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].

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, balance 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 positive values.

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 replicates 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 converged 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 involving comparisons of balance, but were used for comparisons of times of the given events (see below).

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 determined 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 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 summary statistics are reported as means ± two standard errors.

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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

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, evolutionary 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 from what a Yule process could generate), a second phase ensued whereby the degree of imbalance—measured by strongly positive values of I_C—increased sharply over Yule zone values (the Yule zone breakout).

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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.

1. a). t = 165, trait variance approximately 1, increasing
2. b). t = 320, trait variance at half-maximum, increasing
3. c). t = 400, maximum variance
4. d). t = 420, half-maximum, descending
5. e). t = 520, variance < 1 but still strong imbalance, descending.
6. f). t = 600, variance at end-simulation

https://doi.org/10.1371/journal.pone.0179553.g003

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 treatment, 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, consistent 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 differ significantly from corresponding Controls at any intensity, while SOR differed from Control 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).

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Table 1. Mean differences in balance between mass extinction treatments at point of clade-size recovery.

https://doi.org/10.1371/journal.pone.0179553.t001

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Table 2. Comparison of treatments vs. corresponding control at CSR.

https://doi.org/10.1371/journal.pone.0179553.t002

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Table 3. Dunnett contrasts between tree balance at CSR for each extinction treatment and immediate pre-treatment as a reference standard.

https://doi.org/10.1371/journal.pone.0179553.t003

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).

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Table 4. Mean differences in balance between mass extinction treatments at CSR/END midpoint.

https://doi.org/10.1371/journal.pone.0179553.t004

For special consideration of the Control relative to treatments at CSR and post-CSR intervals (see Methods), Random differed significantly from corresponding Controls only at a few points, and then only weakly (Tables 2 and 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 significant differences were weak. Only SOD differed strongly and consistently from corresponding Control values at CSR and later points (Fig 2, Tables 2 and 5; Table E and Table G in S2 Data).

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Table 5. Comparison between treatments vs. corresponding Control values at CSR/END midpoint.

https://doi.org/10.1371/journal.pone.0179553.t005

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 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 imbalanced 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 values, only SOD at μ_M = 0.9 differed significantly from Control (Table 7).

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Table 6. Mean differences in balance between mass extinction treatments at end of simulation.

https://doi.org/10.1371/journal.pone.0179553.t006

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Table 7. Dunnett contrasts between tree balance at end-simulation for each extinction treatment, using end-control as a reference standard.

https://doi.org/10.1371/journal.pone.0179553.t007

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 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 simulation 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).

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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

In extinction treatment replicates, root loss depended on both treatment type and intensity. 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 distribution 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 replicates 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.

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-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 evolutionary 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 balancing 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 compared 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 eventually 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 & 2 vs. 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 treatments had different short-term effects on the distribution of root ages, and that this distribution 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, consistent 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 imbalance is due primarily to the retention of basal clades, and the reference point for measuring balance changes with the loss of those clades (Fig 3), the resulting tree will be phylogenetically 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 recovery 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 feasible phenotypes;
4. there is no mechanism for isolating slowly-diversifying clades from very rapidly-diversifying ones. It is unclear whether such mechanisms in fact exist; although there are some possible 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 characteristic 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. 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 evolution and diversification of most real-world taxa actually resembles those of simulated branching 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 suggest 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]. Speciation 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 population (to be clear, we are not advancing a species selection argument here). The inevitable “takeover” 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 diversification 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, initially 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 phylogenetic 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 mentioned 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 environments, and to higher-level taxa diversifying across larger spatial scales.

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 extinction for a given extant clade’s phylogeny. Here, we know the timing and nature of the extinction 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].