Results and Discussion

Because the rate of morphological evolution has varied considerably among mammals throughout their history, branch lengths measured in time can overestimate or underestimate the amount of change expected under a homogeneous Brownian motion model (19). We therefore scale time by an amount reflecting the rate of morphological evolution along individual branches of the mammalian phylogeny (19) (SI Text). Longer rate-scaled branches have experienced more change than would be expected, given their length in time (Methods). If body size increase has been disproportionally favored, we expect to find that longer rate-scaled branches are linked to larger increases in size throughout the phylogeny. If this pattern has been repeated over many branches, we expect to find them associated with a long-term historical trend toward increasing size (6).

Across all mammals, we find a significant positive relationship between path-wise rates (the sum of all rate-scaled branches along the evolutionary path leading to individual species; Methods) and body size [likelihood ratio (D) test, compared with a homogeneous Brownian motion model: D = 359.85, P < 0.001, df = 2; Fig. 1A; this relationship holds in all of 500 randomly selected trees from the posterior distribution of rate-scaled phylogenies]. Allowing the slope of the relationship between size and path-wise rate to vary among orders (separate-slopes model; Fig. 1B) significantly improves on the model relying on a single common slope (D = 252.24, P < 0.001, df = 31; this relationship also holds in all of 500 randomly selected trees from the posterior distribution of rate-scaled phylogenies) and reveals that the positive relationship is maintained separately within 10 of 11 mammalian orders (Fig. 1B and Table S1). The only exception is the marsupial order Diprotodontia, where the path-wise rate is largest in the evolutionary paths leading to smaller species (Fig. 1B).

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Fig. 1.

Faster path-wise rates have led to larger body size in mammals. (A) Relationship across all mammals is plotted, and data points are colored by order (n = 3,321). The black line is the fitted phylogenetic slope of the relationship between body size and path-wise rates (Methods) across all mammals. (B) Fitted phylogenetic slopes of the relationship within each of the 11 mammalian orders investigated here. Orders that contain aquatic groups are indicated by an asterisk; for these orders, only the terrestrial members are plotted. Aquatic groups are plotted separately (Cetacea, pinnipeds, and Sirenia).

We visualize the importance of detecting variation in the rate of evolution by simulating body sizes from the separate-slopes regression model (Methods) and from a conventional homogeneous Brownian motion model assuming a single uniform rate of change. The separate-slopes model simulates values that symmetrically bracket the observed body size distribution (Fig. 2). By comparison, the homogeneous model systematically overestimates small sizes and underestimates large sizes (Fig. 2, Inset). This poor fit to the real data arises by virtue of the homogeneous model missing the historical bias toward rapid rates leading to larger size.

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Fig. 2.

Comparisons between the cumulative distribution of observed mammalian body sizes (n = 3,321, black lines) and simulated data (n = 1,000, colored lines). The real data are compared with simulations generated from our separate-slopes regression model (blue lines) and a conventional homogeneous Brownian motion model (red lines, Inset).

Using our separate-slopes model, we infer the ancestral body size at each internal node of the mammalian phylogeny (Methods, Fig. 3A, and Fig. S2). The tendency for body size increase can be studied quantitatively by finding the difference in body size from the start to the end of each branch of the phylogeny (n = 5,233). We term these differences “phylogenetic ancestor-descendant” (PAD) comparisons to contrast with the paleontological approach, where “fossil ancestor-descendant” (FAD) comparisons (12, 20, 21) are made between the sizes of taxonomically paired species found in the fossil record.

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Fig. 3.

PAD comparisons and reconstructed ancestral sizes. (A) Projection of ancestral state reconstructions into a phylomorphospace (n = 5,234, including all tips and internal nodes). Points are connected by phylogeny, and each internal node of the tree has been reconstructed using the parameters of our separate-slopes regression model. Our estimate for the therian root (24.5 g) falls within the ranges given by the paleontological data (20–25 g, midpoint indicated by the pale blue square). This estimate is in contrast to the estimate made by a conventional homogeneous Brownian motion model, which is more than an order of magnitude too large (pale pink square, 610.7 g). Orders that contain aquatic groups are indicated by an asterisk; for these orders, only the terrestrial members are plotted. Aquatic groups are plotted separately (Cetacea, pinnipeds, and Sirenia). (B–D) PAD changes (Δlog₁₀ body size) across every branch of the mammalian phylogeny (n = 5,233). The red dashed line indicates no change in size. (B) Frequency (f) distribution of Δlog₁₀ body size across individual branches. There is a significant bias toward body size increase (exact binomial test, P < 0.001). (C) Plot of the inferred rate of evolution along individual branches (Methods) against Δlog₁₀ body size. The regression line is significantly positive (β = 0.015, P < 0.0001). (D) Ancestral body size plotted against body size change across individual branches. The gray bars represent the SD of Δlog₁₀ body size calculated from the variance associated with each data point (σ²_{Δlog10 body size}; Methods). The regression line and the SDs in D have been corrected for the regression to the mean artifact (Methods and SI Text). The slope of the relationship between ancestral size and Δlog₁₀ body size is significantly positive (β = 0.020, P = 0.0006). Highlighted by a red square on each of these plots is the branch leading to modern bats.

Our PAD comparisons demonstrate that not only are size increases more common but they also tend to be greater in magnitude and occur at a faster rate compared with body size decreases (Fig. 3). Of the 5,233 PAD comparisons, 3,496 or 66.8% showed an increase in size (exact binomial test, P < 0.001). On average, descendant species are 0.10 ± 0.004 log₁₀ units, or 6 ± 0.25%, larger than their ancestors (Fig. 3B), although this figure varies between 1.4% and 16.9% in individual orders (−3.8 ± 0.63% in Diprotodontia; Table S2). These figures compare favorably with results from paleontological data, where North American Cenozoic mammals are, on average, 9% larger than their ancestors (12).

We find that on a branch-by-branch basis, the largest increases in size are associated with the fastest rates of evolution (β = 0.015, P < 0.001; Fig. 3C). One argument for such a pattern is based on the premise that phyletic increases in size arise simply as a consequence of evolutionary divergence away from a small ancestral value, where there is some lower physiological limit on size (22, 23). In this scenario, a taxon’s “maximal potential adaptive zone” (22) is always skewed such that larger species will evolve and those species will be specialized (6, 22).

We use our PAD comparisons to test for the presence of a lower bound by drawing on ideas developed in the paleontological literature (12, 21, 23, 24) while explicitly accounting for shared ancestry. If some lower boundary on size is enforced, we expect most ancestor-descendant size changes to be positive when the ancestral size is near to that limit; it is only possible to get larger. However, as the ancestral state moves away from that limit, we predict that the distribution of body size change will become increasingly centered about 0 (i.e., size decreases are equally likely as size increases) (24). Taken over all branches of the phylogeny, this pattern predicts a negative relationship between a branch’s ancestral size and the average body size change observed along that branch (12, 21). When ancestral size is small, changes will tend to be positive, but when ancestral size is large, size can change in either direction.

We do not find the predicted negative relationship (Fig. 3D and SI Text). Instead, we find that size change actually slightly increases in magnitude when ancestral size is larger (β = 0.020, P < 0.001; Fig. 3D). This pattern is also found in the paleontological data using FAD comparisons (12). To retain the idea that some physiological lower limit could produce these PAD changes and results from paleontological data (12), proponents would have to invoke a new physiological lower limit for each new species that comes into existence. Why or according to what processes these mysterious and dynamically shifting constraints arise imposes a steep hill for this explanation to climb.

The notion that “adaptive zones” litter the morphological landscape has often been wielded as a driver for large-scale macroevolutionary patterns (25⇓⇓⇓–29). With this view, one might expect fast evolutionary rates to be the result of shifts from one zone to another or in the position of the adaptive peak through time (26, 29⇓–31). If the occupation of new adaptive zones is constantly associated with changes toward large size or there is some sort of continuously moving optima, such that large size is favored, this view would be consistent with the pattern we observe here, although there is nothing in the pattern we observe that requires the existence of discrete adaptive zones.

It has been suggested that large-bodied species may have an inherently faster rate of evolution owing to the relaxation of some unspecified size-linked constraint (26, 32) (e.g., genetic, developmental, biomechanical). If such constraints were operating, we would expect to observe that larger bodied species change disproportionately more along the branches of the phylogeny than smaller bodied ones, leading to the prediction that the variance of body size change should be positively correlated with ancestral size: Small-bodied species change less than large-bodied ones. We calculated the variance for all PAD comparisons (σ²_{Δlog10 body size}, n = 5,233) after adjusting for the regression to the mean artifact (12, 33) (SI Text). We then regressed log-transformed σ²_{Δlog10 body size} onto log-transformed ancestral size (i.e., size reconstructed at the start of a branch) across all branches of the phylogeny. We do not find the expected positive relationship (β = −0.017, t = −1.47, P = 0.14; Fig. 3D). Therefore, and in agreement with previous work (34, 35), we see no reason to invoke the release of constraints as a force driving rate variation or size changes in mammals.

A possible difficulty for our model is that it predicts that mammals will become increasingly and indefinitely larger over long periods of time even though there must be some physical limit on the maximum size a terrestrial vertebrate can attain. Usefully, it seems that mammals have not reached those limits; even the largest ever-known terrestrial mammals (36, 37) fall well below the proposed maximum masses for terrestrial animals of between 20,000 to 1 million kg (38, 39). If extant mammals had reached their maxima, it would be reflected in additional parameters (quadratic effects) in our model that would account for a slowing of the trajectory toward increasing size; however, at least for now, quadratic models are not necessary (SI Text).

A second difficulty is that if large body size is continuously favored, one would expect that there must have come a point at which it was advantageous for species to become small, exploiting niches made available by continued size increases in competing taxa. In fact, size reduction was common in the evolutionary history of mammals (1,737 of our PAD comparisons or 33.2%) and often occurred at rapid rates (40) (Fig. 3C). For example, there was rapid evolutionary change toward body size decrease in the branch leading to extant bats, although subsequent evolution within this group returned to a general pattern of body size increase (Figs. 1B and 3). In the special case of Diprotodontia, it appears that rapid changes resulting in smaller size dominated, although we do still observe some large body size increases in this group. A possible explanation for this pattern is that these species might have become smaller in response to nutrient-poor environments in Australian habitats (41, 42).

The consistent signal for directional evolutionary change in size implies a relatively small common ancestor of mammals. Previously, ancestral state reconstruction in the face of such a trend has been problematic; conventional comparative methods make it impossible to detect evolutionary trends using extant data. Incorporating fossils into a phylogeny improves ancestral state estimates (43⇓⇓–46); however, here, we test a long-posited suggestion that it is possible to infer from extant data alone the existence of ancient forms whose size or shape is not intermediate to the range of present diversity (17). If our characterization of mammalian size evolution is a good description of the historical processes that led to contemporary mammal species, we should be able to infer ancestral states that are closer to those ancestral states observed in the fossil record than estimates derived from conventional homogeneous models without using fossil data. These expectations are borne out (Fig. 3A). We estimate that the ancestral size at the root of therian mammals was 24.5 g. This value falls within the fossil body size range (20–25 g) of Eomaia scansoria (10), which has recently been suggested to lie close to the root of all placental and marsupial mammals (9). In contrast, the homogeneous Brownian motion model reconstructs the ancestral body size to be greater than 600 g, which is more than an order of magnitude too large.

It may be wrong to assume that fossil species are directly ancestral to extant groups (47). Accordingly, we reconstructed body sizes for 65 unique fossil taxa (Table S3) that represent the oldest or basal members of several mammal groups (Methods). Homogeneous Brownian motion reconstructions of these taxa yield sizes that are systematically larger than paleontological estimates (t = 4.68, P < 0.001; Fig. 4A). In contrast, the separate-slopes regression model reconstructs body sizes that do not differ significantly from paleontological estimates (t = 0.76, P = 0.45; Fig. 4B).

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Fig. 4.

Comparisons of reconstructed body sizes with fossil estimates. The solid colored lines in both plots are the predicted phylogenetic slopes from a regression model of fossil sizes as given in the paleontological literature against reconstructed values (n = 65). The dashed black lines indicate a one-to-one relationship, which is the expected slope if models are predicting body sizes accurately. (A) Predicted body sizes from a homogeneous Brownian motion model compared with fossil estimates. (B) Predicted body sizes from our separate-slopes model in comparison to the fossil record.

Taken together, our results demonstrate that mammals have consistently evolved toward larger size, almost certainly reflecting an adaptive response to new selective circumstances, such as competition (48), climate changes (7, 49), or dietary specialization (11). These results are not compatible with purely passive explanations for trends through time (24, 50). Instead, rapid and repeated instances of evolutionary change toward bigger body size have consistently shaped mammalian diversity, allowing mammal species to attain larger sizes over the millions and millions of years of their evolutionary history. Our findings represent unique support for an adaptive explanation for Cope’s rule, one of the most enduring and iconic notions in evolutionary biology. The ability to detect and characterize trends within extant taxa provides the attractive opportunity to study a broad number of taxonomic groups using the vast amounts of data available for extant species. Such analyses should be viewed as complementary to work based on fossil evidence, which benefits from the ability to study morphology directly through time.