Main

Phylogenetic statistical methods13,14 provide us with the opportunity to formally test whether BMR has been linked to Tb or ambient temperature (Ta) throughout the evolution of birds and mammals. By accommodating for and identifying heterogeneity in the rate of phenotypic evolution, these methods can detect and reconstruct accurate historical evolutionary processes15. Evaluation of the evolutionary coupling between BMR and Tb has direct consequences for several longstanding ecological and evolutionary theories2,3,4,5,6,7,8 (including the metabolic theory of ecology) that assume coupling between BMR and Tb.

We first quantified and compared rates of evolution for BMR and Tb along each branch of the time-calibrated phylogenetic trees of birds and mammals (hereafter, branch-wise rates (r); Methods). r is a rate scalar by which the background rate of evolution (σ2b) is multiplied to increase or decrease the pace of evolution; it measures how fast a trait evolved along an individual phylogenetic branch (Methods). If BMR and Tb were coupled during the evolution of endotherms, the amount of change along phylogenetic branches for both traits should be positively associated—in cases in which rBMR is high, we expect it to be high for \({r}_{{T}_{{\rm{b}}}}\) (Fig. 1 b). We tested this prediction against alternative evolutionary scenarios. First, we cannot make any inferences about coupling or decoupling in cases in which there is no rate heterogeneity for both BMR and Tb (r = 1 for all branches in the tree for both traits) (Fig. 1a). Second, we infer decoupled evolution if both traits show rate heterogeneity, for which the magnitudes of r values are negatively correlated (that is, branches that evolve at a high rate for BMR but a low rate for Tb, and vice versa) (Fig. 1c). We suggest this scenario indicates decoupled evolution because a negative correlation most probably indicates that one trait tends to be conserved while the other evolved rapidly. Third, we infer decoupled evolution if only one trait shows rate heterogeneity while the other evolved at a constant rate (Fig. 1d, e) or if both traits show heterogeneity but the branch-wise rates are not associated (Fig. 1f).

Fig. 1: Possible evolutionary scenarios for BMR and Tb given their branch-wise rates in a bivariate space.
figure 1

a, Both traits evolve at a single constant rate across all branches of the tree (rBMR = 1 and \({r}_{{T}_{{\rm{b}}}}=1\)); in this case, we have no statistical power to evaluate an association between BMR and Tb. b, A positive correlation between rBMR and \({r}_{{T}_{{\rm{b}}}}\) indicates that both traits are coupled—in cases in which BMR changed more, Tb also changed. c, A negative correlation between rBMR and \({r}_{{T}_{{\rm{b}}}}\) implies that both traits are decoupled because when BMR changed more, Tb changed less. d–f, Correlations indicate that both traits are decoupled—when BMR evolved at a single constant rate, Tb evolved at a variable rate (d) or vice versa (e); or both traits evolved at variable rates (\({r}_{{\rm{BMR}}}\ne 1\) and \({r}_{{T}_{{\rm{b}}}}\ne 1\)) but their magnitudes were not statistically correlated (f). Grey colour represents the constant background rate (r = 1). Red colours represent rates that are faster than the background rate (r > 1) and blue colours represent rates that are slower than the background rate (r < 1), which might be related to past events of positive17 and stabilizing selection24, respectively. Point fill colours represent the magnitudes of rBMR and point outline colours represent magnitudes of \({r}_{{T}_{{\rm{b}}}}\).

Full size image

As BMR, body mass (M), Tb and Ta are—at least to some extent—correlated in extant birds and mammals, and such correlations may vary between orders16, we estimated the branch-wise rates for BMR and Tb while accounting for their covariates across extant species using the phylogenetic variable-rate regression model17 (Methods). This approach enables the simultaneous estimation of both an overall relationship between—for instance—BMR as a function of M and Tb across extant species, and any shifts in branch-wise rates that apply to the phylogenetically structured residual variance in the relationship. In both birds and mammals, the phylogenetic variable-rate regression model fits the data significantly better than the constant-rate regression models, which assume a single constant rate (r = 1) across all branches (Methods and Supplementary Tables 1–8). The best-fitting phylogenetic variable-rate regression model for mammalian BMR includes both M and Tb with a single slope for each trait that is estimated across all orders (Supplementary Tables 1, 2). For mammalian Tb, the best-fitting model includes M and BMR as covariates, also with a single slope across all orders (Supplementary Tables 3, 7). In birds, the best model for BMR includes only M, with a single slope for all orders (Supplementary Table 4). Finally, the best-fitting model for avian Tb includes M only in Columbiformes (Supplementary Table 6).

The branch-wise rates estimated for the best-fitting models show that mammalian BMR evolved at a constant rate (r = 1) in only 11.2% of branches and at faster rates (r > 1) in 88.8% of branches (Fig. 2a). Mammalian Tb evolved at a constant rate in 70.3% of branches and faster rates in 29.7% of branches (Fig. 2b). In birds, BMR evolved at a constant rate in 90.5% of branches and at faster rates in 9.5% of branches (Fig. 2d). Avian Tb evolved at a constant rate in 69% of branches and at faster rates in 31% (Fig. 2e). When the branch-wise rates for BMR and Tb were compared, we found that in mammals both traits evolved at a constant rate in 10.6% of branches (Fig. 3a, consistent with Fig. 1a). In 60.2% of branches, only one trait evolved at faster rates while the other trait diverged at a constant rate. This indicates that BMR and Tb evolved in a decoupled manner along these branches (Fig. 3a, consistent with Fig. 1d, e). We found that 29.2% of branches had an increased rate for both BMR and Tb. However, the magnitudes of the branch-wise rates were not significantly correlated (the percentage of the posterior distribution crossing zero as assessed by Bayesian Markov chain Monte Carlo (MCMC), PMCMC = 9%) (Fig. 3a, consistent with Fig. 1f; Supplementary Table 9). This also suggests that evolution was decoupled in those branches—probably because of distinct selection pressures that acted separately on BMR and Tb. On the other hand, both traits evolved at a constant rate in 63.8% of branches for birds (Fig. 3c, consistent with Fig. 1a). In 32% of branches, only one trait evolved at fast rates while the other trait diverged at a constant rate (Fig. 3c, consistent with Fig. 1d, e). In the remaining 4.2% of branches, both traits evolved at faster rates, but the magnitudes of r were not statistically correlated (PMCMC = 16.9%) (Fig. 3c, consistent with Fig. 1f; Supplementary Table 10).

Fig. 2: Branch-wise rates of BMR, Tb and Ta on the mammalian and avian phylogeny.
figure 2

a–c, Branch-wise rates for mammalian BMR (a), Tb (b) and Ta (c). d–f, Branch-wise rates for avian BMR (d), Tb (e) and Ta (f). The r values for each phylogenetic branch are shown in colours, and indicate whether the trait evolved at a constant background rate (r = 1, grey branches), at rates slower than the background rate (r < 1, blue-gradient branches) or at rates faster than the constant rate (r > 1, red-gradient branches). All silhouettes were obtained from http://phylopic.org/. Mammalian silhouettes were created by the following individuals (from top to bottom): Monotremata, S. Werning; Marsupialia, M. Callaghan; Hyracoidea, by S. Traver; Tubulidentata, P. Scott; Macroscelidea (uncredited); Pilosa, FunkMonk; Eulipotyphla, B. Barnes; Artiodactyla, nicubunu; Pholidota, S. Traver; Carnivora (uncredited); Chiroptera, Y. Wong; Scandentia, T. M. Keesey; Primates, T. M. Keesey; Lagomorpha, A. Caravaggi; and Rodentia (uncredited). Avian silhouettes were created by the following individuals from top to bottom: Anseriformes, M. Martyniuk; Galliformes (uncredited); Columbiformes, F. Sayol; Podicipediformes, D. Backlund; Procellariiformes, M. Hannaford; Suliformes, F. Sayol; Pelecaniformes, S. Traver; Cuculiformes, F. Sayol; Gruiformes, F. Sayol; Caprimulgiformes, F. Sayol; Apodiformes, F. Sayol; Charadriiformes (uncredited); Accipitriformes, S. Traver; Bucerotiformes, S. Traver; Coraciiformes, F. Sayol; Piciformes, S. Traver; Strigiformes, F. Sayol, Coliiformes, E. J. Wetsy; Falconiformes, R. Groom; Psittaciformes, F. Sayol; and Passeriformes, P. Pattawaro.

Full size image
Fig. 3: Branch-wise rates of BMR, Tb and Ta in bivariate space for mammals and birds.
figure 3

a, b, Bivariate space of mammals for rBMR and \({r}_{{T}_{{\rm{b}}}}\) (a) or \({r}_{{T}_{{\rm{a}}}}\) (b). c, d, Bivariate space of birds for rBMR and \({r}_{{T}_{{\rm{b}}}}\) (c) or \({r}_{{T}_{{\rm{a}}}}\) (d). a, In mammals, rBMR was decoupled from \({r}_{{T}_{{\rm{b}}}}\) in 89.4% of branches because either only one trait showed rate heterogeneity while the other evolved a single constant rate (in 60.2% of branches; grey filled and red outlined dots, and grey outlined and red filled dots, consistent with Fig. 1d, e), or because both traits evolved at fast rates but the magnitudes of rBMR and \({r}_{{T}_{{\rm{b}}}}\) were not correlated (in 29.2% of branches; red filled and outlined dots, consistent with Fig. 1f). In the remainder of the branches, 10.6%, (grey middle dot, consistent with Fig. 1a) there was no variation in either rBMR or \({r}_{{T}_{{\rm{b}}}}\). b, Bayesian generalized least squares analyses indicate that fast rBMR and slow to fast \({r}_{{T}_{{\rm{a}}}}\) (red filled and blue and red outlined dots) were statistically correlated in 74.9% of mammalian branches (PMCMC = 0; n = 602 branches; black line). In 18.2% of branches, the rBMR was decoupled from \({r}_{{T}_{{\rm{a}}}}\) because only one trait shows rate heterogeneity (grey filled and red outlined dots and grey outlined and red filled dots). In the remainder of the branches, 6.9%, (grey middle dots), there was no variation in either rBMR or \({r}_{{T}_{{\rm{a}}}}\). c, In birds, rBMR was decoupled from \({r}_{{T}_{{\rm{b}}}}\) in 36.2% of branches because either only 1 trait showed rate heterogeneity (in 32% of branches) or because the magnitude of fast rates in both traits were not correlated (in 4.2% of branches). There was no rate variation for either trait for the remaining 63.8% of branches. d, Avian rBMR was decoupled from \({r}_{{T}_{{\rm{a}}}}\) in 77.9% of branches, because either only one trait showed rate heterogeneity (in 68.4% of branches) or because the magnitude of fast rates in both traits were not correlated (in 9.5% of branches). There was no variation in either trait for the remaining 22.1% of branches.

Full size image

As rapid bursts in the evolution of BMR were not coupled with the evolutionary changes in Tb, we evaluated the alternative hypothesis that postulates that BMR evolved in response to Ta. This hypothesis suggests that colder environments increase the rate of heat loss from organisms and that this loss is subsequently compensated for by increases in BMR9,10,11,12. These increases in BMR could have occurred over long periods of time because of global cooling18—generating a long-term directional trend in BMR during the radiation of mammals and birds. This expectation is consistent with the plesiomorphic–apomorphic endothermy model6,7,8. By assuming that BMR and Tb are coupled in endotherms and that they can both be used as a proxy for the degree of endothermy, the plesiomorphic–apomorphic endothermy model predicts a general tendency towards higher endothermic levels over time (from basoendothermic ancestors; Methods) associated with the global cooling during the Cenozoic era. However, global cooling is not the only source of variation in Ta. Long-term directional increases in BMR may have also been driven by historical dispersals of endotherms towards higher latitudes19. In either case, if a long-term decrease in Ta drove adaptation through increases in BMR, and Tb followed the same trajectory (as assumed by the plesiomorphic–apomorphic endothermy model), we expect to find a positive correlation between the branch-wise rates of BMR and the branch-wise rates of Ta. With this in mind, we also expect a positive trend towards higher values of BMR and Tb for basoendothermic ancestors and a negative trend towards lower Ta for warmer ancestral environments. We used the phylogenetic variable-rate regression model to estimate the branch-wise rates for Ta while accounting for latitude as, generally, Ta decreases from the equator to the poles (Methods and Supplementary Table 11).

The phylogenetic variable-rate regression model significantly improved the fit to the Ta data over the constant-rate regression model in both mammals and birds (Supplementary Table 11). Ta evolved at a constant rate in 21.2% of mammalian branches, and with rate heterogeneity in the remaining 78.8%—including 72.2% of branches with faster rates and 6.6% with slower rates (r < 1) (Fig. 2c). This indicates that most ancestral mammalian lineages (72.2%) faced abrupt historical changes in their Ta environment, while far fewer lineages (6.6%, most of which were bats) survived and continued to exist in similar thermal environments. In birds, 77.6% of branches show faster rates of change in Ta, 22.1% show changes at a constant rate and in only a single branch did the Ta change at a slower rate (Fig. 2f).

When branch-wise rates of mammalian BMR and Ta evolution were compared, we found that they were coupled in 74.9% of branches (PMCMC = 0%) (Fig. 3b, consistent with Fig. 1b; Supplementary Table 12). To evaluate further whether decreases in Ta were linked to increases in BMR in the 74.9% of mammals for which both traits were coupled (that is, to ascertain the direction of change), we evaluated the expected positive trend in BMR as a response to the long-term decrease in Ta. We conducted Bayesian phylogenetic regressions between extant values of these two variables (in turn) and the path-wise rates15 (sum of rate-scaled branches along the path from the root of the tree to each terminal species; Methods). We found a negative effect of path-wise rates on Ta across all mammals (Fig. 4b and Supplementary Table 14), which supports a long-term directional trend towards habitats with lower Ta over time. However, we did not find evidence for any trend in mammalian BMR evolution—increases and decreases in BMR showed equal probabilities in our sample (Supplementary Table 14). Our results suggest that in colder environments, in which resources were available to fuel metabolic elevation, selection favoured higher mammalian BMR20. Another possibility might be that the increase in BMR was a correlated response to direct selection on other physiological traits, such as the maximum metabolic capacities for thermogenesis, for which the benefits outweigh the energetic cost of BMR elevation20. Otherwise, selection may have always favoured decreases in BMR in an ever-colder environment20.

Fig. 4: Mammals and birds evolved towards both colder Tb and Ta over their evolutionary history.
figure 4

a–d, Path-wise rates had a significant negative effect on mammalian Tb (a; PMCMC = 4%; n = 502 species) and avian Tb (c; PMCMC = 3%; n =  367 species) and on mammalian Ta (b; PMCMC = 0; n = 2,922) and avian Ta (d; PMCMC = 0; n = 6,142 species), supporting a negative macroevolutionary trend15 for both Tb and Ta in mammals and birds. Lighter blue and dark blue lines indicate the posterior distribution of slopes and the mean slope, respectively, estimated from the Bayesian phylogenetic generalized least squares (Methods).

Full size image

In contrast to mammals, most avian branches that experienced rapid shifts in Ta did not show evidence for coupled changes in BMR—68.4% of branches had fast rates of Ta evolution but a constant rate of BMR evolution (Fig. 3d, consistent with Fig. 1d, e). Moreover, the small fraction of branches for which BMR evolved at fast rates (9.5%) were not linked to rapid shifts in Ta (Fig. 3d, consistent with Fig. 1f; Supplementary Table 13). Avian BMR did not show a positive evolutionary trend despite the fact that birds also experienced colder environments over time (Fig. 4d and Supplementary Table 15). Birds might not have responded to colder temperatures by changes in their BMR because their lower thermal conductance may have helped them to retain internal heat9. Alternatively, other physiological strategies, such as torpor, may have been selected for in colder environments21.

Finally, we found a negative effect of path-wise rates on Tb in both mammals (Fig. 4a and Supplementary Table 14) and birds (Fig. 4c and Supplementary Table 15). This suggest that—on average—endotherms evolved towards colder bodies from warmer-bodied ancestors. These directional models predict a mean Tb of 35.3 °C and 40.4 °C for the most recent common ancestor (MRCA) of mammals and birds, respectively (Fig. 4a, c), suggesting that early birds and mammals were mesoendotherms rather than basoendotherms (Methods). This result does not support the idea that ancestral mammals could not attain Tb > 30 °C owing to the increased metabolic rates that would be necessary to compensate for heat loss in cold environments22. However, if the Tb − Ta differential (ΔT) determines how hot early mammals were, we expect that a mammalian MRCA with a Tb of 35.3 °C could survive in an environment that was warm enough to have a low ΔT. Our model that describes the negative trend in Ta predicts that the MRCA of mammals lived in an environment that was 23 °C on average (Fig. 4b), resulting in a ΔT of 15.3 °C. This ancestral ΔT is very conservative compared with the ΔT values that have been observed in extant mammals. For example, there are small mammals that achieve a Tb higher than 39 °C (such as Microdipodops pallidus16) and that can survive in environments of 11 °C19 (ΔT = 28 °C). Furthermore, some larger mammals have a stable Tb even in extreme environmental conditions—the Arctic hare (Lepus arcticus) can maintain its Tb of 38 °C16 in temperatures as low as −12 °C19 (ΔT = 50 °C).

Taken together, our results show that BMR was not coupled to Tb across the evolution of endothermic species. As environments became colder mammals survived by changing their BMR, while birds probably survived owing to their high thermal insulation. Evaluating the isolated and/or combined effects of environmental variables on physiological attributes has implications for evidence-based projections for the future23. In this sense, the previously unappreciated complexity, interplay and decoupled nature of the evolutionary history of BMR, Tb and Ta may point to the undetected resilience of endotherms in the face of modern global challenges.

Methods

Data

We used a time-calibrated phylogenetic tree of extant mammals (n = 3,321)25, and data for M, BMR and Tb were obtained from a previously published study16 (n = 632). After identifying species in the tree that have trait information, we obtained a final mammalian dataset of 502 species, which includes representatives from 15 orders (Supplementary Information).

For birds, we used the consensus time-calibrated tree from a previous study19. This tree was inferred from the samples of trees that have previously been published26. Data for BMR, Tb and M were obtained from a previously published study9. After matching this database with the phylogenetic tree, we obtained a final sample of 164 species, which includes representatives from 21 orders (Supplementary Information). The dataset used to evaluate evolutionary trends in Tb (see below) has previously been published27, and contains 367 species with phylogenetic information.

Data for Ta and latitude for extant mammals and birds were extracted from a previous publication19. These datasets include 2,922 species of mammals and 6,142 species of birds, which have phylogenetic information. The Ta for extant endothermic species is the temperature of the environments that birds and mammals inhabit today—measured as the mean ambient temperature for the mid-point latitude of each species distribution19. The Ta at which a species exists today may not be a heritable trait per se. However, the evolution of Ta can still be inferred using phylogenetic methods as habitat selection reflects adaptations of the species (traits) to some characteristics of the environment. This interrelationship should leave a phylogenetic signal in the Ta at which endothermic species live. Accordingly, we found a significant phylogenetic signal in the Ta of both mammals (λPosteriorMean = 0.77; Bayes factor = 665) and birds (λPosteriorMean = 0.8; Bayes factor = 1,404). Furthermore, the phylogenetic signal for Ta is very high (λ = 1) in birds and mammals when estimated using the median-r scaled tree.

Finally, to evaluate the endothermic levels for the MRCA of mammals and birds that have previously been proposed7,8, we followed this categorization of endothermic species: as basoendotherms (TbBirds < 40.4 °C; TbMammals < 35.0 °C), mesoendotherma (40.4 °C ≤ TbBirds ≤ 42.5 °C; 35 °C ≤ TbMammals ≤ 37.9 °C) and supraendotherms (TbBirds > 42.5 °C; TbMammals > 37.9 °C).

Inferring the branch-wise rates of evolution

We identified heterogeneity in the rate of evolution along phylogenetic branches (branch-wise rates) by dividing the rate into two parameters: a background rate parameter (σ2b), which assumes that changes in the trait of interest (for example, BMR) are drawn from an underlying Brownian process, and a second parameter, r, which identifies a branch-specific rate shift. A full set of branch-wise rates are estimated by adjusting the lengths of each branch in a time-calibrated tree (stretching or compressing a branch is equivalent to increasing or decreasing the phenotypic rate of change relative to the underlying Brownian rate of evolution). Branch-wise rates are defined by a set of branch-specific scalars r (0 < r < ∞) that scale each branch to optimize the phenotypic rate of change to a Brownian process (σ2b × r). If phenotypic change occurred at accelerated (faster) rates along a specific branch of the tree, then r > 1 and the branch is stretched. Decelerated (slower) rates of evolution are detected by r < 1 and the branch is compressed. If the trait evolves at a constant rate along a branch, then the branch will not be modified (that is, r = 1).

We estimated the r values of evolution for BMR, Tb, and Ta using the phylogenetic variable-rate regression model in a Bayesian framework17. This model is designed to automatically detect shifts in the rate of trait evolution across phylogenetic branches while accounting for a relationship with another trait or traits across values for extant species. This approach enables the simultaneous estimation of both an overall relationship between—for instance—BMR as a function of M and Tb across extant species, and any shifts in the rate r that apply to the phylogenetically structured residual variance in the relationship. As residual variance is explained by shifts in rate across phylogenetic branches (r) we can, for example, determine how much BMR has changed in the past after accounting for its covariation with M and Tb in the present (the relationship between the values across extant species). Thus, if the amounts of change in BMR along individual phylogenetic branches were coupled with the amounts of change of Tb, then we should find the rBMR values to be positively associated with the \({r}_{{T}_{{\rm{b}}}}\) values. The branch-wise rates for Tb evolution can be estimated while accounting for its covariation with other traits or factor across extant species. Previous studies on the association between BMR and Tb that only used values for extant species have not evaluated the association in evolutionary terms, even when they use phylogenetic methods.

We evaluated 24 phylogenetic variable-rate regression models and 24 phylogenetic constant-rate regression models (Supplementary Tables 1–8). The selection of the regression model was conducted using Bayes factors (B) using marginal likelihoods estimated by stepping stone sampling. B is calculated as the double of the difference between the log marginal likelihood of the complex model and the simple model. By convention, B > 2 indicates positive evidence for the complex model, B = 5–10 indicates strong support and B > 10 is considered very strong support28. We inferred the rBMR and \({r}_{{T}_{{\rm{b}}}}\) values with the phylogenetic variable-rate regression models that best fit the data for our samples of mammals and birds (Supplementary Tables 7, 8). We also estimated the \({r}_{{T}_{{\rm{a}}}}\) values after accounting for the effect of the latitude of the distribution of species (Supplementary Table 11) and, consequently, we accounted for the geographical variation of Ta across the distribution of extant species. We used BayesTraits v.3.029 to detect the magnitude and location of r in a Bayesian MCMC reversible-jump framework, which generates a posterior distribution of trees with scaled branches lengths according to the rate of evolution. There is no limit or prior expectation in the number of the r branch scalars, r numbers vary from zero (no branch is scaled) to n, in which n is the number of branches in the phylogenetic tree. Regarding the values of each r parameter, we used a gamma prior, with α = 1.1 and a β parameter that is rescaled such that the median of the distribution is equal to 1. With this setting, the numbers of the rate increases and decreases that are proposed are balanced13. We ran 50,000,000 iterations sampling every 25,000 to ensure chain convergence and independence in model parameters in BMR and Tb analyses. We discarded the first 25,000 iterations as burn-in. For the Ta analysis in mammals, we ran 200,000,000 iterations sampling every 100,000, and we discarded the first 100,000 iterations as burn-in. For Ta analysis in birds, we ran 400,000,000 iterations discarding the first 100,000,000 as burn-in, and we sampled every 200,000. Regression coefficients were judged to be significant according to a calculated PMCMC value for each posterior of regression coefficients for cases in which <5% of samples in the posterior distribution crossed zero; this indicates that the coefficient is significantly different from zero.

Testing the relationship between the branch-wise rates of evolution

We first estimated the consensus branch-scaled tree for BMR and Tb from the posterior sample of branch-scaled trees obtained with the phylogenetic variable-rate regression model. The consensus branch-scaled tree was generated by using the median r from the posterior distribution. We evaluated the correlation between the rBMR and \({r}_{{T}_{{\rm{b}}}}\) values using a Bayesian generalized least squares regression in BayesTraits v.3.0. The same analyses were conducted to evaluate the correlation between rBMR and \({r}_{{T}_{{\rm{a}}}}\). We used a uniform prior for the β (slope coefficient), which ranged from −100 to 100. We ran 50,000,000 iterations sampling every 25,000 to ensure chain convergence and independence in model parameters. We discarded the first 25,000 iterations as burn-in. Significance of regression coefficients was determined as above.

Detecting trends

We evaluated the direction of change in BMR, Tb and Ta across all mammals and birds using the path-wise rates of these variables (Supplementary Tables 15, 16). The path-wise rate is the sum of all of the rate-scaled branches along the path of a species, which lead from the root (the MRCA) to the tips of the tree, and it accounts for the total amount of change that the species has experienced during its evolution15. If high path-wise rates have disproportionately been associated with trait increases or decreases, we expect to find that species with greater path-wise rates will have high or low trait values in the present. For instance, if ancestral mammals experienced progressively colder environmental temperatures owing to climate change or colonization of colder habitats as they were evolving from their MRCA, we expect a negative correlation between the path-wise rate of Ta and the Ta of extant species. We performed six Bayesian PGLS regressions in BayesTraits v.3.0 to evaluate the relationship between BMR, Tb, Ta and their path-wise rates (Supplementary Tables 15, 16). We used a uniform prior for the β (slope coefficients) that ranged from −100 to 100 to allow all possible values to have an equal probability. Finally, we ran 50,000,000 iterations sampling every 25,000 to ensure chain convergence and independence in model parameters. We discarded the first 25,000 iterations as burn-in. Significance of regression slopes was determined as above.

Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this paper.