The diffused evolutionary dynamics of morphological novelty

Significance

Why rates of phenotypic evolution vary across the tree of life is still not well known. A widespread view holds that fast rates result from the colonization of empty adaptive zones, or sets of similar niches, followed by rate deceleration with the crowding of available niche space. By developing a flexible phylogenetic model that examines how rates vary across lineages and applying it to thousands of extinct and extant species, I find that morphological rates of evolution for body size have not slowed down, regardless of the increase in phenotypic varieties. Rather, macroevolutionary trends result from persistent evolution of lineages’ body size followed by their selective extinction, suggesting unattenuated evolutionary dynamics.

Abstract

Rates of evolution are fundamental to understand the processes that shaped the history of life. The predominant view holds that high rates of phenotypic evolution result from lineage transitions across peaks in an adaptive landscape, with subsequent slow-downs, but evidence remains debated. I developed a phylogenetic “diffused Brownian motion” model that characterizes nuanced variations in evolutionary rates and use it to comprehensively assess body size evolution and its underlying rates for 2,950 extinct and 792 extant species that span over 450 Mys of evolution. I find that evolutionary rates do not conform to expectations from adaptive landscape theory, but rather have been stable, unaffected by the accumulation of phenotypic disparity. Long-term evolutionary trends, such as several net increases in clade-average body size, result both from sustained evolution at the lineage level and the sorting of species phenotypes and their underlying evolutionary rates at the clade level, sometimes acting in opposite directions. These findings substantiate an active role of species in shaping their environment that generate continuous novelty of life forms.

A fundamental theme in evolutionary biology revolves around the tempo and mode of species’ niche diversification during evolutionary radiations, which stems from the observed variation in rates of phenotypic novelty (1, 2). Most notable is the common pattern of geologically “abrupt” appearances of many new taxa in the fossil record, particularly at higher levels, followed by comparatively slower modifications (1, 3, 4). Condoning some redundancy that ensues from defining taxa based on similarity, a rapid and early phenotypic diversification appears to characterize several evolutionary radiations together with a paucity of “transitional” fossils between higher taxa (1, 3, 5). Simpson canonized Wright’s adaptive genetic landscape metaphor at the organism level (6) into phenotypic terms at the species level where a continuous function with peaks and valleys represent species fitness (or “adaptive value”) in phenotypic space (1). This phenotypic adaptive landscape (henceforth, simply “adaptive landscape”) depicts an adaptive topography where external factors generate multiple local fitness maxima along phenotypic space toward which species are positively selected, and which he called “adaptive zones” or “peaks.” These adaptive peaks are separated by valleys of low fitness, with gradients representing the intensity of selection (1). Simpson explained these infrequent (un)observed instances of rapid evolution as species movements from one “adaptive zone” or “peak” to another (1, 7, 8). Colonization of adaptive zones can happen progressively, or, Simpson continued, during “adaptive radiations,” which he defined as almost “simultaneous” transitions into divergent adaptive zones from one ancestral “adaptive type,” as in the origin of most higher taxa (2, 9, 10).

I refer to this idea of species evolving within and across shared adaptive peaks as “adaptive landscape theory.” Here, the opening of “ecological opportunities,” including acquisition of “key innovations” that enable access to new resources, dispersal to new environments, or removal of previous occupants, facilitate the colonization of new adaptive zones (2, 11). In turn, entry into a zone often triggers a steep increase in rates of lineage and phenotypic diversification, that is, an “adaptive radiation” (2, 11, 12). Because these adaptive zones represent discontinuous sets across phenotypic space, after this initial phase of explosive divergence, further accumulation of disparity within zones decelerates as lineages subdivide available (“intrazonal”) adaptive space (2). While a combination of diversification of taxa and ecologically important traits is expected (2, 13), the importance of the former resides mostly in that adaptation to different zones must entail separate lineages. That is, there can be taxonomic diversification without disparity, but not the other way around. It seems pertinent then to study the evolution of species phenotypes and their underlying rates to test the general predictions behind adaptive landscape theory. Namely, that at one or few points during the evolutionary history of the clade there are sharp increases in evolutionary rates as a consequence of the colonization of new adaptive zones, and that subsequent evolutionary rates slow down as a result of partitioning a limited niche space (13, 14) (Fig. 1).

Fig. 1.

Expectations under classic adaptive landscape theory. Pictogram illustrating expected patterns for (A) the evolving trait and (B) the underlying evolutionary rate under the classic paradigm of adaptive landscape theory (2). Some tip names (i to viii) are included to ease correspondence between trait and rate evolution pattern plots. Here, there are two further transitions among “adaptive peaks,” one leading to the tips that include ii, iii, and vii, and a subsequent one leading to the tips that include vi.

Despite the pervasive influence and adoption of Simpson’s phenotypic adaptive landscape iconography that underlie adaptive landscape theory, its pertinence, importance, and prevalence in macroevolutionary dynamics remain debated (14–21). Arguably, this partly derives from the difficulty in laying out and identifying its predictions when applied to empirical observations. Early on, adaptive radiations have been broadly singled out based on a relatively rapid and, for fossil groups, an early, accumulation of phenotypic disparity, that is, trait variance (2, 3, 5, 13, 22). However, focusing on the ancestor-descendant (i.e., phylogenetic) distribution of phenotypic evolutionary rates allows to directly measure lineage evolution through time; that is, using tempo to infer mode (1, 14, 23, 24). In this regard, the pioneering “early burst” phylogenetic models, where Brownian motion (BM) evolutionary rates are allowed to decrease through time, introduced a formal examination of adaptive landscape theory (14, 25). Implicit in these previous tests, however, are several potentially misleading assumptions. First, that the taxonomic delimitation of the empirical clade matches the (only) adaptive radiation (i.e., that the adaptive radiation initiated at the ancestor of the designated group of organisms). Second, that there were no additional adaptive transitions involved. And, third, that all lineages share the same exact evolutionary rate, which is only allowed to decrease, disregarding any between-lineage rate heterogeneity. A clade with rate increases scattered along some lineages, expected from nested adaptive radiations, would not lead these methods to detect an overall decreasing rate, as has indeed been found (24–27). Thus, even if life arose from a series of adaptive radiations, as previously advocated (2, 12), wherein evolutionary rates predominantly decelerate after punctuated increases at adaptive zones transitions (Fig. 1), one would be unlikely to recover the recurrent early bursts pattern.

Unraveling mode from tempo demands a flexible model capable of characterizing a range of evolutionary rate dynamics along separate lineages, including those expected under adaptive landscape theory (Fig. 1).

A Diffused Model of Evolutionary Rates

Here, I developed the “diffused Brownian motion” (“DBM”) model, which allows evolutionary rates to diffuse continuously along a phylogenetic tree, enabling a fine-grained characterization of rate dynamics (SI Appendix, Fig. S1; Materials and Methods). Specifically, I expand the “strict” Brownian motion (BM) process, wherein the instantaneous stochastic diffusion (evolutionary) rate is constant, to a process where instantaneous stochastic rates are themselves also continuously and separately diffusing according to a geometric Brownian motion process (“GBM;” Materials and Methods). The choice of a GBM is natural since it reflects the nonnegative nature of rates and assumes a multiplicative, rather than additive, diffusion (i.e., based in percentage rather than absolute value), as expected from multiplicative interactions among determining factors (21, 28–31). Unlike previous major methodological developments that account for rate heterogeneity during trait evolution (Materials and Methods), the DBM model allows for separate lineage-specific rates that change continuously through time.

At the start of the DBM process there is one lineage with continuous trait x₀ and underlying evolutionary rate ${\sigma }_0^2$ (i.e., the instantaneous diffusion rate), which represents the expected accumulation of trait variance after a unit time (i.e., units $\frac{x^2}{\text{time}}$; SI Appendix, Fig. S1). With time, lineages evolve their specific trait $x_i(t)$ under a concomitantly evolving evolutionary rate ${\sigma }_i^2(t)$, and, at speciation, lineages inherit both their trait and their rate to their descendants (SI Appendix, Fig. S1). Overall trends in traits are reflected in the drift α_x and, for evolutionary rates, in the drift α_σ, with an expectation to increase or accelerate when positive or to decrease or decelerate when negative. Finally, the diffusion of the logarithm of ${\sigma }_i^2(t)$, takes place with rate ${\gamma }^2$, interpreted as the percentage expected change in evolutionary rates (units $\frac{{({\sigma }^2)}^2}{\text{time}}$), and can be understood as the variation in rates across time and lineages, or the evolution of evolutionary rates (SI Appendix, Fig. S1).

Estimating the likelihood under a process where BM diffusion rates follow a GBM process remains intractable (31), but I was able to perform full probabilistic estimation under the DBM using Bayesian data augmentation (“DA;” Materials and Methods). The solution is to “augment” the data such that the evaluation of the likelihood given the augmented data becomes possible and viable, leading to an estimation of the parameters’ posterior distribution using Monte Carlo sampling (32), and has been successfully employed previously in phylogenetic models (21, 33–35) (SI Appendix, Fig. S1; Materials and Methods). For the DBM, this entails the imputation of trait, $x(t)$, and evolutionary rate, ${\sigma }^2(t)$, histories (i.e., the full diffusion paths) along the phylogenetic tree in such a way that they remain consistent with the observed data (SI Appendix, Fig. S1). Missing data or variance around species traits can be organically integrated into the estimation of these probabilities. Finally, this procedure returns not only the posterior distribution of the major process parameters (i.e., x₀, ${\sigma }_0^2$, α_x, α_σ and ${\gamma }^2$) but also of the augmented processes, which facilitate post hoc analyses and visualizations (SI Appendix, Fig. S1; Materials and Methods) (21, 34). I developed, implemented, and validated a DA algorithm to perform inference under the DBM model (SI Appendix, Fig. S2; Materials and Methods). The DBM model takes a time-calibrated phylogenetic tree with or without fossils together with trait information with or without uncertainty for some or all extinct and extant organisms in the tree.

Importantly, the DBM tests the predictions from adaptive landscape theory. Foremost, a slow-down in evolutionary rates is demonstrated by a negative evolutionary rate drift parameter α_σ. Second, the few, if any, lineages that underwent zone transitions are readily accounted for by the model. Unlike the “early burst” models in which the assumption is that all lineages share the same (decaying) rate at any moment in time (14, 25), a negative α_σ would be congruent with the core expectations of adaptive landscape theory by indicating a tendency for evolutionary rates for each lineage to wane with time, regardless of their magnitude, while allowing for deviations from it.

Rate Dynamics of Phenotypic Evolution

I applied the DBM model to examine phenotypic rate variation across evolutionary radiations. Jointly incorporating available paleontological and neontological information not only substantially improves the reconstruction of past evolutionary dynamics but might support evolutionary models that conflict when applied to extant taxa alone (36–41). Thus, I considered $17$ groups for which available phylogenetic information included a representative sample of extinct and extant species and was estimated under Fossilized Birth–Death (FBD) model (42, 43) (Materials and Methods). Together, these groups comprise over $2,800$ extinct and $700$ extant species across taxonomically diverse groups, with species representing archosaurs (including nonavian dinosaurs, birds, pseudosuchians), sphenodonts, mammals, turtles, therocephalians, ray-finned fishes, and arthropod groups, that together span the last $450$ Mys (SI Appendix, Table S1, Materials and Methods). Moreover, they embody dramatic ecological transitions, including shifts between aerial, terrestrial, and aquatic environments, as well as displaying a great variety of ways of life.

To assess their phenotypic evolutionary dynamics I focused on species average body size. Size is a fundamental feature of every organism, profoundly interrelated with most of their ecological, physiological, and behavioral features (44–48) and should be indicative of patterns expected from adaptive landscape theory (49). As such, its evolutionary dynamics across a wide range of taxa has been much studied in elucidating general patterns and underlying processes of species evolution (14, 18, 25, 41, 50–52). Besides its biological importance, body size can be estimated for a large number of species, including extinct specimens with fragmentary evidence, enabling a comparable and comprehensive analysis. I compiled body size information from the literature for the majority of species within the $17$ taxa, using weight, body length, and, in some cases, body measurement proxies (SI Appendix, Table S1 and Dataset S1; Materials and Methods). Missing information and, when available, intraspecific variance, measurement error, or uncertainty around the estimates was integrated (SI Appendix, Table S1). To examine body size evolutionary dynamics, I performed inference under the DBM model on each group, across a sample of $20$ empirical trees to account for phylogenetic uncertainty.

Body size has been extraordinarily dynamic, with several groups exhibiting differences exceeding an order of magnitude (Fig. 2 and SI Appendix, Figs. S3–S19). Some of the largest and long-lived radiations, including sea scorpions, pseudosuchians, and dinosaurs (Fig. 2A, D, and G and SI Appendix, Figs. S3, S6, S9, and S20 A, D, and G), saw a relatively early and rapid accumulation in body size disparity, in ostensible accordance with adaptive landscape theory. Most others, however, display either a gradual accumulation of body size differences, as in turtles, tetraodontiform fish, sloths, and new world monkeys (Fig. 2E, H, M, and O and SI Appendix, Figs. S7, S10, S15, S17, and S20 E, H, M, and O), or a delayed diversification as in penguins, short-faced kangaroos, and canins (Fig. 2I, N, and P and SI Appendix, Figs. S11, S16, S18, and S20 I, M, and P).

Fig. 2.

Diffused evolution of body size across distinct evolutionary radiations conflict with expectations from classic adaptive radiation. Inference on trait and rate evolutionary patterns under the diffused Brownian motion process, where traits and its underlying rates undergo separate yet concomitant diffusion processes, as described by the stochastic differential equations on the Top Left. For each group (A–Q), the first column shows the average posterior reconstruction for body size, colored by the underlying rates (i.e., color gradient from black to yellow). The second column represents the stacked posterior distributions of the drift in traits, α_x, over $20$ sample posterior of trees [except for (G and M), where only one empirical tree was used; see Materials and Methods]. Distributions with a strong positive or negative trend (i.e., those where $0$ does not overlap the 95% Credible Interval) are shown in red or blue, respectively. The third column depicts the evolution of the underlying evolutionary rates, colored by the evolving trait (i.e., color gradient from blue to red). For visual clarity only one phylogenetic tree out of $20$ from the posterior tree distribution is shown. The fourth column follows the description of the second, but for the evolutionary rate drift, α_σ. The evolutionary radiations represented, and their measurements for body size, are (A) sea scorpions (Eurypterida; body length [mm]), (B) therocephalians (skull length [mm]), (C) Sphenodontidae (lower jaw length [mm]), (D) pseudosuchians (compound proxy for body size), (E) turtles (Testudinata; carapace length [mm]), (F) pterosaurs (wingspan in M), (G) nonavian dinosaurs (body mass [kg]), (H) tetraodontiform fish (body length [cm]), (I) penguins (Spheniscidae; body mass [kg]), (J) proboscideans (body mass [kg]), (K) brontotheres (body mass [kg]), (L) cetaceans (body length [mm]), (M) sloths (Folivora; body mass [kg]), (N) short-faced kangaroos (Sthenurinae; body mass [kg]), (O) new world monkeys (Platyrrhini; body mass [kg]), (P) Caninae (body mass [kg]), and (Q) horses (Equinae; body mass [kg]). Silhouettes from phylopic.org.

The Unfit Macroevolutionary Adaptive Landscape

While evolutionary rates also varied substantially within radiations, usually by orders of magnitude (Fig. 2 and SI Appendix, Figs. S3–S19), they did not exhibit a tendency to decrease, as predicted by adaptive landscape theory. Remarkably, rather than slowing down, most groups sustain their evolutionary rates throughout their evolutionary history (i.e., ${\alpha }_{\sigma }=0$; Fig. 2), with turtles even revealing accelerating rates during their ca.$250$ Mys of evolution (95% Highest Posterior Density for ${\alpha }_{\sigma }>0$ across phylogenetic uncertainty; Fig. 2E). The addition of variation around trait values for clades without this information does not affect results (SI Appendix, Fig. S22). Only one out of all $17$ groups, the new world monkeys, fulfilled the expectation of a general decrease in evolutionary rates (i.e., 95% Highest Posterior Density for ${\alpha }_{\sigma }<0$ across phylogenetic uncertainty, Fig. 2O), with the exception of two lineages, as would be expected from subsequent zone transitions (Fig. 2O and SI Appendix, Fig. S17). For groups that initiated after or endured abrupt extinction events, there is no evidence of an increase in rates in their aftermath to then be followed by a renewed decrease (Fig. 2 and SI Appendix, Fig. S23), as expected from ecological opportunity after the opening of previously occupied adaptive zones. Finally, an increasing accumulation of phenotypic disparity, usually posited as evidence for adaptive landscape dynamics (3, 5), was not associated with decreasing trends in evolutionary rates (Fig. 2 and SI Appendix, Fig. S20).

Together, these results contradict the basic tenets of adaptive landscape theory, yet remain contingent on the pertinence of using body size and the DBM model to examine its predictions. By maximizing taxonomic coverage in the search for general patterns, I focused only on species body size, which, while determining several facets of organismic biology, ignores the multivariate complexity of phenotypes (20, 53). The uncommonness of rate decreases in body size, however, would imply that, even in the extreme case where rates for other functionally relevant phenotypic axes slowed down, body size would seem to continuously supply an axis of evolutionary versatility. Given that one given body size can accommodate various phenotypes, considering the intricacies of forms on top of their body size can only increase their total amount of change. Since organisms are “integrated entities” (54), sustained evolution in at least one relevant biological variable, here body size, seems to dispute the basic expectations from adaptive landscape theory.

Another concern is the ability of the DBM model to accurately capture trait dynamics under an adaptive landscape. For instance, if evolutionary rates do not diffuse but rather undergo instantaneous shifts. While the Brownian diffusion assumption of rates may lead to smoothing of trait and rate variation through time, the empirical reconstructions evince some ability to recover sudden changes (see, e.g., >10× increase in rates in less than $3$ Mys in Equidae, SI Appendix, Fig. S19). Regardless of the mode of trait and rate evolution, if the total amount of trait change decreases, as expected from periodic early burst patterns, the DBM should still be able to capture a tendency of rates to slow down.

An argument could be made, however, for a more intricate adaptive landscape beyond that from its original formulation, wherein fluctuating ecological opportunities or frequent transitions among adaptive zones account for the absence of a general decrease in rates of evolution. That is, since adaptive zones (or peaks) across phenotypic space can take all shapes and forms, in terms of their number, narrowness, distribution, and displacement (1), it could be argued to still have generated the observed evolutionary patterns across groups. Paradoxically, given that any evolutionary pattern can be described by retrospectively reaccommodating the dynamics of the adaptive zones themselves, or, put another way, no empirical pattern can refute the existence of a phenotypic adaptive landscape, this widespread view faces the logical flaw of not being empirically falsifiable (55). In practice, this is compounded by the common procedure of defining these zones post hoc by the very existence of species (e.g., “there is a penguin adaptive zone because there are penguins”), quickly becoming tautological (15). Although imaginary constructs, or models, such as the phenotypic adaptive landscape, help us make sense of the world, the problem is often that, once created, we tend to consider them as objective realities (56). Those for which no evidence can refute their validity (or whose ontological status is no longer even questioned), can give the false appearance of explanation.

Prominence of Species Sorting in Determining Macroevolutionary Trends

Rather than mapping the peaks of an adaptive landscape, with species assumed to be in an optimal state, the distribution of species phenotypes (and their underlying rates) can instead reflect the differential proliferation and removal of species within clades (27, 57, 58). Under this view, evolutionary trends are not predetermined by some adaptive zones available from the outset, but by the differential survival of species that constructed those spaces with time (50, 57, 59). Germane to this study is the much discussed trend of an increase in species size over evolutionary time, dubbed “Cope’s rule” (60, 61). Most of the groups studied here do seem to follow this pattern, with a net increase in average body size since the start of the radiation ($14$ out of $17$, with therocephalians, turtles, and penguins as exceptions; SI Appendix, Figs. S3–S19). Most of these enlargements, however, seem to be driven by the differential diversification of species rather than by increases at the lineage-level, as evinced by the drift in body size, α_x (Fig. 2). From those groups that increased in average size, only nonavian dinosaurs, cetaceans, tetraodontiform fish, and sloths presented a lineage tendency to increase in size (i.e., ${\alpha }_x>0$). Illustrative examples include clades notorious for attaining gigantic sizes, such as proboscideans and brontotheres, which did not reflect size increase at the lineage level (Fig. 2 and SI Appendix, Figs. S12 and S13), and, turtles that, despite a lineage trend to become larger, did not do so at the clade level (Fig. 2 and SI Appendix, Fig. S7).

I then examined the extent to which species sorting accounts for changes in average body size relative to lineage-level evolution (Fig. 3). Without explicitly incorporating unobserved speciation events and their relation to trait dynamics into past reconstructions, one cannot disentangle phenotypic evolution due to speciation from anagenetic change. However, one can have a minimum estimate of how the disappearance of observed species generated the empirical evolutionary trends (50, 62). I estimated group-average body size trajectories (i.e., “trends”) and estimated the amount of change in the trend explained by the removal of species, which I call the “prominence” of species sorting. Species sorting should not be confused with species-level selection (a cause of sorting) (63), and I emphasize that the prominence of species sorting used here only quantifies the relative importance of observed species disappearance compared to both observed speciation and anagenetic change (rather than of speciation and extinction compared to anagenetic change). These analyses were made possible by using the posterior data augmented trait histories rather than focusing on the trait and rate posterior averages, since the latter are not themselves DBM processes. Prominence ranges from $[-1,1]$, with sign denoting whether sorting has a decrease or increase effect on trends, and magnitude reflecting the proportion of change explained (Fig. 3; Materials and Methods). Intuitively, the extinction of species with similar body size with respect to the current clade average results in a prominence close to $0$, whereas if larger or smaller species are selectively pruned out, prominence will be close to $-1$ and $1$, respectively (Fig. 3A–C).

Fig. 3.

Prominence of species sorting in driving evolutionary trends. Two illustrative examples on how the selective removal of species can lead to evolutionary trends in clades. (A–C) At about $200$ Mya, coinciding with the Triassic-Jurassic extinction event, average turtles (Testudinata) body size was reduced drastically. (A) Shows the posterior average carapace length (m) with 50% and 95% Credible Intervals (CI) in lighter shades. (B) Five posterior lineage-specific evolutionary trajectories, showcasing the prominence of morphology removal over their transformation in generating evolutionary trends. (C) Average prominence of species sorting (i.e., the amount of average change explained by species removal over species change) through time, with 95% CI shown (red) when not overlapping $0$, as at $200$ Mya. (D–F) During the Lower Devonian, a loss of diversity of sea scorpions (Eurypterida) caused a slow-down in body size evolutionary rates. (D) Average evolutionary rate of body length (m) with 50% and 95% CI shown in lighter shades. (E) Lineage-specific evolutionary rates for five posterior samples. (F) Prominence of species sorting in determining rate trends, with 95% CI shown (red) when not overlapping $0$, as is the case at the ca.$413$ Mya and ca.$401$ Mya decreases.

Among hundreds of strong trend changes (those consistent across posterior trait histories) across groups, over 70% were explained by the disappearance of species (when measured at $1$ My intervals, ca. 60% at the $2$ Mys interval; SI Appendix, Figs. S23 and S24). When summed across all change in mean body size, species sorting explained, on average, $0.42$ and ranged from $0.19$ in sphenodontids to $0.66$ in nonavian dinosaurs (mean of $0.48$ with range $0.23$ to $0.7$ at the $2$ Mys interval; SI Appendix, Fig. S25). Nonetheless, simulations show that the total amount of average trait change explained by species sorting is almost entirely determined by the reconstructed phylogenetic tree (SI Appendix, Fig. S25). Much more relevant is then the directionality of prominence (which simulations confirm it does not depend on the empirical trees, as expected; SI Appendix, Fig. S26). The sorting of species sizes was not always random but its directionality was clade-specific (SI Appendix, Fig. S26): On average, smaller species were selectively pruned out in pterosaurs, proboscideans, brontotheres, short-faced kangaroos, and horses, while larger species were selectively removed in pseudosuchians, turtles, tetraodontiforms, cetaceans, and sloths. Thus, for some groups, species sorting was largely responsible for their average increase in body size, while, for others, most notably turtles, tetraodontiform fish, and cetaceans, species sorting acted against their lineage-level tendency for enlargement.

Species sorting could happen for evolutionary rates as well if, say, fast-evolving lineages are more likely to survive, so I carried on the same analysis using body size evolutionary rates (Fig. 3D–F). A notable, yet lower proportion of strong trend changes in evolutionary rates were explained by the sorting of species (about 44% and 39% at $1$ My and $2$ Mys interval, respectively). I found no consistent signal of selectively pruning fast (or slowly) evolving species: While on average, fast-evolving lineages were pruned out in pseudosuchians, turtles, and canins, slowly evolving species were more often removed in proboscideans, short-faced kangaroos, and new world monkeys (SI Appendix, Fig. S26). Unexpectedly, these results for rates again show that tendencies below the species level can oppose in directionality those above the species level, as with turtles, showing accelerated rates of lineage evolution but a selective pruning of fast-evolving species, or with new world monkeys, with decreasing rates of body size evolution yet the pruning of slowly evolving species.

Together, these findings suggest that a large extent of long-term evolutionary trends are shaped by the differential survival of species, and that the causes of the birth and death of organisms can differ from those of species (16, 27, 50).

Conclusions

It has been long recognized that the tempo and mode in evolution is reflected in the variation and distribution of evolutionary rates across the tree of life (1, 16). Incorporating the hyperdimensionality in phenotypes beyond body size, together with assessing how speciation determines phenotypic rate variation, as expected, for instance, by speciational evolution (62), are exciting avenues for future research made possible through the combination of the algorithms presented here and before (21, 34). While the findings in this study highlight the strong heterogeneity in evolutionary rates within and among taxa, their dynamics challenge the longstanding view of macroevolution wherein species are predetermined to fill a limited set of “adaptive zones” (15, 64). Adaptive landscape theory presumes the preexistence of a fitness gradient common to all species, autonomously determined by environmental factors [as epitomized in Ornstein–Uhlenbeck models (65)], and where species are reduced to passive entities (64, 66). This view predicts that evolutionary dynamics leads to determinate and relatively stable phenotypes that have been prestated before the emergence of species (66, 67). Although overarching physical constraints evidently exist (e.g., pressures of life on land), this schematic view ignores how organisms modulate and shape their environment, actively constructing their individual selection pressures, in a self-referential feedback that undermines the predictability embodied by adaptive landscape theory (66, 68). The findings here support instead an ever-expanding diversification of forms, curtailed by selective extinctions to assemble what, on aggregate, generate long-term macroevolutionary trends. Since one function can have a limited number of forms, but any one form has uncountable functions, species’ phenotypes should not be considered as composed of optimal adaptations to preexisting adaptive zones, but rather as enablements that continuously supply new possibilities (58, 69, 70). This is consistent with a more contingent perspective of evolution, indeterminate and far from equilibrium, where organisms actively explore, manipulate, and influence their ever changing environment (68, 71), in a continuous profusion of life forms.

Materials and Methods

Rate Heterogeneity in Trait Evolution Models.

One of the simplest models used to describe the evolution of continuous traits along a phylogenetic tree is BM. Here, the evolution through time of the average trait value of lineage i, denoted $x_i(t)$, is assumed to follow a Brownian diffusion process described by the stochastic differential equation (SDE): $d{x}_i(t)=\sigma dW(t)$, where $W(t)$ denotes the Wiener process (i.e., the standard Brownian motion) and ${\sigma }^2$ represents the rate of evolution, which is assumed to be time-constant and homogeneous across lineages. This last assumption of lineage-homogeneous rates has been shown to be biologically unrealistic and unfit for testing various hypotheses about the tempo and mode of evolution, encouraging the emergence of more flexible models of trait evolution that allow for heterogeneity in evolutionary rates across lineages and time.

Some phylogenetic models of trait evolution directly test whether their rate has not been constant through time. Here, all lineages alive at some time share the same rate, but the rate is allowed to fluctuate as a function of time or, for instance, following an environmental covariate (72). Pertinent to this study is the “early burst” model (EB) (14), later expanded by the nested EB (25). These models identify only one increase in rates, which for the EB is defined as having happened just before the crown of the tree while the nested EB identifies its location among the branches in the tree, and estimates a parameter that controls how rates slow down afterward. It is important to note that rates are only allowed to be constant or decay, and do not test if rates could have actually increased. Again, the decaying rate is assumed to be the same across all lineages within the clade delineated by the initial shift.

Others rather attempt to extract rate patterns from the data. To this end, they assign distinct evolutionary rates, which might be correlated or not, by either dividing the tree into subtrees, or to each branch in the tree. The Relaxed Random Walk (73) assigns an independent rate to each branch, which becomes identifiable when rates are assumed to share the same prior. FossilBM (74) and BayesTraits (18, 75) identify the number of distinct and uncorrelated rates (and drifts) across the tree. Within each branch, or subclade, rates and drifts are shared and are assumed constant. MuSSCRat (76) examines whether some of the estimated rate heterogeneity in a continuous trait is explained by another discrete character. Finally, models in which rates of evolution themselves follow a GBM have been recently developed in a Maximum Likelihood framework (30), and in a Bayesian framework “evorates” (31). I build on these important developments, which still rely on approximations of the likelihood of a “true” GBM-type rate model by resorting to branch or node specific average rates (30, 31), and add several new features as described below.

Diffused Brownian Motion Model.

Here, I assume that both the trait value and its rate of evolution for a given lineage follow a process of continuous diffusion through time (SI Appendix, Fig. S1). That is, the trait evolves under a stochastic process such that its rate of evolution is itself determined by another stochastic process, a particular instance of “stochastic volatility.” Specifically, the average trait for lineage i, $x_i(t)$, and the associated evolutionary rate, ${\sigma }_i^2(t)$, evolve following the coupled system of SDEs:

$$\begin{array}{cc}\hfill d{x}_i(t)& ={\alpha }_{x}dt+{\sigma }_i(t)dW(t)\hfill \end{array}$$ [1]

$$\begin{array}{cc}\hfill d\text{ln}({\sigma }_i^2(t))& ={\alpha }_{\sigma }dt+\gamma dW(t),\hfill \end{array}$$ [2]

where α_x and α_σ represents the drift (or average tendency) for traits and evolutionary rates, respectively, and γ the diffusion speed for evolutionary rates (SI Appendix, Fig. S1). That is, if ${\alpha }_x>0$, traits tend to increase with time, while if ${\alpha }_x<0$, traits are expected to decrease over evolutionary time. Similarly, if evolutionary rates have a tendency to accelerate, then ${\alpha }_{\sigma }>0$, or, contrarily, if the tendency is to decelerate, then ${\alpha }_{\sigma }<0$. Note that these drifts do not assume that rates are the same for all lineages alive at any time t (as in the EB or nested EB models), but rather describe a tendency for separate lineages to increase or decrease, regardless of their current trait or rate value. The degree of heterogeneity in evolutionary rates across lineages is represented by γ. The use of a GBM for the evolution of rates, ${\sigma }_i^2(t)$, is congruent with their nonnegative nature and with multiplicative drivers, such as the environment–organism interactions (66). At cladogenesis, the trait and associated rate are inherited identically among both daughter lineages. That is, for parent lineage a that gives rise to daughter lineages d₁ and d₂ at time t_a, we have that $x_a(t_a)=x_{d_1}(t_a)=x_{d_2}(t_a)$ and that ${\sigma }_a^2(t_a)={\sigma }_{d_1}^2(t_a)={\sigma }_{d_2}^2(t_a)$. The assumption that rates are inherited follows from long-standing observations (2), but also from understanding their proximal mechanisms, such as the build up of genetic variation, which are themselves expected to be inherited (mutation rates, generation times, among others). I call this process the “diffused Brownian motion” (DBM) model of trait evolution. Note that when ${\alpha }_x=0$, ${\alpha }_{\sigma }=0$ and as γ becomes infinitely small, the DBM converges to a simple BM process.

Likelihood.

Let a DBM process start at time $0$ with initial value $x_i(0)$ and initial rate ${\sigma }_i^2(0)$, then the probability after some time t, for the trait value and rate is

$$\begin{array}{cc}\hfill \text{ln}({\sigma }_i^2(t))\sim & \text{N}(\text{ln}({\sigma }_i^2(0))+{\alpha }_{\sigma }t,{\gamma }^{2}t)\hfill \\ \hfill x_i(t)\sim & \text{N}(x_i(0)+{\alpha }_{x}t,{\int }_0^t{\sigma }_i^2(s)ds),\hfill \end{array}$$

where ${\int }_0^t{\sigma }_i^2(s)ds$ is the stochastic integral representation.

Closed expression for this probability remains untractable (31), so I resort to numerically solving it using the Euler–Maruyama method. I partition time into a discrete grid of length m, where time steps are spaced from one another by a sufficiently small period δ, such that $t_0<t_1<...<t_{m-1}$ and where $t_j-t_{j+1}=\delta$, and generate sample paths for both $x_i(t)$ and ${\sigma }_i(t)$ at these times. The probability for the DBM process can then be straightforwardly computed as

$$\begin{array}{cc}& p(x_i(t),{\sigma }_i^2(t)|{\alpha }_x,{\alpha }_{\sigma },\gamma )\hfill \\ \hfill & ={\displaystyle \prod _{j=1}^m}p(x_i(t_j)|x_i(t_{j-1}),{\alpha }_x,\overline{{\sigma }_i^2}(t_j))p({\sigma }_i^2(t_j)|{\sigma }_i^2(t_{j-1}),{\alpha }_{\sigma },\gamma )\hfill \end{array}$$ [3]

where

$$p(x_i(t_j)|x_i(t_{j-1}),{\alpha }_x,\overline{{\sigma }_i^2}(t_j),\delta )=\text{N}(x_i(t_{j-1})+{\alpha }_x\delta ,\overline{{\sigma }_i^2}(t_j)\delta ),$$

$$\overline{{\sigma }_i^2}(t_j)=\text{g}({\sigma }_i^2(t_j),{\sigma }_i^2(t_{j-1})),$$

with $\text{g}$ being the geometric mean, and

$$p({\sigma }_i^2(t_j)|{\sigma }_i^2(t_{j-1}),{\alpha }_{\sigma },\gamma )=\text{N}({\sigma }_i^2(t_{j-1})+{\alpha }_{\sigma }\delta ,{\gamma }^2\delta ).$$

Let Ψ be a rooted and time-calibrated phylogenetic tree with or without sampled fossils with E edges. For clarity, if a fossil is a sampled ancestor (i.e., a fossil with at least one sampled descendant), I treat the edge before and after as two different edges. Then, based on a vector of trait values observed from extant or fossil species X, then the total likelihood for the process along the tree is the product of the likelihood (Eq. 3) across all edges

$$\begin{array}{c}\hfill p(X,x(t),{\sigma }^2(t)|{\alpha }_x,{\alpha }_{\sigma },\gamma ,\mathrm{\Psi })={\displaystyle \prod _{i=1}^E}p(x_i(t),{\sigma }_i^2(t)|{\alpha }_x,{\alpha }_{\sigma },\gamma ),\end{array}$$ [4]

while taking into account the tree structure in the inheritance of traits and rates.

Inference.

I developed Bayesian DA techniques to perform full probabilistic inference on the DBM model given a time-calibrated phylogenetic tree, with extinct and extant lineages, and trait values with their respective measures of uncertainty (if available) for all or some of the sampled lineages (SI Appendix, Fig. S1). In DA, one is able to estimate the posterior density $p(\theta |o)$ (i.e., the probability of θ, the set of model parameters, given the observed data o) by including augmented data a, such that $p(\theta |o)={\int }_{A}p(\theta |o,a)p(a|o)da$ (32). In DBM, given mean trait values X with associated uncertainty measures S, and phylogenetic tree Ψ, I can estimate the posterior probability for α_x, α_σ, γ, x₀ (the ancestral trait), and ${\sigma }_0^2$ (the ancestral evolutionary rate) as well as the whole diffusion paths describing the evolutionary history of the trait and rates along the tree, that is, arrive at $p(x(t),{\sigma }^2(t),{\alpha }_x,{\alpha }_{\sigma },\gamma |X,\mathrm{\Psi })$. Uncertainty around missing trait information is naturally and properly incorporated in the inference procedure while simultaneously generating posterior predictions for unobserved traits (as well as all rate values).

I start by estimating the evolutionary rate under a simple Brownian motion under phylogenetic independent contrasts (77). I then generate sample paths of the DBM process along the tree using this rate so that they match the observed X, sampling every small time step δ. In practice, edge lengths are not a multiple of δ, so the last time step is always smaller, but I remove this intricacy for clarity and simplicity in the following description. I then use Markov chain Monte Carlo (MCMC) to iteratively sample from the joint posterior distribution, integrating over all likely DBM histories given the data, with the following specific updates. This procedure yields posterior samples of the full trait and respective rate evolution which can be used for post hoc analyses and visualizations (SI Appendix, Fig. S1).

Rate diffusion path updates.

For a diffusion process $y(t)$ along a tree with drift a, I make use of the general conjugate relationship where the distribution for a bifurcating node with ancestral lineage q and descendant lineages d₁ and d₂, with respective edge lengths of t_q, $t_{d_1}$, and $t_{d_2}$ and absolute rates of s_q, $s_{d_1}$, and $s_{d_2}$,

$$\begin{array}{cc}& y_q{(t_q)}^{\prime }\sim \hfill \\ \hfill & \text{N}\left(\left(\frac{y_q(t_0)+a{t}_q}{s_q}+\frac{y_{d_1}(t_{d_1})-a{t}_{d1}}{s_{d_1}}+\frac{y_{d_2}(t_{d_2})-a{t}_{d_2}}{s_{d_2}}\right)s_n^{-1},s_n^{-1}\right),\hfill \end{array}$$ [5]

where $s_n^{-1}=s_q^{-1}+s_{d_1}^{-1}+s_{d_2}^{-1}$. Similarly, for the distribution at a sampled ancestor node, with only one ancestor and one descendant edge, I use the following general conjugate distribution

$$\begin{array}{cc}& y_q{(t_q)}^{\prime }\sim \hfill \\ \hfill & \text{N}\left(\frac{\left(y_q(t_0)+a{t}_q)s_{d_1}+(y_{d_1}(t_{d_1})-a{t}_{d1})\right)s_q}{s_q+s_{d_1}},\frac{s_q{s}_{d_1}}{s_q+s_{d_1}}\right).\hfill \end{array}$$ [6]

Initial attempts at sampling the rate diffusion paths using the full conditional distribution were computationally inefficient, so I use simple Metropolis–Hastings (MH) updates for ${\sigma }^2(t)$. I first randomly and uniformly select an internal node in the tree. If the node is a bifurcating node, I propose a new rate value ${\sigma }_q^2{(t_q)}^{\prime }$ (note that ${\sigma }_q^2{(t_q)}^{\prime }={\sigma }_{d_1}^2{(t_0)}^{\prime }={\sigma }_{d_2}^2{(t_0)}^{\prime }$) conditional on the rates at the start of the ancestor and at the end of the daughters using Eq. 5, where $y(t)=\text{ln}({\sigma }^2(t))$, $a={\alpha }_{\sigma }$, and $s_i=t_i{\gamma }^2$. If the node is a sampled ancestor, I propose a new rate value conditional on the rates at the endpoints of the ancestor and daughter using Eq. 6. I then make diffusion path proposals ${\sigma }^2{(t)}^{\prime }$ using Brownian bridges conditional on the endpoints and the new proposed value at the node for each lineage. To sample a Brownian bridge for a diffusion process along lineage i, $y_i(t)$, starting at $t_0=0$ and ending at t_i, conditional on $y(t_0)=y_s$ and $y(t_i)=y_f$, I use the conjugate relationship

$$p(y_i(t)|y(t_0)=y_s,y(t_i)=y_f)=y_i(t)-\frac{t}{t_i}{y}_f.$$

Note that the drift, α_σ, cancels out in this distribution. Finally, if the node leads to a terminal edge, I make a forward BM simulation for $\text{ln}({\sigma }^2(t))$ starting at the node’s value.

Since the proposal probability cancels out with the diffusion of ${\sigma }^2(t)$ in the likelihood, the MH acceptance ratio, a, for lineage i becomes

$$\begin{array}{c}\hfill \text{ln}(a)={\displaystyle \sum _{j=1}^{m-1}}\frac{{(x_i(t_j)-x_i(t_{j-1}))}^2}{2\delta }\left(\frac{1}{\overline{{\sigma }_i^2}{(t_j)}^{\prime }}-\frac{1}{\overline{{\sigma }_i^2}(t_j)}\right)+\\ \hfill \frac{(\text{ln}({\sigma }_i^2(t_{j-1}))+\text{ln}({\sigma }_i^2(t_j))-\text{ln}({\sigma }_i^2{(t_{j-1})}^{\prime })-\text{ln}({\sigma }_i^2{(t_j)}^{\prime }))}{4}.\end{array}$$ [7]

I also added a scaling update for the rates, that is, I multiply all rates by a positive scalar s, itself drawn from a log Normal distribution, such that ${\sigma }^2{(t)}^{\prime }=s{\sigma }^2(t)$, and accepted following the MH ratio.

Trait diffusion path updates.

To update the trait diffusion paths I use the full conditional distribution $p(x_i(t)|X,{\sigma }_i^2(t),{\alpha }_x)$ ($p(x_i(t)|·)$ is conditionally independent of α_σ and γ), that is, I use Gibbs sampling. One can sample directly from this distribution given that the full path of ${\sigma }^2(t)$ is available. As with the rate updates, I use the conjugate relationships in Eqs. 5 and 6 to update internal nodes, where $y(t)=x(t)$, $a={\alpha }_x$, and $s_i={\int }_0^{t_i}{\sigma }_i^2(s)ds$. If the internal node leads to a sampled ancestor with trait information (i.e., available in X), I simply sample Brownian bridges conditioned on the observed trait value and the rate diffusion path. When there is uncertainty around the observed trait value, I assume it follows a Gaussian distribution with the average observed trait as mean and the respective uncertainty as variance, and then sample using conjugate relationships. Other probability distributions could readily be used as priors for observed trait uncertainty, but for simplicity I assume a Normal variance. When there is no information in trait values, I perform forward DBM simulations. This properly and naturally incorporates extant and fossil missing trait information as well as uncertainty around observed traits. Moreover, following the Bayesian paradigm where posterior inference and prediction are done simultaneously (78), the data augmentation algorithm generates posterior predictions of trait values given the other observed data and the model.

α_x, α_σ, and γ updates.

I take advantage of the conjugate relationship of the Normal and Inverse Gamma distribution for the drift in traits, α_x, and rates α_σ, as well as for the diffusion of rates, γ, to perform Gibbs sampling. Specifically, I specify a Gaussian distribution as prior on α_x, such that $p(\alpha )=\text{N}(\nu ,\tau )$, leading to the following full conditional posterior distribution

$$p({\alpha }_x|·)=\text{N}\left(\frac{X_s{\tau }^2+\nu }{L_s{\tau }^2+1},\frac{{\tau }^2}{L_s{\tau }^2+1}\right),$$

where $L_s=\sum _{i=1}^E\sum _{j=1}^{m-1}\frac{{\delta }_j}{{\overline{{\sigma }_i(t_j)}}^2}$ and $X_s=\sum _{i=1}^E\sum _{j=1}^{m-1}\frac{x_i(t_{j+1})-x_i(t_j)}{{\overline{{\sigma }_i(t_j)}}^2}$. Here, $\overline{{\sigma }_i(t_j)}$ is the geometric mean of the evolutionary rates between t_j and $t_{j+1}$. A derivation of this distribution can be found in SI Appendix.

For α_σ, I also specify a Gaussian distribution, $p({\alpha }_{\sigma })=\text{N}(\iota ,ϵ)$, leading to the full conditional posterior distribution

$$p({\alpha }_{\sigma }|·)=\text{N}\left(\frac{{(\frac{\gamma }{ϵ})}^2\iota +{\sum }_{i=1}^E(\text{ln}({\sigma }_i^2(t_m))-\text{ln}({\sigma }_i^2(t_0)))}{{(\frac{\gamma }{ϵ})}^2+L},\frac{{\gamma }^2}{{(\frac{\gamma }{ϵ})}^2+L}\right),$$

where L is the tree length (sum of all edge lengths). For γ, I specify an Inverse Gamma distribution, such that $p(\gamma )={\mathrm{\Gamma }}^{-1}(\kappa ,\beta )$, which leads to the full conditional posterior distribution

$$\begin{array}{cc}& p({\gamma }^2|·)=\hfill \\ \hfill & {\mathrm{\Gamma }}^{-1}\left(\kappa +\frac{N}{2},\beta +\frac{1}{2\delta }{\displaystyle \sum _{i=1}^E}{\displaystyle \sum _{j=1}^m}{(\text{ln}({\sigma }_i^2(t_j))-\text{ln}({\sigma }_i^2(t_{j-1}))-{\alpha }_{\sigma }\delta )}^2\right),\hfill \end{array}$$

where $N=\sum _{i=1}^E\sum _{j=1}^{m}1$. A derivation of these distributions for α_σ and γ, can be found in ref. 21 and corresponds to the results in ref. 79.

Validation.

I assessed the behavior of the DBM model inference using a simulation study. I first simulated $200$ trees of at least $50$ sampled extant or extinct species at the tips using the constant FBD model, with speciation rate and extinction rate of $1.5$, and fossilization rate of $0.1$ during $15$ time units (21). This resulted in trees with an average of $75$ and a range of about $50$ to $240$ tips. I then simulated on each of these trees a DBM process where I uniformly sampled the trait root state following $x_0\sim \text{U}(-0.5,0.5)$, the root rate state ${\sigma }_0^2\sim \text{U}(0,0.4)$, the traits drift ${\alpha }_x\sim \text{U}(-0.3,0.3)$, and the rates drift ${\alpha }_{\sigma }\sim \text{U}(-0.3,0.3)$, and the rates diffusion $\gamma \sim \text{U}(0.0,0.4)$. For each simulation I performed inference assuming the priors $\alpha \sim \text{N}(0,100)$ and $\gamma \sim {\mathrm{\Gamma }}^{-1}(0.05,0.05)$, and running an MCMC chain for $5.5\times {10}^6$ iterations, discarding the first $5\times {10}^5$ as burn-in and sampling every $5\times {10}^3$.

SI Appendix, Fig. S2 shows the comparison between the simulated and posterior values, with good overall model and inference behavior. For the trait and rate root values, x₀ and ${\sigma }_0^2$, respectively, as well as the drifts for traits α_x and rates α_σ, there is proper accuracy and proper coverage, with about 95% of the true values falling within the 95% Highest Posterior Interval (HPD) for these parameters (SI Appendix, Fig. S2). Similarly, when sampling the simulated and the posterior distribution of both $x(t)$ and ${\sigma }^2(t)$ diffusion processes along the tree at regular intervals, there is no bias, good accuracy, and proper average coverage at over 95% (SI Appendix, Fig. S2). The estimates for γ, the diffusion of evolutionary rates, increased concomitant with the simulated values but display lower accuracy and coverage than all the other parameters (SI Appendix, Fig. S2). While there seems to be some information in the data, the specific parameterization of the prior, ${\mathrm{\Gamma }}^{-1}$, exerts considerable influence on the shape of the posterior, as found also in birth–death models with diffusion of rates (21). This proportionality suggests that at least one can compare relative, if not absolute, values of γ. Importantly, mediocre accuracy and coverage does not seem to have an impact on our ability to recover the simulated trait and rate diffusion values.

Implementation.

All simulation and inference algorithms were implemented and are available as part of the “Tapestree” package for Julia software (80), available at https://github.com/ignacioq/Tapestree.jl (81).

Body Size Evolution.

I compiled phylogenetic and body size information for $17$ groups with a wide taxonomic coverage, detailed in SI Appendix, Table S1. I selected phylogenetic trees that were time-calibrated using the fossilized birth–death model (43), and where more than half of the (known) species were represented in the tree. I compiled and supplemented body size information from the primary literature to have the widest coverage for the species within the phylogenetic trees as possible (Dataset S1). When available, I added trait uncertainty (either due to known error, intraspecies variance, or other; SI Appendix, Table S1). In total, this dataset contains $2,950$ extinct and $792$ extant species represented across the phylogenetic trees, with body size data for $2,788$ species. I randomly sampled $20$ trees from the posterior for each taxa, except for nonavian dinosaurs and sloths (Folivora) for which I could not obtain the posterior distribution of trees.

I parameterized ambiguous priors: For α_x and α_σ, I used a $\text{N}(0,10)$ and for γ a ${\mathrm{\Gamma }}^{-1}(0.05,0.05)$. I ran the DBM model for each of the trees of each of the groups using the DA procedure for $5.5\times {10}^6$ iterations with the first $5\times {10}^5$ iterations discarded as burn-in and sampling every $2\times {10}^4$. Note however that one iteration actually comprises multiple parameter updates. Together, this comprises $302$ separate MCMC chains and each returned $250$ posterior samples containing full trait and rate histories and the governing parameters (i.e., α, γ) for each posterior tree for each taxonomic group. I manually checked for chain convergence and Effective Sample Sizes. All analyses, manipulations, post hoc analyses, including posterior average and variance estimation, and plots were conducted in the “Tapestree” package for Julia (80, 81). All the data used together with the code are available as SI Appendix. Group specific results are displayed in SI Appendix, Figs. S3–S19.

Influence of trait variance.

This implementation of the DBM model can account for trait variance due to measurement error, uncertainty, or within-species variation. However, in the empirical analyses, I was only able to include information for trait variance for three (i.e., Proboscidea, Cetacea, and Caninae) out of all the analyzed taxonomic groups. Trait variance can overestimate rate information, particularly between closely related species (31, 82, 83), and thus could, contingent on the data configuration, bias against, or toward finding decaying or increasing evolutionary rates. Consequently, I carried further analyses to explore whether and how the main results could be biased by not accounting for trait uncertainty.

First, I carried a simple simulation study to test how α_σ can be influenced when adding tip variance, where I simulated $5$ DBM models on fossilized birth–death trees, with equal parameters: $x_0=0$, ${\sigma }_0^2=0.2$, ${\alpha }_x=0$, γ = 0.2, and, importantly, with ${\alpha }_{\sigma }=-0.2$. I then made inference assuming no trait variance (the “truth” in this scenario), and the same trait variance of $0.05$ and $0.1$ for all species, respectively representing about 10% and 20% of between species variance. I found that including trait variance has a deflating effect on α_σ, with higher trait uncertainty yielding a more negative rate drift (SI Appendix, Fig. S21). This could be explained by the model allocating part of the evolutionary rate into trait variance (thus underestimating rates between closely related lineages, increasing the slowing down effect).

Second, and given the above, I ran the DBM model again for all groups for which I did not include trait variation. Namely, I estimated the average amount of trait variance from Cetaceans per their logarithmic unit of size, which was about $0.005$ SDs, and used this to add variances around trait information particular to each group’s size measurement. Adding this trait variance had negligible effects on the estimates of α_σ, as shown in SI Appendix, Fig. S22, suggesting that the absence of rate slow downs in body size evolution seem not to be an artifact of discounting measurement errors, uncertainty, or within species variation.

Prominence of Species Sorting.

I estimated the effect of species sorting on the evolutionary trend of each clade, which I call the “prominence” of species sorting. Because I am not explicitly modeling the birth–death process, I cannot differentiate if trait change is due to unobserved speciation events, or from anagenetic evolution. However, I can measure the minimal effect that the disappearance of species has had in fashioning trends. While, model-wise, there should not be a bias in the traits of unobserved extinct species, certain phenotypes are more liable to fossilization than others, including body size. Indeed, ceteris paribus, larger body sizes are more prone to being represented in the fossil record than smaller organisms (84). Thus, a caveat of this analysis is not accounting for unobserved species, whose probability of being represented is likely size-dependent.

Prominence ranges from $[-1,1]$, estimating both the directionality and magnitude of the effect of species sorting on the average trait trend of the taxonomic group. A negative value of prominence indicates that the removal of species contributes to a decrease in the trend, and vice versa (Fig. 3). Its absolute magnitude indicates the proportion of change explained by species sorting, with $1$ denoting that all the change in average trait change was explained by species sorting. Prominence is measured for the change over a given time interval. Let $t_0<t_1$ be the start and end time where we sample the vector of traits $\mathbf{x}(t_0)$ and $\mathbf{x}(t_1)$, respectively. The total change in trend is then the difference of the two averages, $\mathrm{\Delta }x=\overline{\mathbf{x}({\mathbf{t}}_{\mathbf{1}})}-\overline{\mathbf{x}({\mathbf{t}}_{\mathbf{0}})}$. This total change can be totally or partly explained by the anagenetic change of each lineage i alive at t₁. If there are n lineages alive at time t₁, then this amounts to the average of their change, $\mathrm{\Delta }{x}_a=\frac{1}{n}\sum _i{x}_i(t_1)-x_i(t_0)$. Note that some of the n lineages can be species that arose in the interval $[t_0,t_1]$, so I take into account the effect of new species on top of the anagenetic evolution. Prominence, the role of species sampled at time t₀, but not at t₁, is then what remains, standardized, $(\mathrm{\Delta }x-\mathrm{\Delta }{x}_a)/|\mathrm{\Delta }x|$, and later constrained so as to remain between $[-1,1]$. Unlike the average trait change or the anagenetic change, the standardization and limits imposed on Prominence cause it to have a skewed distribution. In particular, note that very small changes in average traits can still generate large values (close to $-1$ or $1$) of Prominence.

Taking advantage of the posterior DA samples of the full trait and rate histories, I estimated the prominence of species sorting every $1$ My and every $2$ Mys for each one. I then combined all samples per taxa and highlighted those intervals with strong changes in traits and rates, that is, those where the 50% Credible Interval of changes across DA samples did not overlap $0$. Similarly, I highlighted those intervals in which the 50% Credible Interval of prominence across DA samples did not overlap $0$. The results were similar regardless of measuring every $1$ or $2$ Mys, so I highlight only the former ones in Fig. 3 and SI Appendix, Figs. S21 and S22.

To estimate the total amount of change explained species sorting for each DA tree, for each taxonomic group, I estimated the proportion of the total amount of absolute change in traits and rates that is explained by species sorting. Specifically, this is the sum of absolute changes multiplied by the prominence of sorting across every $1$ or $2$ Mys in traits or rates, divided by the sum of all absolute changes, that is, for every j interval of $1$ or $2$ Mys out of m, $\frac{{\sum }_j^m|\mathrm{\Delta }{x}_j||{\text{p}}_j|}{{\sum }_j^m|\mathrm{\Delta }{x}_j|}$, where ${\text{p}}_j$ is the prominence of species sorting for interval j. The results for each clade for intervals of $1$ or $2$ Mys are shown in SI Appendix, Fig. S23. Similarly, to estimate if species were selectively removed based on their size or their rates, I estimated the average prominence for each DA tree. If large species were selectively pruned out, the average prominence of traits should be less than $0$, while if smaller species were selectively removed, average prominence should be larger than $0$. Likewise with evolutionary rates, where a prominence in rates below $0$ reflects the removal of fast-evolving species, while a prominence larger than $0$ presents evidence for the selective pruning of slow rate species. The results for each clade for intervals of $1$ or $2$ Mys are shown in SI Appendix, Fig. S24.

Finally, to estimate the extent to which the particular empirical trees could explain the differences observed in the total amount of change and the directionality explained by species sorting, I conducted a simulation study. Specifically, I simulated $20$ Brownian motion processes for each empirical tree for each clade, and then carried out the same analyses as above. These null simulations show that the total amount of change explained by prominence is almost completely determined by the empirical trees (plotted as gray shadows in the background for each taxonomic group in SI Appendix, Fig. S25). However, as expected, the number of consistent trait changes and prominence was $0$, and the directionality of prominence was not biased (also plotted as gray shadows in the background for each taxonomic group in SI Appendix, Fig. S26).

Supplementary Material

Appendix 01 (PDF)

Dataset S01 (CSV)

Data, Materials, and Software Availability

Simulation and inference algorithm data have been deposited in GitHub (https://github.com/ignacioq/Tapestree.jl) (81). All other data are included in the manuscript and/or supporting information.