A new method for testing evolutionary rate variation and shifts in phenotypic evolution

Abstract

1. Quantifying phenotypic evolutionary rates and their variation across phylogenetic trees is a major issue in evolutionary biology. A number of phylogenetic comparative methods (PCMs) currently perform such task. However, available PCMs can locate rate shifts pertaining to entire portions of the phylogeny, but not those expected to occur at the level of individual species and lineages, such as with the idea that body size changes more rapidly in insular vertebrates. Still, most PCMs cannot deal with fossil phylogenies, albeit fossils provide highly desirable information when it comes to understand trait variation and evolution.
2. We developed a PCM based on phylogenetic ridge regression, which we named RRphylo, which assigns an evolutionary rate to each branch of the phylogeny, and is designed to locate rate shifts relating to entire clades, as well as to unrelated tree tips. We tested RRphylo on simulated trees and data to assess its performance under different conditions. Then, we repeated its application with two real case scenarios, the evolution of flight in ornithodirans and mammals and body size evolution in insular mammals, which are usually subsumed to evolve under different range regimes than terrestrial and continental species respectively.
3. RRphylo performs well across all different conditions. The simulation experiments demonstrated it has low Type I and Type II error rate. We found significant evidence that flight accelerates the rate of body size evolution in vertebrates, and that the acquisition of very large body size slows down the rate. Still, insular mammals body size evolution is not faster than in continental species.
4. RRphylo is a new PCM ideal to estimate variation and shift in the rate of phenotypic evolution with fossil data. In addition to testing evolutionary rate variation, it is open to a variety of further questions, such as the evolution of rates in time, the estimation of ancestral states and the estimation of phenotypic trends over time.

1 INTRODUCTION

Animal clades show surprisingly large differences in their rates of phenotypic evolution (Adams, 2014; Harmon, Schulte, Larson, & Losos, 2003). Such dissimilarity in rates may depend on ecological variation (Collar, O'Meara, Wainwright, & Near, 2009; Mahler, Revell, Glor, & Losos, 2010; McPeek, Shen, Torrey, & Farid, 2008; Raia & Meiri, 2011), differences in developmental and life‐history traits (Okie et al., 2013; Thomas, Freckleton, & Székely, 2006), on the deployment of evolutionary novelties (Clarke, Lloyd, & Friedman, 2016; Garcia‐Porta & Ord, 2013), and often take place during adaptive radiations (Arbour & Santana, 2017; Clavel & Morlon, 2017; Cooney et al., 2017). At studying the fossil record, differences in evolutionary rates were traditionally expressed in terms of e‐fold (Euler's number) changes in a trait over one million years (i.e. “darwins”), phenotypic standard deviations per generation (i.e. “haldanes”) (Gingerich, 1993; Haldane, 1949), comparing the realized phenotypic divergence to the expectation based on random genetic drift (Lynch, 1990), or contrasting trait variance between groups within a realized morphospace (Benson, Frigot, Goswami, Andres, & Butler, 2014; Brusatte, Benton, Ruta, & Lloyd, 2008). Under all these approaches, the basic expectation is that rate variation (disparity) differs between taxa. However, disparity is better modelled by considering the time evolution took to produce it (a true rate), and taking into account expected trait variance (Hunt, 2012; O'Meara, Ané, Sanderson, & Wainwright, 2006). Hence, phylogenetic comparative methods (PCMs) offer the most obvious tool for studying rate variation in fossil, as well as in living taxa, since both disparity (Revell, Harmon, Langerhans, & Kolbe, 2007) and rates (Adams, 2013; Eastman, Alfaro, Joyce, Hipp, & Harmon, 2011; O'Meara, 2012; Rabosky, 2014; Revell, Harmon, & Collar, 2008) are properly assessed with phylogenetic trees and data. Surprisingly, there has been limited use of PCMs to study rate variation in the fossil record (Lloyd, Wang, & Brusatte, 2012). There are a number of reasons for this. First, the available phylogenetic information for fossil species is rather limited as compared to living taxa (Diniz‐Filho, Loyola, Raia, Mooers, & Bini, 2013). Second, although a number of PCMs are designed to locate significant shifts in the rate of evolution along a phylogeny (Rabosky, 2014; Revell, Mahler, Peres‐Neto, & Redelings, 2012; Slater, 2013), these methods work with entire clades, whereas several alleged cases of evolutionary accelerations or slowdowns regard individual species and lineages, such as the extremely slow rate of evolution in living fossils (Clarke et al., 2016; Li & Ni, 2016), the rate of body size evolution in insular species (Millien, 2011; Raia & Meiri, 2011) and the rate of brain size evolution in our own lineage (Diniz‐Filho & Raia, 2017; Shultz, Nelson, & Dunbar, 2012). Third, although there are a number of methods available in the literature to apply model‐free computations of the evolutionary rates (Thomas & Freckleton, 2012), many of them do not work with fossil phylogenies (e.g. rpanda Morlon et al., 2016; BayesTraits Pagel & Meade, 2014; bamm Rabosky, 2014; Rabosky, Donnellan, Grundler, & Lovette, 2014), or are computationally very intensive (Thomas & Freckleton, 2012). Eventually, within the context of PCMs, deviations from the background evolutionary rate are usually assessed as departures from the Brownian motion model, which predicts that species mean phenotypes evolve through a flat adaptive landscape, whereas evolution towards peaks in the fitness landscape (adaptive optima) implies a slow‐down in the evolutionary rate (Pennell & Harmon, 2013). While this potential limitation does not pertain to the application of PCMs to fossil phylogenies per se, it must be considered at interpreting patterns of rate variation, and the potential process behind them.

Herein, we present a new method for testing the existence of rate shifts in phenotypic evolution, using a PCM approach. The method, RRphylo, is based on phylogenetic ridge regression (Kratsch & McHardy, 2014), and was designed to search for significant evolutionary rate variation across a phylogeny as applied to entire clades, or sparsely across the phylogeny, for both univariate and multivariate data. Phylogenetic ridge regression applies no evolutionary model a priori, and by assigning a distinct rate to each branch of the tree, it is apt to study rate variation down to the level of individual, unrelated species. RRphylo is explicitly thought to deal with phylogenies including extinct species, which is a further advantage over methods that cannot locate change in rates with fossil phylogenies, and is welcome because the inclusion of fossils is crucial to retrieve the correct information about the tempo and mode of phenotypic evolution (Schnitzler, Theis, Polly, & Eronen, 2017; Slater, Harmon, & Alfaro, 2012).

We applied RRphylo to simulated trees and data first, and assessed its performance under different intensity and ubiquity of rate variation in phylogenetic trees. Eventually, we applied it to two different real case scenarios, the rate of evolution in insular mammals, which includes a rich record of recently extinct species, and is viewed as either exceptionally fast by some authors (Lister, 1989; Millien, 2011), or quite unexceptional by others (Raia & Meiri, 2011), and the evolution of body size in ornithodiran archosaurs, the clade that includes both the largest land vertebrates ever, sauropod dinosaurs (Sander et al., 2011), and the small, rapidly diversifying bird lineages (Lee, Cau, Naish, & Dyke, 2014a).

2 MATERIALS AND METHODS

2.1 Phylogenetic ridge regression

RRphylo develops on phylogenetic ridge regression as described in Kratsch and McHardy (2014), and Gubry‐Rangin et al. (2015). It applies penalized ridge regression to the tree and species data. The difference between the phenotype at each tip and the phenotype at the tree root is the sum of a vector of phenotypic transformations along the root to tip path, given by the equation ΔP = β_1l1 + β_2l2 +… + β_nln where the β_ith and l_ith elements represent the regression coefficient and branch length, respectively, for each i_th branch along the path. As regression slopes, the β coefficients represent the actual rate of phenotypic transformation along each branch. The matrix solution to find the vector of β coefficients for all the branches is given by the equation  = (L^T L + λI)⁻¹ L^T y (James, Witten, Hastie, & Tibshirani, 2013); where L is the matrix of tip to root distances of the tree (the branch lengths), having tips as rows. For each row of L, entries are zeroes for the branches outside the tip to root path, and actual branch lengths for those branches along the path. The vector is the vector of phenotypes (tip values), is the vector of regression coefficients and λ is a penalization factor that avoids perfect predictions of , therefore allowing for the estimation of the vector of ancestral states (computed as , where Lʹ is the node to root path matrix, calculated in analogy to L, but with nodes as rows).

Kratsch and McHardy (2014) applied L2 (quadratic) penalization to estimate λ. We departed from this approach and applied a biologically oriented, conservative solution to the penalization problem, finding the maximum likelihood estimate of λ minimizing the rate (β coefficients) variation along the root to tip paths.

The R function we provide to compute rates is named RRphylo, it takes a tree and a phenotype (either univariate or multivariate) as arguments, and produces the objects: $tree, the fully dichotomous version of the tree argument; $tip.path, the L matrix; $node.path, the L′ matrix; $rates, the vector of evolutionary rates; $ace, the vector of ancestral state estimates; $y.estimates, the vector of estimated tip states; and $lambda, which is the fitted penalization factor, as in the examples below (developed in the R environment):

• ## produce a random, non‐ultrametric tree

• library(ape)

• rtree(100)‐>tree

## setBM produces a phenotypic vector or matrix with a desired trend in either the phenotype over time or in the evolutionary rate over time, see the vignette for full explanation of this function

• setBM(tree,nY=1,type=“brown”)‐>y

• ## run phylogenetic ridge regression

• RRphylo(tree,y)‐>RR

The computation of the penalization factor uses the function optL (embedded within RRphylo), to find the maximum likelihood estimate of λ minimizing the rate variation from the tree root towards the tips. Large absolute values of λ are consistent with very high phylogenetic signal (meaning that phylogenetically close species will tend to have very similar phenotypes, see the vignette for full explanation). We empirically found that λ values from 0 to 1 are consistent with the Brownian motion model of evolution.

2.2 Searching for rate shifts

For a rate shift to be real, the β coefficients attached to the branches evolving under a distinctive rate regime must be either statistically larger or smaller than the coefficients calculated for the other branches of the tree. The basic procedure we devised to assess hypotheses about rate shifts was to compute the difference of mean rates between branches hypothesized to evolve under different rate regimes, and then to assess for the significance of such difference of means through randomizations. Since RRphylo assigns a specific rate to each branch of the tree, it is feasible to apply indifferently when the different rate regimes pertain to distinct clades, or to a number of unrelated species across the phylogeny. We refer to these two distinct situations as “clade”‐level and “sparse” (phylogenetically) distributed conditions. Under the “sparse” condition, a clade level reconstruction is theoretically possible given appropriate estimation of the states. Yet, we preferred avoiding inference on ancestral states since the currently available methods rest on the often‐violated assumption that the trait of interest evolves at a uniform rate across the tree (King & Lee, 2015).

The R function we provide to locate evolutionary rate shifts and test specific hypothesis about the rate attached to different clades or tip states is search.shift. It takes an object produced by RRphylo, and can be used to automatically locate the shifts, test different clades where distinct rate regimes are presumed to apply, or test for rate differences among different tip states.

## automatic detection of clades with either significantly high or low average absolute rates, this function also produces a .pdf image highlighting clades with distinctive rates. The file is stored in the R working directory

• search.shift(RR,auto.recognize=“yes”,status.type=“clade”,covariate= “FALSE”)

## testing a specific hypothesis about clades (corresponding to nodes 150 and 160 in the example below) presumed to evolve at different rates as compared to each other, and to the rest of the tree

• search.shift(RR,auto.recognize=“no”,status.type=“clade”,covariate= “FALSE”, node=c(150,160),test.single=“yes”)

## testing the hypothesis that rates differ depending on species status (as defined by the argument “state”)

• search.shift(RR,auto.recognize=“no”,status.type=“sparse”,covariate= “FALSE”,test.single=“no”,state = state)

Eventually, search.shift can further test the effect of a covariate on the rate values, and take the residuals of the rate versus covariate regression (instead of the absolute rate values fitted by RRphylo) to contrast rates among different branches. It is important to notice that the covariate must be the same length as the rate vector (i.e. twice the number of tips, minus one). If the covariate is the very phenotypes the rates are computed for, the user should just specify the phenotype as the argument “cov.” Otherwise, if a different phenotype is selected as the covariate, rates for this second phenotype must be subjected to RRphylo first, and then the ancestral estimates and the tip values collated in this order and fed to search.shift as the “cov” object:

## factoring out the effect of a covariate in search.shift:

# if the covariate is the same as the phenotype the rates are computed for:

• RRphylo(tree,y)‐>RR

• search.shift(RR,auto.recognize=“no”,covariate=“TRUE”,cov=y,…)

# if the covariate is a different phenotype:

• RRphylo(tree,y)‐>RR

• RRphylo(tree,yy)‐>RRcov

• c(RRcov$ace,yy)‐>yy.cov

• search.shift(RR,auto.recognize=“no”,covariate=“TRUE”,cov=yy.cov,…)

The function search.shift automatically plots the real difference of rates per species status (or amongst specified clades), superimposed on the distribution of random rate difference, and provides the p‐values for the rate variation test. If the argument covariate is set to “TRUE” and the covariate specified, a vector of rate residuals (of the absolute rate values against the covariate) is added.

The whole set of functions written to use the RRphylo method, along with a vignette explaining details and providing written examples to work with the ornithodiran data is available at https://doi.org/10.5281/zenodo.1041611.

2.3 Simulations

We devised a number of simulation experiments to test for the appropriateness of RRphylo. We produced 100 random, non‐ultrametric trees of 100 species. For each tree, we simulated a vector of phenotypes according to the Brownian motion (BM) model of evolution, taking care that there was no trend in the data. To test the “clade” distributed condition, we randomly selected a node N subtending one‐tenth to one‐half of the species in the tree, and multiplied the phenotype of these species by a factor F = 10 (to simulate phenotypes evolving under increased rates) or F = 0.1 (to test for rate decrease). The expectation is that the mean rate of evolution (i.e. the mean value of the absolute β coefficients) computed along the z branches descending from N was statistically higher than for the branches not descending from N in the first case, and smaller in the second. We assessed the significance of these expectations by randomly partitioning 10,000 times the tree branches into a group of size z and another including the rest of the tree branches, and then computing the difference of the mean absolute rates between the two groups. The actual difference was finally contrasted to the distribution of the 10,000 randomly generated differences. Differences in means were computed both before and after modifying the phenotypes assigned to a different rate regime. This allows estimating both Type I (detecting a difference in means when it is not real) and Type II (failing to detect a real difference) errors.

Under the “sparse” condition, it is not possible to apply the same procedures as with the “clade” case. This happens because the starting phenotypes to multiply to F could be very different from each other, whereas under the “clade” condition, they are more similar than expected by chance because of their phylogenetic proximity. In other words, with F = 10 the phenotypes evolving under faster rate will be more different from each other than with the “clade” case, forcing RRphylo to produce high rates for these species and therefore increase Type I error. Similarly, with F = 0.1 the small rates produced will make the test conservative. Hence, to test RRphylo under the “sparse” case, we first calculated the rates for the species under the untransformed . Then, we sampled a number n of species (with 10 < n < 50) among the 50 species with the smallest rates for the “decreased rate” situation, and among the top 50 to test for the “increased rate” situation. This way we avoided forcing RRphylo to compute “extreme” rates for the selected species, which would maintain the test fair, although it makes it impossible to estimate Type I error. We assigned these n species to the group evolving under the shifted rate regime, and multiplied their phenotypes by F. After this, we recalculated the rates and assessed significance of rate change as with any other case. The additional, critical test performed in these simulations was to contrast the new rates to the rates originally calculated for these same n species, under the expectation that with F = 10 the new rates computed for the n species become larger, and with F = 0.1 they become smaller. Overall, we ran four sets of simulations. Rate increase under the “clade” case C+, rate decrease in the “clade” case C−, rate increase under the “sparse” case S+ and rate decrease in the “sparse” case S−. We computed Type II error for all the four sets, Type I error for C+ and C−, and the difference of rates for the species selected to evolve under different rate regimes, before and after the application of the F multiplier, for S+ and S−.

2.4 Sensitivity analysis

In our simulations we assumed that species evolving under a shifted evolutionary rate had average phenotypes, respectively, one‐tenth lower or ten times higher than those expected under BM. Although arbitrary, these multiplication factors are much smaller than with many examples of “unusual” phenotypes reported in literature. For instance flying vertebrates are smaller than non‐flying vertebrates by several orders of magnitude, and marine vertebrates attain body sizes far exceeding those of terrestrial animals. However, conservative our F values were, we wanted to test the sensitivity of our method to varying tree size, rate change magnitude and commonness (i.e. of the proportion of species affected by the rate shift). As such, for each of the 4 possible situations (C+, C−, S+ and S−) we ran 250 simulations randomly varying, at each repetition, the number of species between 50 and 150 species, F in between 1 and 20 for C+ and S+, and between 0.05 to 1 for C− and S−, and the number of species affected by F in between 10% and 50% of the tree size. After completing the simulations, we produced by interpolation the three‐dimensional surface of the probability to find a significant rate shift, as influenced by the proportion of tips evolving under a distinctive rate regime, and by the magnitude of F.

2.5 Real case scenarios

In addition to simulation experiments, we applied the method to search for rate shifts to real data. We focused on body size, which is the most obvious and readily available physical characteristic for fossil species, and the most common locus of investigations on possible instances of rate change and (the evolutionary consequences of) alleged evolutionary constraints (Alexander, 1998).

We started by assembling a phylogeny of ornithodirans taking the phylogeny and body mass data for dinosaurs from Benson, Campione, et al. (2014), for early birds from Lee et al. (2014a), Lee, Cau, Naish, and Dyke (2014b) and for pterosaurs from Villalobos, Olalla‐Tarraga, Vieira, Mazzei, and Bini (2017). Data were supplemented with various sources (as indicated on Dryad at https://doi.org/10.5061/dryad.26443). We used this phylogeny and data to test for rate shifts in body size evolution as propelled by the acquisition of flight, which impinges on the pterosaur and early bird and bird‐like dinosaurs clades. We additionally tested for the existence of differences in the evolutionary rate regimes pertaining to different types of locomotion. Ornithodirans had four possible stances, bipedal (as in theropods, and early ceratopsians), quadrupedal (as in sauropods and large ornitischians), a combination of both (as in several hadrosaurs and prosauropods which were able to use both a two‐limbs or four‐limbs gaits, Maidment, Linton, Upchurch, & Barrett, 2012), and flight (in pterosaurs and birds). The body size rate regime linked to flight falls under the “clade” condition, whereas those involving transitions to bipedal, quadrupedal, mixed and flight locomotions regard the “sparse” condition, since more than one stance occur within individual clades (e.g. ceratopsians, sauropodomorphs, theropods, Maidment et al., 2012).

In keeping with the reptile data, the second real case scenario regards the possible rate shift linked to flight (which is limited to bats) in mammal body size. We finally tested the idea that insularity produces acceleration in the rate of body size evolution (e.g. Lister, 1989; Millien, 2006). This is a case of a phylogenetically “sparse” case, as insularity occurs ubiquitously across the mammal tree. We took the mammal data and insularity status (available at https://doi.org/10.5061/dryad.26443) from Raia, Carotenuto, and Meiri (2010).

The rate values in RRphylo are regression coefficients between parent/descendant pairs. As such, the magnitude of the rates (i.e. coefficients) heavily depends on the trait values. With body size data, this means rates between pairs of large species will be larger than rates between small species, even if they represent a smaller, proportional amount of phenotypic change. As explained above, the RRphylo method allows regressing the rates against the phenotype (or any other covariate upon indication), and using the absolute value of the residuals of such regression in the place of the original rate values. Whether to use the original rates or factoring out the effect of a covariate depends on the trait being considered, and the scientific question being answered. In our real case scenarios, we factored out body size from the rate calculation, after having verified that rates actually scale with body size (see supplementary material, and Figures S2–S5). RRphylo allows both automatic detection of rate shifts (see the associated vignette for full explanation), and testing the specific hypotheses that the change in rate regards specific clades or unrelated species in the tree. For both ornithodirans and mammals, we ran the automatic detection first, and then tested our hypotheses about the effects of locomotor stance and insularity on the rate of body size evolution.

3 RESULTS

3.1 Simulations and sensitivity analysis

Under the “clade” condition, Type I error is consistently low (Table 1). The ability of RRphylo to retrieve instances of rate change is close to 95% (on average, Table 1). As expected, under S‐ the rates calculated for the species submitted to rate change by applying the F multiplier were lower than before applying F in 100% of the simulations. Rates calculated for S+ were larger than before the application of F in 98% of the cases (Table 1).

Table 1. Results of the simulations conducted on both the “clade” and “sparse” conditions. The percentages refer to the number of Type I and Type II errors out of 100 simulations

Rate change	Clade		Sparse
	Type I	Type II	Type I	Type II	Change in rate
Increase	2%	6%	—	3%	98%
Decrease	3%	1%	—	2%	100%

Sensitivity analysis revealed weak but significant relationships between tree size and the probability to find the rate shift in three cases out of four (Table 2). The expected effect of F applies in three out of four cases. The commonness of the altered rate regime across the tree is marginally significant for S− (Table 2).

Table 2. Results of the sensitivity analysis. The table reports multiple regression statistics of the probability to find the change in evolutionary rate versus the size of the tree (Tree Size) the magnitude of F, and the percentage of species evolving under a different rate regime (Commonness)

	Slope	SE	t‐value	p‐value
Clade condition, rate increase C+
Tree Size	−0.001	0.000	−2.452	.015
F	−0.013	0.002	−6.484	.000
Commonness	−0.119	0.109	−1.090	.277
Clade condition, rate decrease C−
Tree Size	−0.001	0.000	−3.086	.002
F	0.321	0.038	8.545	.000
Commonness	−0.071	0.102	−0.700	.484
Sparse condition, rate increase S+
Tree Size	−0.001	0.000	−2.478	.014
F	−0.011	0.002	−5.499	.000
Commonness	−0.158	0.098	−1.616	.107
Sparse condition, rate increase S−
Tree Size	0.000	0.000	−1.263	.208
F	−0.008	0.020	−0.415	.678
Commonness	−0.090	0.049	−1.833	.068

We inspected the simulations to find at which magnitude of F the RRphylo method is able to retrieve significant indications for rate shift (at α = 0.05).

Under C+, a F multiplier >5 gives significant indication of rate increase in 176 out of 183 simulations (96.2%), irrespective of the size of the tree and the commonness of species applied to rate shift. With F < 0.2 the shift was found to operate in 45 out of 46 simulations in C−.

Under S+, at F > 10 the RRphylo method turns out to find >95% significant instances of increased rate (118 simulations out of 124, 95.2%). Under S−, the method recognized the decreased rate in more than 95% of the simulations at F < 0.4 (90 out of 94 cases, 95.7%).

3.2 Real case scenarios

3.2.1 Evolution of body size in ornithodirans. The effect of locomotory type

Rates calculated for the bird (Avialae, exclusive of Confuciusornithidae) and pterosaur clades within ornithodirans are significantly higher than for the rest of the tree (p < .001) also when tested alone (p < .001 for both clades). RRphylo automatically recognized two additional clades showing significantly small rates (Figure 1, Figure S3): Ornitopods, and Sauropodomorpha (Figure 1a).

Figure 1

(a) Density plot of the absolute rate values versus body mass regression residuals, for the clades showing statistically distinctive rates. Pterosaurs (light blue) and early birds (deep blue) have significantly high rates. Ornithischians (orange) and Sauropoda (red) have significantly low rates. (b) Density plot of the absolute rate values versus body mass regression residuals per locomotory type in Ornithodirans. Flying (deep blue) species have significantly high rates. Quadrupedal species (red) have significantly low rates. The density plot of the entire Ornithodiran tree absolute rate residuals is shown in dark grey

In keeping with our hypothesis, we found statistically different rates to pertain to different stances in ornithodirans. Quadruped species show the smallest average rates, whereas flying species show significantly higher rates than with any with other stance type (Figure 1b). By contrasting rates among species with different stances, we found quadruped species to show statistically smaller rates than bipedal (p = .005), and flying species (p = .001). No other pairwise difference was significant.

3.2.2 Rates of body size evolution in mammals. The effect of flight and life on islands

Through the automatic detection procedure, RRphylo found instances of significantly high rates for the clade “Afrotheria” (Figure 2, node 7635), for dasyurids (Figure 2, node 7866), leporids (Figure 2, node 5714), anteaters and sloths (Figure 2, node 7559), and sigmodontine rodents (Figure 2, node 4818). Significantly small rates accrue to the white‐toothed shrews (Figure 2, node 7371), and to murine rodents of the Rattus division (Figure 2, node 4416). The most interesting case regards bats. While Yinpterochiroptera bats (exclusive of flying foxes) show significantly large rates, Vespertilionidae offer a case of small rates (Figure 2, nodes 6709 and 7074 respectively). Yet, the bat clade tested as a whole shows significantly larger rates than the rest of the tree (p < .0001). Eventually, we found that no statistically significant difference in rates of body size evolution between continental, and insular endemic mammals (p = .149, Figure 3b).

Figure 2

The mammal tree with clades having significantly low (red) or high (blue) rates indicated, taking the residuals of the absolute rate values versus body mass regression. Nodes: 4416 murinae rodents (Rattus division), 4818 sigmodontine rodents, 5714 leporids, 6709 Yinpterochiroptera, 7074 vesper bats, 7371 white‐toothed shrews, 7559 anteaters and sloths, 7635 afrotheria, 7866 dasyurids

Figure 3

(a) Density plot of residuals of the absolute rate values versus body mass regression, for the clades showing statistically distinctive rates. (b) Density plot of residuals of the absolute rate values versus body mass regression per insularity status in mammals. Continental (dark blue) and insular (light blue) species have statistically the same average absolute rates. The density plot of the entire mammal tree absolute rate residuals is shown in dark gray

4 DISCUSSION

We devised a new method, RRphylo, to search for significant deviations in the rate of phenotypic evolution on phylogenies. One obvious advantage of RRphylo over existing PCMs is that it allows testing for significant rate shifts even at the level of species, rather than entire clades. One additional advantage is that by being free from any strong a priori assumption about the tempo and mode of phenotypic evolution, RRphylo takes full advantage from the inclusion of fossil forms in the tree, which is important because phylogenies limited to extant species give a poor (and phylogenetically restricted) depiction of the diversity of any animal group with a rich fossil record.

After assessing through simulations the appropriateness of RRphylo in retrieving rate changes, we tested both naïve and more firmly debated instances of rate shifts advocated to impinge upon the evolution of a single trait, body size, of paramount importance to both palaeontologists and evolutionary biologists, for its pervasive influence on species ecology and life history (Calder, 1984).

RRphylo is well suited to find such shifts. The simulations demonstrated it has low rates of both Type I and Type II errors, even under mild evolutionary rate change. Importantly, it works with variable tree sizes, and, under most circumstances, when the proportion of species affected by the rate shift is as low as 10% (FigureS1). Crucially, RRphylo performs well even when the deviation in the phenotypic rate affects disparate, unrelated species in the phylogeny (the “sparse” condition) that is something impossible to test with any of the currently available PCMs. This is further important because rate shifts are often reported to act at the level of species (e.g. accelerated body size evolution with insularity, Lister, 1989; Millien, 2006), which is best understood with phylogenetic and fossil information at hand (Schnitzler et al., 2017; Slater et al., 2012). We found that RRphylo works well with the “clade” condition, whereas under the “sparse” case either more important rate change effect (under S+) or more ubiquitous occurrence of the hypothesized shift across the phylogeny (S−), are required (FigureS1). Under C+, RRphylo pervasively finds out increased rates with a multiplying factor F down to 5 (or 1/5 in the case of C−). Translated in more familiar terms, this means a 5‐fold change in the mean of a given trait over BM predictions, hence 25‐fold change in the Brownian rate. While this figure might seem substantial, the distribution of body size in vertebrate clades is consistent with even larger rate shifts. For instance, changes in animal body size per type of locomotion usually go beyond two orders of magnitude. The mean body mass of the sauropodomorph dinosaurs analysed here is five times the average mass of the entire ornithopod clade (including sauropodomorphs), but nearly 2,000 times the average mass of pterosaurs, and some 10,000 times the early bird average. The corresponding figures for bats (or rodents) as compared to rorquals (balenopteridae whales) are one order of magnitude larger still. The case of rorquals and bats is particularly indicative, considering that the two clades have comparable ages. We confirmed the idea that flight is paralleled by a significant shift in the body size evolutionary rate in vertebrates. We additionally went through the idea that locomotory type, in general, does affect the rate of evolution. We were moved from the simple observation that bipedal animals tend to be smaller sized than quadrupedal species, and that quadrupeds themselves might experience limits on body size evolution stirring ad hoc adaptations, such as the acquisition of graviportal legs as in proboscideans and sauropods (Biewener, 1989). Ornithopods are especially well suited to study such effects, since the clade includes the whole gamut of possible locomotory types for limbed animals (exclusive of flight), and all the categories are present in more than one clade, making the application of the “sparse” condition (which is exclusive to RRphylo in the current PCM toolbox) necessary. We found that bipeds did experience slower rate of body size evolution than flying animals, but both categories’ body size evolves faster than in quadrupedal animals. In keeping with our results, it has been noticed that in sauropods the acquisition of erect forelimbs evolved in parallel to phyletic gigantism (Sander et al., 2011). Unsurprisingly, the most pervasive instances of significantly high rates in mammals regard Afrotheria, the clade including both the small bodied dassies (Hyracoidae) and the only mammals with graviportal legs, elephants, and the South American folivores of the Pilosa clade, which includes animals as small as pigmy anteaters (genus Cyclopes) to the end Pleistocene 6‐tons ground sloths (which are present in the tree).

The limits on body size evolution imposed by body stance and bauplan do not imply size itself could not evolve, but just that the rate regimes are locomotory type‐specific. As a matter of fact, Cope's rule applies to sauropodomorphs (Sander et al., 2011), but also to pterosaurs (Villalobos et al., 2017). Interestingly, Benson, Campione, et al. (2014) noted that pterosaur body size evolved under constraint during the first 70 mya of the clade history, to move to a different selection regime (and to the acquisition of very large body size) once birds had occupied the small‐size flying vertebrate niche by the Early Cretaceous. Hence, the sustained trend for body size decrease in avian dinosaurs (Lee et al., 2014a) could have been instrumental to the acquisition of flight in dinosaurs, as well as to the application of Cope's rule in pterosaurs, and both factors justify the exceptionally high rates of body size evolution we found in flying ornithodirans.

The results for mammals are entirely consistent with those for Mesozoic reptiles. Bats as a whole confirm that flight propelled accelerated rates of body size evolution. Yet, significantly small rates accrue to vesper bats, which have been already noted in the past (Dzeverin, 2008; Ruedi & Mayer, 2001), while large rates were calculated for Yinpterochiroptera (Pteropodiformes) exclusive of megabats, which is conceivable given they are more variable than megabats in terms of body size. A similar case regards the rodent family. Although there are cases of >100 kg rodents in the past (e.g. blunt toothed giant jutίa Amblyrhiza inundata, McFarlane, MacPhee, & Ford, 1998), body size evolution in rodents might be constrained by gut anatomy, and by competition to foregut fermenting herbivores (Demment & Vansoest, 1985). Yet, there are clades, such as rice mice (Oryzomyni) which have been shown to have had a very dynamic body size evolution (Avaria‐Llautureo et al., 2012). Perhaps unsurprisingly, we found a significant rate increase pertaining to the sigmodontini, the rodent clade including rice mice. It is probably not a coincidence that the largest rodents (such as Amblyrhiza, and the giant pacarana Josephoartigasia) either lived on islands, or away from ruminants. Insular gigantism is commonplace among fossil rodents (Adler & Levins, 1994). Indeed, there is a common perception that insular species deviate significantly in body size from their mainland relatives. The evolution of such unusual body sizes is said to come about fast (Lister, 1989; Millien, 2006) because of the ecological release insular species experience. However, we found no statistical difference between the rates of evolution of insular, as compared to continental, mammals. The mammal tree we used is 4,004 species wide, inclusive of extinct species, and as many as 747 insular endemics. The percentage of insular species (18.6%) and the size of the tree are both large enough to be confident that the application of the “sparse” condition would safely identify any sizeable rate shift between the two categories. Our results confirm the idea that rate of body size evolution is not faster on islands (Raia & Meiri, 2011; Thomas, Meiri, & Phillimore, 2009), which conflates on the observation that islands contain no more “extreme‐sized” species per clade than expected by chance (Meiri, Raia, & Phillimore, 2010).

In this paper, we present a new method, named RRphylo, to calculate evolutionary rates and test for the presence of rate shifts in phylogenies. One crucial feature of RRphylo is that it could detect distinctive rate regimes that apply to individual species, even when they occur sparsely across the phylogeny. RRphylo consistently works across variable intensity and commonness of rate changes. We applied RRphylo to the evolution of flight in bats, pterosaurs and birds, and found evidence for increased rate of body size evolution in all cases. Whereas quadrupedal animals, like proboscideans and sauropods, experienced low evolutionary rates, clades including animals with highly variable sizes, like afrotherids and sloths, unsurprisingly show high evolutionary rates. We found no evidence that, in mammals, the rate of evolution is faster on islands.

ACKNOWLEDGEMENTS

We thank Francesco Carotenuto for help with the interpolation method necessary to produce Supplementary Figure S1. Paolo Piras kindly gave us support in writing the R code for RRphylo at an early stage of its preparation. The authors state no conflict of interest.

AUTHORS’ CONTRIBUTIONS

P.R. and S.C. conceived the study and wrote the R codes. M.P. and G.T. collected the data. C.S., M.M. and A.M. assembled the phylogenies. S.C. and M.M. prepared the figures. P.R., M.D.F. and S.C. produced the vignette associated to this manuscript. All the authors contributed in preparing and writing the manuscript.

DATA ACCESSIBILITY

The R code is available at https://doi.org/10.5281/zenodo.1041611. Raw data and phylogentic trees for both ornithodirans and mammals are available at https://doi.org/10.5061/dryad.26443 (Castiglione et al., 2017).