidence level of 95% was assumed for all comparisons. For com-
parisons of key times, in order to maintain a balanced experimental design, if balance did not
return to the Yule zone within the allotted time of the simulation, the time was considered the
maximum length of the simulation. These analyses were performed in R v.3.2.3 (R Core Team
2015) with the aov and TukeyHSD functions.
Comparisons to control and pre-treatment reference points. We were also interested in
whether the various extinction treatment outcomes differed systematically from the control
and pre-treatment reference points. To that end, we also performed Dunnett’s tests [61], using
either pre-treatment or the control treatment as the reference standard. For CSR trees, only
pre-treatment was used as the reference, whereas for end-simulation, comparisons were made
using both Control and pre-treatment as reference points. For comparisons involving pre-
treatment as the standard, all treatments including Control were considered as single factors.
These analyses were performed in R v.3.2.3 using the glht function (part of the multcomp
library), using the “Dunnett” option for contrasts.
As CSR was not defined for Control runs, we analyzed differences between treatments and
control as follows for CSR and post-CSR interval times. For each treatment replicate, we deter-
mined the time of CSR, and associated value of tree balance. We then determined tree balance
at the same time in the corresponding Control run. This way, each series of treatment values
could be compared to a different series of Control values through conventional two-tailed t-
tests. For simplicity of graphical display, we determined the approximate grand mean times
for CSR and post-CSR intervals across all treatments (about t = 335, 405, 470, and 535
Erasure of tree balance signature by continued evolution
PLOS ONE | https://doi.org/10.1371/journal.pone.0179553 June 23, 2017 7 / 26

respectively), and found the corresponding Control values for these times; the averages of
these latter values are what appear on Fig 2 as the Control points for those key times. All sum-
mary statistics are reported as means ±two standard errors.
Results
General trajectory of tree balance through time under trait-biased model
of diversification
Under the models of trait evolution and trait-biased speciation probabilities used here, evolu-
tionary change in tree balance followed a variable, yet still stereotyped trajectory (Fig 2,S1a
Fig). An exemplar Control replicate, in which the changing phylogeny is shown with changes
in the trait/rate values of taxa over time, is presented in Fig 3 (the associated distributions of
trait values are in S5 Fig). After an initial period of growth to equilibrium size and wandering
in the Yule zone (indicating trees whose degree of balance was still insignificantly different
Fig 2. Effect of mass extinction and recovery beyond clade-size recovery using Blum et al.’s [21] Yule-standardized version of
Colless’ [15] index of imbalance. CSR = clade-size recovery; CSR/END 1QTR, MID, 3QTR = CSR/end simulation first-quarter, midpoint
and three-quarter points; END SIM = end-simulation. RAND = random extinction; SOD = selective-on-diversifiers; SOR = selective-on-relicts.
0.5, 0.75, and 0.9 refer to extinction intensity. Short-dashed lines above and below the zero line indicate boundaries of inner Yule zone; long-
dashed lines indicate outer Yule zone boundaries. All data points are averages of 100 replicates ±2 standard errors. See Methods for
statistical analysis and special statistical treatment regarding Control.
https://doi.org/10.1371/journal.pone.0179553.g002
Erasure of tree balance signature by continued evolution
PLOS ONE | https://doi.org/10.1371/journal.pone.0179553 June 23, 2017 8 / 26

Fig 3. Exemplar phylogenetic trees showing change in balance and trait/rate values over time. Branch lengths are scaled in MeSA
absolute time. These trees correspond to the histograms of trait variance shown in S5 Fig. Tips are coloured according to trait value ranges
shown in colour scale at bottom.
a) t = 165, trait variance approximately 1, increasing
b) t = 320, trait variance at half-maximum, increasing
c) t = 400, maximum variance
d) t = 420, half-maximum, descending
e) t = 520, variance <1 but still strong imbalance, descending.
f) t = 600, variance at end-simulation
https://doi.org/10.1371/journal.pone.0179553.g003
Erasure of tree balance signature by continued evolution
PLOS ONE | https://doi.org/10.1371/journal.pone.0179553 June 23, 2017 9 / 26

from what a Yule process could generate), a second phase ensued whereby the degree of imbal-
ance—measured by strongly positive values of I
C
—increased sharply over Yule zone values
(the Yule zone breakout).
Breakout time varied substantially among replicates (mean breakout time 319 ±20 ticks for
all replicates, 373 ±14 for 66/100 replicates for breakout time 300 ticks), but it always
occurred. Once this escape from the Yule zone occurred, tree imbalance would rise to a peak
value. However, this heightened degree of imbalance was not sustainable indefinitely, as I
C
would then decline from this peak until back within Yule zone boundaries. Even so, only 46%
of replicates returned to the Yule zone within the initial allotted time of the simulation (mean
time of return 527 ±18 ticks). In S3 Data, we show in more detail how this trajectory results
from the erosion of trait/rate variance when limits on trait values are reached.
When the “breakout” behaviour happened after the fixed extinction time, the extinction
type and intensity could alter the time at which key events (Yule zone breakout, time of CSR,
Yule zone return time) occurred. The greatest differences were associated with the SOD treat-
ment, which substantially delayed breakout time and CSR compared to Random and SOR, but
accelerated Yule zone return time (more detailed explanations and statistics given in S1 Data).
Among-treatment differences in balance at key times in evolutionary
trajectory
We focused primarily on the differences in tree balance between treatments at CSR, post-CSR
interval times, and end-simulation.
Significant differences in balance among treatment/intensity combinations were found at
all key times. Initial inspection of the data suggested three groups of CSR outcomes based on
treatment type (Fig 2, “CSR”), with Random producing the most imbalanced trees, SOD the
most balanced trees, and SOR intermediate between the other two treatment groups. Random
extinction always differed significantly from SOD and from SOR at μ
M
>= 0.75 (Table 1).
Although the greatest imbalancing effect was produced by Random at μ
M
= 0.75 (Table 2, con-
sistent with [45]), within treatment types, no intensity differed significantly from any other,
and model reduction indicated non-significance of the interaction term. Random did not dif-
fer significantly from corresponding Controls at any intensity, while SOR differed from Con-
trol only at the higher intensities. Only SOD differed systematically from Control (Fig 2,
Table 2). We then compared balance after the mass extinction treatments to the pre-extinction
state (the comparison standard); only SOD differed significantly at all intensities, Random at
the two higher intensities, and SOR only at the highest intensity (Table 3).
Between treatment differences decayed progressively over the course of the post-CSR
period. Despite the more mildly balancing effect of SOR, imbalance continued to increase for
both Random and SOR trees at all intensities up to the CSR/end first-quarter point, though
SOR at μ
M
= 0.9 still remained significantly less imbalanced than Random (Fig 2, Table D in
S2 Data) and corresponding Control (Fig 2; Table E in S2 Data). SOD trees remained much
more balanced, further magnifying the difference between SOD and other treatments (Fig 2;
Table D in S2 Data). By CSR/end midpoint, Random and SOR no longer differed significantly
from each other at any intensity (Fig 2,Table 4), and this persisted to the end of the simulation
(Fig 2; Table G in S2 Data). All SOD trees remained more balanced than the other treatments,
with even SOD_0.5 still distinguishable from the other treatments (Fig 2, time “CSR/END
MID”; Table 4), though even this difference began to fade by the CSR/end three quarter point
(Fig 2; Table G in S2 Data).
For special consideration of the Control relative to treatments at CSR and post-CSR inter-
vals (see Methods), Random differed significantly from corresponding Controls only at a few
Erasure of tree balance signature by continued evolution
PLOS ONE | https://doi.org/10.1371/journal.pone.0179553 June 23, 2017 10 / 26

points, and then only weakly (Tables 2and 5; Table E and Table G in S2 Data, “Random”
entries). CSR values for SOR differed from corresponding Controls only at μ
M
0.75, while
SOD differed significantly at all intensities. At post-CSR interval points, both Random and
SOR tended to be less imbalanced than corresponding Controls, although any statistically sig-
nificant differences were weak. Only SOD differed strongly and consistently from correspond-
ing Control values at CSR and later points (Fig 2, Tables 2and 5; Table E and Table G in S2
Data).
By end-simulation, most between-treatment differences that had existed previously had
been eroded or disappeared completely, having declined from previous higher imbalance
values (Fig 2,Table 6). The only significant differences all involved SOD at μ
M
= 0.9, which
Table 1. Mean differences in balance between mass extinction treatments at point of clade-size recovery.
RANDOM SOD SOR
0.5 0.75 0.9 0.5 0.75 0.9 0.5 0.75 0.9
RANDOM 0.5 - - - - - 0.317 0.08 2.35**** -2.66**** -2.95**** 1.01 -1.42*-2.22****
0.75 - - - - - -0.24 2.67**** 2.98**** -3.27**** 1.33*1.74*** -2.54****
0.9 - - - - - 2.43**** 2.74**** 3.03**** 1.093 1.5** 2.23****
SOD 0.5 - - - - - -0.312 -0.60 -1.34*0.93 0.13
0.75 - - - - - -0.29 -1.65** -1.24 0.44
0.9 - - - - - -1.94*** -1.53** -0.73
SOR 0.5 - - - - - -0.407 -1.21
0.75 - - - - - -0.8
0.9 - - - - -
See Methods for statistical analysis. Significance levels:
no asterisk, difference not significant;
‘*’, 0.01 p<0.05;
‘**’ 0.005 p<0.01;
‘***’ 0.0001 p<0.005;
‘****’ p <0.0001.
https://doi.org/10.1371/journal.pone.0179553.t001
Table 2. Comparison of treatments vs. corresponding control at CSR.
TREATMENT INTENSITY AVERAGE AT CSR AVERAGE FOR CORRESPONDING CONTROL
Random 0.5 3.62 3.24
0.75 3.93 3.34
0.9 3.7 3.44
SOR 0.5 2.60 2.97
0.75 2.19 2.96*
0.9 1.4 3.01****
SOD 0.5 1.26 3.75****
0.75 0.95 3.8****
0.9 0.66 4.44****
See Methods for statistical analysis. Significance levels:
no asterisk, difference not significant;
‘*’, 0.01 p<0.05;
‘**’ 0.005 p<0.01;
‘***’ 0.0001 p<0.005;
‘****’ p <0.0001.
https://doi.org/10.1371/journal.pone.0179553.t002
Erasure of tree balance signature by continued evolution
PLOS ONE | https://doi.org/10.1371/journal.pone.0179553 June 23, 2017 11 / 26

remained substantially more balanced than all other treatment/intensity combinations. Most
of the other treatments had, on average, converged on similar values of I
C
. The most imbal-
anced trees were now on average those of SOD at μ
M
= 0.5, although the differences from
other treatments were not significant. When comparing against end-simulation Control val-
ues, only SOD at μ
M
= 0.9 differed significantly from Control (Table 7).
Change in phylogenetic root
The extinction regimes differed in their effect on the age of the phylogenetic root. Just prior to
treatment, 95/100 replicates had a very deep phylogenetic root, within the first 30 “ticks” of the
Table 3. Dunnett contrasts between tree balance at CSR for each extinction treatment and immediate
pre-treatment as a reference standard.
TREATMENT INTENSITY Mean difference from pre-treatment (std. err. = 0.423)
Random 0.5 1.07
0.75 1.38**
0.9 1.15*
SOD 0.5 -1.28*
0.75 -1.6**
0.9 -1.89***
SOR 0.5 0.055
0.75 -0.35
0.9 -1.15*
See Methods for statistical analysis. Significance levels:
no asterisk, difference not significant;
‘*’, 0.01 p<0.05;
‘**’ 0.005 p<0.01;
‘***’ 0.0001 p<0.005;
‘****’ p <0.0001.
https://doi.org/10.1371/journal.pone.0179553.t003
Table 4. Mean differences in balance between mass extinction treatments at CSR/END midpoint.
RANDOM SOD SOR
0.5 0.75 0.9 0.5 0.75 0.9 0.5 0.75 0.9
RANDOM 0.5 - - - - -0.47 0.125 -4.11**** -5.03**** -5.33**** 0.022 -0.17 -0.74
0.75 - - - - - 0.56 3.64**** -4.56**** -4.87**** -0.49 0.3 -0.272
0.9 - - - - - 4.237**** 5.155**** -5.46**** 0.103 0.296 -0.867
SOD 0.5 - - - - - -0.92 -1.22 4.13**** 3.94**** 3.37****
0.75 - - - - - -0.305 -5.1**** 4.86**** 4.289****
0.9 - - - - - -5.4**** -5.2**** 4.59****
SOR 0.5 - - - - - -0.192 -0.764
0.75 - - - - - -0.571
0.9 - - - - -
See Methods for statistical analysis. Significance levels:
no asterisk, difference not significant;
‘*’, 0.01 p<0.05;
‘**’ 0.005 p<0.01;
‘***’ 0.0001 p<0.005;
‘****’ p <0.0001.
https://doi.org/10.1371/journal.pone.0179553.t004
Erasure of tree balance signature by continued evolution
PLOS ONE | https://doi.org/10.1371/journal.pone.0179553 June 23, 2017 12 / 26

simulation, with the remainder all originating well before the midpoint of the simulation (Fig
4a, dark blue bar series). In Control replicates, root replacement was quite common as the sim-
ulation progressed (Fig 4a). By end-simulation, the majority of replicates (85%) featured root
replacements after equilibrium (mean 2.16 ±0.312), meaning these simulations ended with a
tree whose root was often substantially younger than when equilibrium size was first attained,
or even the midpoint of the simulation (Fig 4a, yellow bar series). Most replacements occurred
after peak trait variance and peak imbalance were attained, and were thus associated with
declining imbalance and return of the tree to a Yule-like state, although not every decrease in
imbalance was associated with root loss (S3a–S3c Fig).
Table 5. Comparison between treatments vs. corresponding Control values at CSR/END midpoint.
TREATMENT INTENSITY AVERAGE AT CSR AVERAGE FOR CORRESPONDING CONTROL
Random 0.5 5.86 6.50
0.75 5.39 6.27*
0.9 5.32 6.37*
SOR 0.5 5.63 6.42
0.75 5.57 6.39
0.9 5.05 6.42*
SOD 0.5 1.64 6.16****
0.75 0.81 6.33****
0.9 0.56 5.88****
See Methods for statistical analysis. Significance levels:
no asterisk, difference not significant;
‘*’, 0.01 p<0.05;
‘**’ 0.005 p<0.01;
‘***’ 0.0001 p<0.005;
‘****’ p <0.0001.
https://doi.org/10.1371/journal.pone.0179553.t005
Table 6. Mean differences in balance between mass extinction treatments at end of simulation.
RANDOM SOD SOR
0.5 0.75 0.9 0.5 0.75 0.9 0.5 0.75 0.9
RANDOM 0.5 - - - - - -0.27 -0.38 -0.527 0.01 -1.573*** -0.028 -0.212 -0.464
0.75 - - - - - -0.11 -0.798 -0.282 -1.301*-0.3 -0.059 -0.193
0.9 - - - - - -0.904 -0.388 1.195*-0.406 -0.165 0.087
SOD 0.5 - - - - - -0.516 -2.1**** 0.498 -0.739 -0.991
0.75 - - - - - -1.583*** -0.018 0.223 -0.475
0.9 - - - - - -1.6** -1.36*-1.108
SOR 0.5 - - - - - -0.241 -0.493
0.75 - - - - - -0.252
0.9 - - - - -
See Methods for statistical analysis. Significance levels:
no asterisk, difference not significant;
‘*’, 0.01 p<0.05;
‘**’ 0.005 p<0.01;
‘***’ 0.0001 p<0.005;
‘****’ p <0.0001.
https://doi.org/10.1371/journal.pone.0179553.t006
Erasure of tree balance signature by continued evolution
PLOS ONE | https://doi.org/10.1371/journal.pone.0179553 June 23, 2017 13 / 26

In extinction treatment replicates, root loss depended on both treatment type and inten-
sity. Random extinction at μ
M
= 0.75 and 0.5 (Fig 4b,S7 Fig) generally did not replace the
pre-extinction root, though mass extinction-associated root loss was more common at μ
M
=
0.9 (S8 Fig). Further loss of deep history through background extinction produced a distribu-
tion of root ages resembling that for Control by end-simulation, though with a somewhat
higher concentration of roots in the 300–330 range (Fig 4b, yellow bar series). Treatment-
associated root loss was most common with SOR, which substantially reduced the number of
replicates with a very deep root and spread out the distribution of root ages, particularly at
high intensity (Fig 4d, compare dark blue and light blue bar series; S7c and S8c Figs). In
stark contrast, SOD resulted in trees where the pre-treatment root was generally preserved
over the post-extinction duration of the simulation (Fig 4c), though this effect was weakest at
μ
M
= 0.5, where the end-simulation distribution of root ages included 5 replicates with root
ages 300 ticks (S7c Fig). At μ
M
= 0.75 and μ
M
= 0.9 respectively, 84/100 and 87/100 repli-
cates retained the pre-extinction root by end-simulation and no replicate had a root of
age 300. Thus, the tendency towards more balanced trees seen in SOD was connected with
longer retention of deep history.
Discussion
In this study, we used branching process models as implemented in MeSA to examine effects
of three types of mass extinction (Random, SOD, and SOR) and recovery on tree balance,
when speciation probabilities are trait-biased, heritable, and evolve in a random walk, tree size
is constrained by background extinction and diversity-dependence, and recovery after mass
extinction continues past the point of clade-size recovery. We showed that:
1. Tree balance followed a trajectory of initially wandering within a “Yule zone”, followed by a
period of heightened imbalance strongly different from a Yule expectation, and eventual
relaxation to Yule-like values.
2. Consistent with previous results, Random mass extinction generally produced more
imbalanced trees after extinction and clade-size recovery (CSR) than did extinction that
Table 7. Dunnett contrasts between tree balance at end-simulation for each extinction treatment,
using end-control as a reference standard.
TREATMENT INTENSITY End-simulation (std. err = 0.378)
Random 0.5 0.234
0.75 -0.0374
0.9 -0.143
SOR 0.5 0.263
0.75 0.0217
0.9 -0.231
SOD 0.5 0.761
0.75 0.244
0.9 -1.339**
See Methods for statistical analysis. Significance levels:
no asterisk, difference not significant;
‘*’, 0.01 p<0.05;
‘**’ 0.005 p<0.01;
‘***’ 0.0001 p<0.005;
‘****’ p <0.0001.
https://doi.org/10.1371/journal.pone.0179553.t007
Erasure of tree balance signature by continued evolution
PLOS ONE | https://doi.org/10.1371/journal.pone.0179553 June 23, 2017 14 / 26

was selective on trait values, but did not differ significantly from corresponding Control
trees. SOD extinction had a stronger tendency to result in more obviously balanced CSR
trees that were generally did not differ from a Yule expectation. For SOR, stronger inten-
sities resulted in more obviously balanced CSR trees, albeit with a weaker effect than
SOD. These effects were due mostly to extinction type, rather than type-by-intensity
interaction.
Fig 4. Shift in the distribution of phylogenetic root ages for a) control, b) Random at μ
M
= 0.75, c) selective-on-diversifiers at μ
M
=
0.75, d) selective-on-relicts at μ
M
= 0.75. Coloured bars show number of replicates (vertical axis) with phylogenetic roots whose time of
origin falls into the specified root age bins (horizontal axis). Distributions of root ages were recorded at the time points shown along the ‘‘time
after extinction” axis (depth axis).
https://doi.org/10.1371/journal.pone.0179553.g004
Erasure of tree balance signature by continued evolution
PLOS ONE | https://doi.org/10.1371/journal.pone.0179553 June 23, 2017 15 / 26

3. Allowing evolution to continue past the point of CSR eroded the effects of the CSR process,
as Random and SOR treatments tended towards degrees of imbalance greater than that pro-
duced by mass extinction/CSR, and so would SOD after a longer time.
4. By the end of the simulation, even the additional effect of heightened imbalance had been
eroded away, with most replicates converging on similar values of tree balance regardless of
treatment type or intensity. Only extinction that was intensively targeted at taxa with high
speciation probabilities differed from all other treatments, with most replicates remaining
within the “Yule zone”.
5. Return from heightened imbalance to Yule-like values was associated with loss of deep his-
tory, often with several replacements of the phylogenetic root before the end of the simula-
tion. Control and Random treatments behaved similarly; SOR showed the greatest amount
of treatment-associated root replacement, while SOD contrasted strongly with the other
treatments in showing longer retention of the pre-treatment root.
Different extinction types display qualitatively different clade-size
recovery behaviours
Our clade-size recovery results largely agree with those of Heard & Mooers [45], and the
underlying causes are the same. SOD extinction removes the most actively diversifying taxa,
leaving survivors with lower, more homogeneous, speciation probabilities. As traits can evolve
in both directions away from the starting value, this pruning may leave a set of survivors with
lower average speciation probability than the seed taxon’s. This was also shown by the notably
longer CSR time for trees subjected to SOD (Table B in S1 Data). SOR leaves survivors with
higher average speciation probabilities and correspondingly more rapid CSR (Table B in S1
Data). As SOR targets taxa in already-depauperate clades, post-extinction and CSR trees are
relatively more imbalanced than for SOD, diluting the effect of trait/rate variance reduction.
This tendency is only exacerbated upon (temporary) relief of diversity-dependent constraints,
since remaining slowly-diversifying taxa are left behind by more rapid diversifiers—an effect
that also occurs with Random extinction. This can be seen by the lower average CSR time of
SOR compared to other treatments (Table B in S1 Data), despite the overall tendency being
towards greater balance at increasing intensity (Fig 2). In contrast to trait-selective extinction,
random mass extinction removes taxa irrespective of trait value or clade membership. Since
Random tends to preserve more of the distribution of trait variance, the resulting imbalance is
more pronounced than for SOR. When compared to Control, Random mass extinction only
slightly exacerbated a tendency towards increased imbalance (Fig 2,Table 3), that was actually
reversed by the selective extinction treatments (Table 3).
Selective-on-diversifiers mass extinction leaves the most enduring
signature
Our interest here goes beyond recapitulating previous results, as we wished to determine
whether there is an enduring signature of extinction in tree balance when evolution continues
past the point of CSR, similar to previous observations using one metric for tree stemminess
[6]. Our results show that only SOD at high intensity consistently and reliably produced such
a signature. As stated above, removal of highly-diversifying taxa may often leave speciation
probabilities lower than the original seed taxon’s. Slowly-diversifying survivors must then
first evolve past these reduced speciation probabilities, and regenerate sufficient trait variance
in order to proceed along the breakout/return trajectory, leading to the prolonged post-
Erasure of tree balance signature by continued evolution
PLOS ONE | https://doi.org/10.1371/journal.pone.0179553 June 23, 2017 16 / 26

extinction meandering within the Yule zone and greatly delayed breakouts we observed
(Table A in S1 Data). SOD had the shortest average Yule zone return time (Table C in S1
Data) because the return is in many cases associated directly with the mass extinction itself. By
contrast, Random and SOR extinctions may either advance or retard progress along the evolu-
tionary trajectory. The overall shorter return times (Table C in S1 Data) and lower heightened
imbalance (Fig 2,Table 4; Table E and Table G in S2 Data) for SOR (as compared to Control
and Random) indicate that particularly at high intensity this treatment advances the trajectory
past the imbalance that would otherwise be attained, moving it more quickly to a phase of
greater homogeneity of trait values and speciation probabilities (albeit higher than previously),
accelerating decline of imbalance and return to Yule-like values. For SOD, on the other hand,
imbalance was actually increasing by the end of the simulation after remaining depressed for
much of the post-CSR period, meaning many replicates had not yet reached their “true” peak
imbalance.
Continued evolution of traits and rates eventually erases the effects of
different extinction types
The imbalancing effect of Random mass extinction we obtained was not enduring and not
very strong considering the corresponding Control behaviour. Neither was the weaker balanc-
ing effect of SOR, and even the strong result for SOD would eventually show the same kinds of
evolutionary dynamics. Indeed, the effects of mass extinction and CSR were rather weak com-
pared to the heightened imbalance resulting from the breakout/decline behaviour. In our
model, the rules of trait and rate evolution continue unchanged following mass extinction,
which also temporarily relieves diversity-dependent constraints. Thus, the same phenomena
that occur in Control replicates (addressed in detail in S3 Data) will eventually occur in those
subjected to a mass extinction treatment; Random mass extinction disrupts those phenomena
the least. The particulars will of course differ, but the long-term qualitative result will eventu-
ally be the same as Control (also see Fig 4). The factors leading to heightened imbalance and
decline from it are then not consequences of mass extinction/CSR, but instead contribute to
erasing the effects of the former, especially for selective extinction. Absent changes to key rules
and parameters, the inevitable outcome of these processes is a return to a tree with increasingly
homogenous trait/rate variance, finally erasing mass extinction/CSR-produced differences
between different treatment types (Fig 2; contrast Tables 1&2vs. Tables 6&7). Our results
show that for Random, SOR, and SOD (at intermediate extinction intensity) the latter effect
happens even before all replicates have completely returned to the Yule zone. Despite similar
I
C
values, the composition of taxa in the end-simulation trees differs substantially between
SOD and the other treatments,
Considering history reduces comparability of topology-based results
Although our major consideration here is of tree balance, we also considered the effects on
evolutionary history using root age as a proxy [6]. Our results show that the different treat-
ments had different short-term effects on the distribution of root ages, and that this distribu-
tion changes considerably over the course of a simulation even without mass extinction (Fig 4,
S7 and S8 Figs). In many cases, tree balance is increasingly measured from different temporal
reference points as a simulation progresses for Control, Random, and especially for SOR at μ
M
0.75. Random mass extinction had the smallest effect on root loss even at μ
M
= 0.9, consis-
tent with previous findings [62], but, just as with tree balance, post-extinction effects were
not enduring. By contrast, SOD had a longer-lasting root-preserving effect, though even
this would eventually erode once highly-diversifying taxa were regenerated. If heightened
Erasure of tree balance signature by continued evolution
PLOS ONE | https://doi.org/10.1371/journal.pone.0179553 June 23, 2017 17 / 26

imbalance is due primarily to the retention of basal clades, and the reference point for measur-
ing balance changes with the loss of those clades (Fig 3), the resulting tree will be phylogeneti-
cally younger and shorter in root-tip length. In our simulations, SOD generally resulted in
more balanced trees with older roots, and longer retention of a common reference point for
measuring balance over time. SOR tended more weakly towards more balanced trees, but
these were often measured from the standpoint of a different, younger root (Fig 4,S7 and S8
Figs). Considering history and balance together, we question whether post-extinction trees are
comparable to pre-treatment trees if they have lost the original reference point for balance and
only more derived taxa remain [2,50]. In such cases, then perhaps the question of the effect of
mass extinction on tree balance is moot.
Mass extinctions can contribute to, but not maintain, increased
imbalance
Our results extend those of Heard and Mooers [45], examining the long-term consequences of
recovery from random vs. selective mass extinctions when speciation probability is determined
by a heritable trait. Our extension goes beyond re-growth of the tree to its previous size,
using background extinction and diversity-dependence to produce turnover of taxa without
unbounded increase in tree size and allow evolution to continue past clade-size recovery. With
these additional considerations, we believe the role of mass extinction in shaping patterns of
tree balance should be re-evaluated.
Although our simulations differ in some details from Heard and Mooers [45], we largely
recapitulated their principal finding that random mass extinction increases tree imbalance.
However, going beyond clade-size recovery shows that this is not an enduring effect if:
1. how traits and rates evolve remain unchanged after the mass extinction, which may be
affected by altered conditions in the post-extinction world; compare the more rapid recov-
ery from the Cretaceous-Paleogene extinction [52,63–68] with the much slower one for the
Permo-Triassic extinction [51,69–74] (but see [75] for an interesting exception);
2. clade dynamics show diversity-dependence [4,9,54,76–78]
3. trait values (and speciation rates dependent on them) are subject to limits—constraints that
may be genetic [79], functional [80,81] or ecological [82,83] that restrict the range of feasi-
ble phenotypes;
4. there is no mechanism for isolating slowly-diversifying clades from very rapidly-diversify-
ing ones. It is unclear whether such mechanisms in fact exist; although there are some pos-
sible examples within Primates [24,84] and Western Hemisphere marsupials (the “possum
effect” [24]), these are uncertain due to undersampling and there is no indication of this
being a widespread phenomenon.
We have shown that if these conditions prevail, all treatments will eventually converge on
trees with similar, Yule-like degrees of tree balance, and that strong selective-on-diversifiers
extinction delays this outcome the longest. Further, random extinction only seems to add
slightly to an already-existing tendency, and post-extinction tree balance often ends up being
measured from different phylogenetic reference points. Thus, we believe the extent to which
random mass extinctions may contribute to building the skewed pattern of diversity character-
istic of many extant phylogenies (see Discussion in [45]) needs to be reconsidered.
First, we must define what it means for a clade to be “sharply imbalanced”. We can use the
boundaries of the Yule zone as a reference, as a Yule process itself can generate a wide diversity
of tree shapes, and trees near its upper edge can be considered already moderately imbalanced.
Erasure of tree balance signature by continued evolution
PLOS ONE | https://doi.org/10.1371/journal.pone.0179553 June 23, 2017 18 / 26

Indeed, it can be very difficult to show that the tree of an evolving clade departs from a Yule
expectation, even for paleontological time series lasting appreciable spans of geological time
[41]. If it truly is the case that a sizeable majority of extant clades both tend towards sharp
imbalance and have been subject to at least one major randomly-acting mass extinction, then
attention should shift towards identifying factors that might maintain the imbalance generated
by the extinction/recovery process, rather than eroding it. Also required is consideration of
how long ago the last mass extinction affecting a clade occurred. To the extent that the evolu-
tion and diversification of most real-world taxa actually resembles those of simulated branch-
ing process models, asexual digital organisms, or single-celled organisms like foraminifera
(whose population dynamics are most likely to resemble the former), clades for whom the
most recent mass extinction event lies far in their evolutionary past may not retain much signal
of short-term post-extinction diversification, especially if there has been much turnover since
that time[78]. Even if a given extant clade’s phylogeny is sharply imbalanced, our results sug-
gest this imbalance may be due to evolutionary events unrelated to the mass extinction itself.
Results blur the distinction between micro- and macro-scales of
evolution, and focus consideration on factors preserving imbalance
A further consideration is to what scale of time and biology our results best apply. Although
we address an issue normally considered the domain of macroevolution, this study was
inspired by a computational simulacrum of microbial experimental evolution. Indeed, many
of our observations and results are understood more readily in experimental evolutionary
terms, particularly as the topologies of our modeled trees are in constant flux as taxa are added
and removed, and nonrandom imbalance need not be the product of singular events [44]. Spe-
ciation probability is a kind of reproductive rate, i.e. fitness, and differences between taxa in
reproductive rates are analogous to differences in fitness among different clones in a popula-
tion (to be clear, we are not advancing a species selection argument here). The inevitable “take-
over” of the tree by taxa with higher speciation probabilities then becomes analogous to a
selective sweep resulting in a shift to a population with a higher average fitness; the real-world
equivalents are the suddenly greater availability of resources and space for expansion due to
reduced competition following a population bottleneck, leading to a temporary burst of diver-
sification that declines once carrying capacity is reached. The evolutionary trajectory thus
reflects the success of one or a few high-fitness subclones within the “population” of taxa, ini-
tially causing sharp imbalance during the initial period of expansion, which then declines
along with variance in fitness when these subclones have risen to dominance. Nor is this
because of a single global fitness optimum; the two-phase simulations described in S3 Data
demonstrate that this behaviour still occurs (albeit to lesser degrees) when trait limits, now
analogous to new fitness optima, are accessed serially with a waiting time between them, akin
to classical periodic selection [85]. For these reasons, our results apply best to phylogenies at
lower levels of taxonomic resolution. We feel justified in drawing such analogies, since there is
no a priori reason why diversifying clades of clonal asexual organisms cannot show phyloge-
netic dynamics like those of obligately sexual organisms as long as strictly branching (as
opposed to reticulate) dynamics apply for both at some level of biological resolution. As men-
tioned above, our results should focus attention on what additional factors not covered in
either of the models we consider can both contribute to and preserve phylogenetic imbalance.
If it be the case that ecological and/or spatial isolation are needed to separate taxa with
markedly different diversification rates, there is again no reason why this cannot apply to both
a single initial species experiencing adaptive radiation into different spatially isolated environ-
ments, and to higher-level taxa diversifying across larger spatial scales.
Erasure of tree balance signature by continued evolution
PLOS ONE | https://doi.org/10.1371/journal.pone.0179553 June 23, 2017 19 / 26

Concluding remarks
Our results again demonstrate that mass extinction that acts randomly on clades with trait-
biased speciation probability produces greater imbalance than that acting in a directionally-
selective manner. However, they also show that these effects are comparatively weak and
short-lived when the evolutionary processes that first produce strong imbalance even without
mass extinction then erodes those effects. As discussed previously [5,6], for most real cases, we
do not know where along its evolutionary trajectory a clade lies (or even what the form of the
trajectory is), or what alternative outcomes could be. Other processes, such as those operating
in the Control runs here, can produce sharp imbalance even without mass extinction (see also
[10,37]). Thus, we cannot solely use tree balance metrics to infer past history of mass extinc-
tion for a given extant clade’s phylogeny. Here, we know the timing and nature of the extinc-
tion events, the pre-extinction and subsequent tree states, and the behaviour that would obtain
without mass extinction, including the form of the evolutionary trajectories of trait variance
and tree balance. To be sure, we are not claiming that a trajectory such as the type obtained
here actually characterizes most real clades, which would depend on factors not modeled here.
However, our results are a further demonstration that as an evolving clade gets further away
from a mass extinction event, subsequent evolution can obscure and eventually erase the initial
phylogenetic effects caused by the extinction/recovery process, though this may depend on
which characteristics of the phylogeny are measured, and by what metrics [6].
Supporting information
S1 Fig. Three representative replicates showing early (purple trace), middle (blue trace),
and late (black trace) Yule zone breakout and return behaviour. The late-breaking replicate
run was extended in order for return to the Yule zone to be clearly shown. Dot-dash vertical
line at t = 300 indicates where mass extinction treatment would occur.
a) Using Blum et al.’s [21] Yule-standardized version Colless’ [15] index of imbalance. Yule
zone boundaries as described in Methods.
b) Using β
A
[16]. Solid traces are maximum likelihood estimates of β
A
, dashed traces are 95%
confidence intervals around the calculated β
A
estimates. β
A
values and confidence intervals
determined with same R code as for Fig 1.
(TIF)
S2 Fig. Effect of different mass extinction treatments on tree balance for the three repre-
sentative replicates shown in S1 Fig (goes with S1 Data). Time of extinction treatment is
t = 300 in all cases. Extinction strength is μ
M
= 0.9 for all cases. Black trace, Control; red trace,
Random; blue trace, selective-on-diversifiers; purple trace, selective-on-relicts.
a) Middle-breaker.
b) Early-breaker
c) Late breaker, unextended simulation. Note that selective-on-diversifiers extinction pre-
vents Yule zone breakout within allotted time of simulation.
(TIF)
S3 Fig. (a-c). Three representative replicates showing connection between change in tree
balance and loss of phylogenetic root during return to Yule zone. Plots show behavior of
Control replicates only. Top panel, trajectory of tree balance; bottom panel, change in root age.
A larger root age value signifies a younger root.
(TIF)
Erasure of tree balance signature by continued evolution
PLOS ONE | https://doi.org/10.1371/journal.pone.0179553 June 23, 2017 20 / 26

S4 Fig. (a-c). Three representative replicates showing offset between maximum trait vari-
ance and peak imbalance (goes with S3 Data). Black trace, tree balance; red trace, trait vari-
ance; dashed horizontal red line, trait variance = 1.0; dot-dash vertical black line, time of
extinction treatment; dashed horizontal red line, time of maximum trait variance; dashed hori-
zontal black line, time of peak imbalance.
(TIF)
S5 Fig. Histograms showing shift in distribution of trait variance over time (goes with S3
Data). Figures correspond to replicate shown in S3c Fig.
a) t = 165, trait variance approximately 1, increasing
b) t = 320, trait variance at half-maximum, increasing
c) t = 400, maximum variance
d) t = 420, half-maximum, descending
e) t = 520, variance <1 but still strong imbalance, descending.
f) t = 600, variance at end-simulation
(TIF)
S6 Fig. Thirty replicates of two-phase experiments showing double peak in trait variance and
offset between trait variance and imbalance peaks for each phase (goes with S3 Data). Each
coloured trace is an individual replicate. Upper panel, trait variance; lower panel, tree balance.
(TIF)
S7 Fig. Shift in the distribution of phylogenetic root ages for a) Random at μ
M
= 0.5, b)
selective-on-diversifiers at μ
M
= 0.5, c) selective-on-relicts at μ
M
= 0.5. Bars and axes as in
main text Fig 4.
(TIF)
S8 Fig. Shift in the distribution of phylogenetic root ages for a) Random at μ
M
= 0.9, b)
selective-on-diversifiers at μ
M
= 0.9, c) selective-on-relicts at μ
M
= 0.9. Bars and axes as in
main text Fig 4.
(TIF)
S1 Data. Effects of mass extinction treatments on Yule zone breakout times, Yule zone
return times, and time of clade-size recovery. Contains Tables A-C.
Table A. Average times of Yule zone breakout (see text for definition) for each treatment
type (goes with S1 Data). All quantities are in simulation time units, expressed as averages ±2
standard errors. Number to left of pipe character is for treatment; number to right of pipe is
for corresponding Control replicates. Number in square brackets indicates number of treat-
ment replicates in which event occurred.
Table B. Average times of three critical points for each mass extinction treatment (goes
with S1 Data). All quantities are in simulation time units, expressed as averages ±2 standard
errors.
Table C.Average times of Yule zone return (see text for definition) for each treatment
type (goes with S1 Data). All quantities are in simulation time units, expressed as averages ±2
standard errors. Number to left of pipe character is for treatment; number to right of pipe is
for corresponding Control replicates. Number in square brackets indicates number of treat-
ment replicates in which event occurred.
(DOCX)
Erasure of tree balance signature by continued evolution
PLOS ONE | https://doi.org/10.1371/journal.pone.0179553 June 23, 2017 21 / 26

S2 Data. Comparison of tree balance in mass extinction treatments to corresponding
controls at clade-size recovery and CSR/end interval points. Contains Tables D-G.
Table D (goes with S2 Data). Mean differences in balance between mass extinction treat-
ments at CSR/end first-quarter point. See Methods for statistical analysis. Significance levels:
no asterisk, difference not significant; ‘’, 0.01 p<0.05; ‘’ 0.005 p<0.01; ‘’ 0.0001 
p<0.005; ‘’ p <0.0001.
Table E (goes with S2 Data). Comparison of treatments vs. corresponding Control at CSR/
end first-quarter point. See Methods for statistical analysis. Significance levels: no asterisk,
difference not significant; ‘’, 0.01 p<0.05; ‘’ 0.005 p<0.01; ‘’ 0.0001 p<0.005;
‘’ p <0.0001.
Table F (goes with S2 Data). Mean differences in balance between mass extinction treat-
ments at CSR/end three-quarter point. See Methods for statistical analysis. Significance levels:
no asterisk, difference not significant; ‘’, 0.01 p<0.05; ‘’ 0.005 p<0.01; ‘’ 0.0001
p<0.005; ‘’ p <0.0001.
Table G (goes with S2 Data) Comparison of treatments vs. corresponding Control at CSR/
end three-quarter point. See Methods for statistical analysis. Significance levels: no asterisk,
difference not significant; ‘’, 0.01 p<0.05; ‘’ 0.005 p<0.01; ‘’ 0.0001 p<0.005;
‘’ p <0.0001.
(DOCX)
S3 Data. Yule zone breakout and peak imbalance behaviour are linked to trait value limits
and exhaustion of trait variance.
(DOCX)
Acknowledgments
We thank Michael Blum for providing R code containing a version of the maxlik.betasplit()
function from the apTreeshape package that can be applied to non-dichotomous trees, and
Stephen Heard (University of New Brunswick, Fredericton, NB, Canada) for his review of and
comments on the manuscript. GY gives special thanks to Jing Zhao for assistance with figure
preparation.
Author Contributions
Conceptualization: GY PMA.
Data curation: G-DY GY.
Formal analysis: G-DY GY.
Funding acquisition: GY.
Investigation: G-DY GY.
Methodology: GY.
Project administration: GY.
Resources: GY.
Software: PMA.
Supervision: GY.
Visualization: G-DY GY.
Erasure of tree balance signature by continued evolution
PLOS ONE | https://doi.org/10.1371/journal.pone.0179553 June 23, 2017 22 / 26

Writing – original draft: GY.
Writing – review & editing: GY PMA.
References
1. Barraclough TG, Birky CW Jr., Burt A. Diversification in sexual and asexual organisms. Evolution 2003;
57: 2166–2172. PMID: 14575336
2. Carlson SJ. Tree balance, clade size distribution and extinction selectivity in Paleozoic terebratulide
brachiopods. Fossils and Strata 2008; 54: 167–172.
3. Crisp MD, Cook LG. Explosive radiation or mass extinction? Interpreting signatures in molecular phy-
logenies. Evolution 2009; 63: 2257–2265. https://doi.org/10.1111/j.1558-5646.2009.00728.x PMID:
19486148
4. Rabosky DL, Lovette IJ. Explosive evolutionary radiations: decreasing speciation or increasing extinc-
tion through time? Evolution 2008; 62: 1866–1875. https://doi.org/10.1111/j.1558-5646.2008.00409.x
PMID: 18452577
5. Liow LH, Quental TB, Marshall CR. When can decreasing diversification rates be detected with molecu-
lar phylogenies and the fossil record? Syst Biol 2010; 59: 646–659. https://doi.org/10.1093/sysbio/
syq052 PMID: 20861283
6. Yedid G, Stredwick J, Ofria CA, Agapow P-M. A comparison of the effects of random and selective
mass extinctions on erosion of evolutionary history in communities of digital organisms. PLoS ONE
2012; 7(5): e37233. https://doi.org/10.1371/journal.pone.0037233 PMID: 22693570
7. McPeek MA. The ecological dynamics of clade diversification and community assembly. Am Nat 2008;
172: E270–E284. https://doi.org/10.1086/593137 PMID: 18851684
8. Alroy J. Speciation and extinction in the fossil record of North American mammals. In: Butlin R, Bridle J,
and Schluter D, eds., Speciation and patterns of diversity. Cambridge, MA: Cambridge University
Press; 2009. pp. 301–323.
9. Phillimore AB, Price TD. Density-dependent cladogenesis in birds. PLoS Biol 2008; 6(3): 483–489.
10. Purvis A, Fritz SA, Rodrı
´guez J, Harvey PH, Grenyer R. The shape of mammalian phylogeny: patterns,
processes and scales. Philos Trans R Soc Lond B Biol Sci. 2011; 366: 2462–2477. https://doi.org/10.
1098/rstb.2011.0025 PMID: 21807729
11. Rabosky DL, Hurlbert AH. Species richness at continental scales is dominated by ecological limits*. Am
Nat 2015; 185: 572–583. https://doi.org/10.1086/680850 PMID: 25905501
12. Shao KT, Sokal RR. Tree balance. Syst Zool 1990; 39: 266–276.
13. Agapow PM, Purvis A. Power of eight tree shape statistics to detect nonrandom diversification: a com-
parison by simulation of two models of cladogenesis. Syst Biol 2002; 51: 866–872. PMID: 12554452
14. Sackin MJ. “Good” and “bad” phenograms. Syst Zool 1972; 21: 225–226.
15. Colless DH. Review of Phylogenetics:The theory and practice of phylogenetic systematics. Syst Zool
1982; 31: 100–104.
16. Aldous DJ. Stochastic models and descriptive statistics for phylogenetic trees, from Yule to Today. Stat
Sci 2001; 16: 23–34
17. Mir A, Rossello
´F, Rotger L. A new balance index for phylogenetic trees. Math Biosci 2013; 241: 125–
136. https://doi.org/10.1016/j.mbs.2012.10.005 PMID: 23142312
18. Slowinski JB, Guyer C. Testing the stochasticity of patterns of organismal diversity: An improved null
model. Am Nat 1989; 134: 907–921
19. Heard SB. Patterns in tree balance among cladistic, phenetic, and randomly generated phylogenetic
trees. Evolution 1992; 46: 1818–1826 https://doi.org/10.1111/j.1558-5646.1992.tb01171.x PMID:
28567767
20. Heard SB. Patterns in phylogenetic tree balance with variable and evolving speciation rates. Evolution
1996; 50: 2141–2148 https://doi.org/10.1111/j.1558-5646.1996.tb03604.x PMID: 28565665
21. Blum MGB, Franc¸ois O. On statistical tests of phylogenetic tree imbalance: The Sackin and other indi-
ces revisited. Math Biosci 2005; 195: 141–153 https://doi.org/10.1016/j.mbs.2005.03.003 PMID:
15893336
22. Blum MGB, Franc¸ois O. Which random processes describe the Tree of Life? A large-scale study of phy-
logenetic tree balance. Syst Biol 2006; 55: 685–691. https://doi.org/10.1080/10635150600889625
PMID: 16969944
Erasure of tree balance signature by continued evolution
PLOS ONE | https://doi.org/10.1371/journal.pone.0179553 June 23, 2017 23 / 26

23. Bortolussi N, Durand E, Blum M, Franc¸ois O. apTreeshape: statistical analysis of phylogenetic tree
shape. Bioinformatics 2006; 22: 363–364 https://doi.org/10.1093/bioinformatics/bti798 PMID:
16322049
24. Heard SB, Cox GH. The shapes of phylogenetic trees of clades, faunas, and local assemblages: explor-
ing spatial pattern in differential diversification. Am. Nat. 2007; 169, E107–E118. https://doi.org/10.
1086/512690 PMID: 17427125
25. Savage HM. The shape of evolution: systematic tree topology. Biol J Linn Soc 1983; 20: 225–244.
26. Slowinski JB, Guyer C. Testing whether certain traits have caused amplified diversification: an improved
method based on a model of random speciation and extinction. Am Nat 1993; 142: 1019–1024. https://
doi.org/10.1086/285586 PMID: 19425946
27. Purvis A, Agapow PM. Phylogeny imbalance: taxonomic level matters. Syst Biol 2002; 51: 844–854.
PMID: 12554450
28. Holman EW. Nodes in phylogenetic trees: the relation between imbalance and number of descendent
species. Syst Biol 2005; 54: 895–899. https://doi.org/10.1080/10635150500354696 PMID: 16282168
29. Kirkpatrick M, Slatkin M. Searching for evolutionary pattern in the shape of a phylogenetic tree. Evolu-
tion 1993; 47: 1171–1181. https://doi.org/10.1111/j.1558-5646.1993.tb02144.x PMID: 28564277
30. Losos JB, Adler FR. Stumped by trees? A generalized null model for patterns of organismal diversity.
Am Nat 1995; 145: 329–342.
31. Purvis A. Using interspecies phylogenies to test macroevolutionary hypotheses. In Leigh-Brown AJ,
Smith JM eds., New uses for new phylogenies. Oxford Univ. Press, Oxford, UK, 1996. pp. 153–168
32. Mooers AØ, Heard SB. Inferring evolutionary process from phylogenetic tree shape. Q Rev Biol. 1997;
72: 31–54
33. Chan KMA, Moore BR. Accounting for mode of speciation increases power and realism of tests of phy-
logenetic asymmetry. Am Nat 1999; 153: 332–346.
34. Harcourt-Brown KG, Pearson PN, Wilkinson M. The imbalance of paleontological trees. Paleobiology
2001; 27: 188–204.
35. Stam E. Does imbalance in phylogenies reflect only bias? Evolution 2002; 56: 1292–1295 PMID:
12144028
36. Paradis E. Statistical analysis of diversification with species traits. Evolution 2005; 59: 1–12. https://doi.
org/10.1554/04-231 PMID: 15792222
37. Purvis A, Jones KE, Mace GM. Extinction. BioEssays 2002; 22: 1123–1133.
38. Harmon LJ, Blum MGB, Wong DHJ, Heard SB. Some models of phylogenetic tree shape. In Gascuel
O. & Steel M. eds., Reconstructing evolution:new mathematical and computational advances, Oxford,
UK: Oxford University Press, 2007. pp. 149–170.
39. Hagen O, Hartmann K, Steel M, Stadler T. Age-dependent speciation can explain the shape of empirical
phylogenies. Syst Biol 2015; 64: 432–440. https://doi.org/10.1093/sysbio/syv001 PMID: 25575504
40. Mooers AØ. Effects of tree shape on the accuracy of maximum likelihood-based ancestor reconstruc-
tions. Syst Biol 2004; 53: 809–814. https://doi.org/10.1080/10635150490502595 PMID: 15545257
41. Heath TA, Zwickl DJ, Kim J, Hillis DM. Taxon sampling affects inferences of macroevolutionary pro-
cesses from phylogenetic trees. Syst Biol 2008; 57: 160–166. https://doi.org/10.1080/
10635150701884640 PMID: 18300029
42. Duchêne D, Duchêne S, Ho SYW. Tree imbalance causes a bias in phylogenetic estimation of evolu-
tionary timescales using heterochronous sequences. Mol Ecol Resour 2015; 15: 785–794. https://doi.
org/10.1111/1755-0998.12352 PMID: 25431227
43. Harcourt-Brown KG. Tree balance, time slices, and evolutionary turnover in Cretaceous planktonic fora-
minifera. Syst Biol 2002; 51: 908–16. https://doi.org/10.1080/10635150290102618 PMID: 12554457
44. Tarver JE, Donoghue PCJ. The trouble with topology: Phylogenies without fossils provide a revisionist
perspective of evolutionary history in topological analyses of diversity. Syst Biol 2011; 60: 700–712.
https://doi.org/10.1093/sysbio/syr018 PMID: 21436106
45. Heard SB, Mooers AØ. Signatures of random and selective mass extinctions in phylogenetic tree bal-
ance. Syst Biol 2002; 51: 889–897. PMID: 12554455
46. Yule GU. A mathematical theory of evolution, based on the conclusions of Dr. J.C. Willis. Phil Trans R
Soc Lond B 1924; 213: 21–87.
47. Harding EF. The probabilities of rooted tree-shapes generated by random bifurcation. Adv Appl Probab
1971; 3: 44–77
48. Erwin DH. Life’s downs and ups. Nature 2000; 404: 129–130. https://doi.org/10.1038/35004679 PMID:
10724147
Erasure of tree balance signature by continued evolution
PLOS ONE | https://doi.org/10.1371/journal.pone.0179553 June 23, 2017 24 / 26

49. Foote M. Morphological diversity in the evolution of Paleozoic and post-Paleozoic crinoids.Paleobiology
1999; 25(suppl.):1–115.
50. McGowan AJ. The effect of the Permo-Triassic bottleneck on Triassic ammonoid morphological evolu-
tion. Paleobiology 2004; 30: 369–395.
51. Benton MJ, Tverdokhlebov VP, Surkov MV. Ecosystem remodeling among vertebrates at the Permian-
Triassic boundary in Russia. Nature 2004; 432:97–100. https://doi.org/10.1038/nature02950 PMID:
15525988
52. D’Hondt S., Donaghay P, Zachos JC, Luttenberg D, Lindinger M. Organic carbon fluxes and ecological
recovery from the Cretaceous-Tertiary mass extinction. Science 1998; 282:276–279. PMID: 9765149
53. Yedid G, Ofria CA, Lenski RE. Selective press extinctions, but not random pulse extinctions, cause
delayed ecological recovery in communities of digital organisms. Am Nat 2009; 173: E139–E154.
https://doi.org/10.1086/597228 PMID: 19220147
54. Price TD, Hooper DM, Buchanan CD, Johansson US, Tietze DT, Alstro¨m P, et al. Niche filling slows the
diversi fication of Himalayan songbirds. Nature 2014; 509(7499):222–5. https://doi.org/10.1038/
nature13272 PMID: 24776798
55. Jetz W, Thomas GH, Joy JB, Hartmann K, Mooers AO. The global diversity of birds in space and time.
Nature 2012; 491: 444–448. https://doi.org/10.1038/nature11631 PMID: 23123857
56. Quental TB, Marshall CR. Extinction during evolutionary radiations: Reconciling the fossil record with
molecular phylogenies. Evolution 2009; 63: 3158–3167 https://doi.org/10.1111/j.1558-5646.2009.
00794.x PMID: 19659595
57. Rabosky DL. LASER: A maximum likelihood toolkit for detecting temporal shifts in diversification rates
from molecular phylogenies. Evol Bioinform Online 2006; 257–260.
58. Paradis E, Claude J, Strimmer K. APE: analyses of phylogenetics and evolution in R language. Bioinfor-
matics 2004; 20: 289–290. PMID: 14734327
59. Revell LJ. phytools: An R package for phylogenetic comparative biology (and other things). Methods
Ecol.Evol. 2012; 3, 217–223.
60. Ruta M, Pisani D, Lloyd GT, Benton MJ. A supertree of Temnospondyli: cladogenetic patterns in the
most species-rich group of early tetrapods. Proc. R. Soc. B 2007; 274: 3087–3095 https://doi.org/10.
1098/rspb.2007.1250 PMID: 17925278
61. Dunnett CW. A multiple comparison procedure for comparing several treatments with a control. J Am
Stat Assoc 1955; 50:1096–1121.
62. Purvis A, Agapow P-M, Gittleman JL, Mace GM. Nonrandom extinction and the loss of evolutionary his-
tory. Science 2000; 288: 328–330. PMID: 10764644
63. Beerling DJ, Lomax BH, Upchurch GR, Nichols DJ, Pillmore CL, Handley LL, Scrimgeour CM. Evidence
for the recovery of terrestrial ecosystems ahead of marine primary production following a biotic crisis at
the Cretaceous-Tertiary boundary. J Geol Soc London 2001; 158: 737–740
64. Sepulveda J, Wendler JE, Summons RE, Hinrichs KU. Rapid resurgence of marine productivity after
the Cretaceous-Paleogene mass extinction. Science 2010; 326:129–132.
65. Friedman M. Explosive morphological diversification of spiny-finned teleost fishes in the aftermath of
the end-Cretaceous extinction. Proc R Soc B 2011; 277:1675–1683.
66. Meredith RW, Janečka JE, Gatesy J, Ryder OA, Fisher CA, Teeling EC, Goodbla, et al. Impacts of the
Cretaceous Terrestrial Revolution and KPg extinction on mammal diversification. Science 2011; 334:
521–524. https://doi.org/10.1126/science.1211028 PMID: 21940861
67. dos Reis M, Inoue J, Hasegawa M, Asher RJ, Donoghue PCJ, Yang Z. Phylogenomic datasets provide
both precision and accuracy in estimating the timescale of placental mammal phylogeny. Proc R Soc B
2012; 279: 3491–3500. https://doi.org/10.1098/rspb.2012.0683 PMID: 22628470
68. Halliday TJD, Upchurch P, Goswami A. 2016 Eutherians experienced elevated evolutionary rates in the
immediate aftermath of the Cretaceous–Palaeogene mass extinction. Proc. R. Soc. B 2016; 283:
20153026. http://dx.doi.org/10.1098/rspb.2015.3026 PMID: 27358361
69. Looy CV, Brugman WA, Dilcher DL, Visscher H. The delayed resurgence of equatorial forests after the
Permian-Triassic ecologic crisis. Proc Nat Acad Sci 1999; 96: 13857–62. PMID: 10570163
70. Yin H-F, Feng Q-L, Lai X-L, Baud A, Tong J-N. The protracted Permo-Triassic crisis and multi-episode
extinction around the Permian-Triassic boundary. Glo Pla Cha 2007; 55: 1–20.
71. Sahney S, Benton MJ. Recovery from the most profound mass extinction of all time. Proc Roy Soc B
2008; 275: 759–65.
72. Wei H, Shen J, Schoepfer SD, Krystyn L, Richoz S, Algeo TJ. Environmental controls on marine eco-
system recovery following mass extinctions, with an example from the Early Triassic. Earth Sci Rev
2015; 149: 108–135.
Erasure of tree balance signature by continued evolution
PLOS ONE | https://doi.org/10.1371/journal.pone.0179553 June 23, 2017 25 / 26

73. Schaal EK, Clapham ME, Rego BL, Wang SC, Payne JL. Comparative size evolution of marine clades
from the Late Permian through Middle Triassic. Paleobiology 42: 127–142.
74. Lau KV, Maher K, Altiner D, Kelley BM, Kump LR, Lehrmann DJ et al. Marine anoxia and delayed Earth
system recovery after the end-Permian extinction. Proc Nat Acad Sci 2016; 113: 2–7.
75. Twitchett RJ, Krystyn L, Baud A. Wheeley JR, Richoz S. Rapid marine recovery after the end-Permian
mass-extinction event in the absence of marine anoxia. Geology 2004; 32: 805–808.
76. Ru¨ber L, Zardoya R. Rapid cladogenesis in marine fishes revisited. Evolution 2005; 59: 1119–1127.
PMID: 16136809
77. Weir JT. Divergent timing and patterns of species accumulation in lowland and highland Neotropical
birds. Evolution 2006; 60: 842–855. PMID: 16739464
78. Ricklefs RE, Losos JB, Townsend TM. Evolutionary diversification of clades of squamates. J Evol Biol
2007; 20: 1751–1762. https://doi.org/10.1111/j.1420-9101.2007.01388.x PMID: 17714293
79. Schlichting CD, Pigliucci M. Phenotypic Evolution: a Reaction Norm Perspective. Sinauer & Associ-
ates, Sunderland, MA, U.S.A., 1998.
80. McShea DW. Mechanisms of large-scale evolutionary trends. Evolution 1994; 4: 1747–1763.
81. Wellborn GA, Broughton RE. Diversification on an ecologically constrained adaptive landscape. Mol
Ecol 2008; 17: 2927–2936. https://doi.org/10.1111/j.1365-294X.2008.03805.x PMID: 18522695
82. Wellborn GA. Size-biased predation and the evolution of prey life histories: a comparative study of
freshwater amphipod populations. Ecology 1994; 7: 2104–2117
83. Rabosky DL. Ecological limits on clade diversification in higher taxa. Am Nat 2009; 173: 662–674.
https://doi.org/10.1086/597378 PMID: 19302027
84. Fabre P-H, Rodrigues A, Douzery EJP. Patterns of macroevolution among Primates inferred from a
supermatrix of mitochondrial and nuclear DNA. Mol Phylo Evol 2009; 53: 808–825.
85. Yedid G, Bell A. Microevolution in an electronic microcosm. Am Nat 2002; 157: 465–487.
Erasure of tree balance signature by continued evolution
PLOS ONE | https://doi.org/10.1371/journal.pone.0179553 June 23, 2017 26 / 26