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EVOLUTIONARY BIOLOGY
The evolution of mammalian brain size
J. B. Smaers1,2*, R. S. Rothman3, D. R. Hudson3, A. M. Balanoff4,5, B. Beatty6,7, D. K. N. Dechmann8,9,
D. de Vries10, J. C. Dunn11,12,13, J. G. Fleagle14, C. C. Gilbert6,15,16,17, A. Goswami18, A. N. Iwaniuk19,
W. L. Jungers14,20, M. Kerney12, D. T. Ksepka21,22,23,24, P. R. Manger25, C. S. Mongle2,3,26,
F. J. Rohlf1, N. A. Smith23,27, C. Soligo28, V. Weisbecker29, K. Safi8,9
Relative brain size has long been considered a reflection of cognitive capacities and has played a fundamental
role in developing core theories in the life sciences. Yet, the notion that relative brain size validly represents selec-
tion on brain size relies on the untested assumptions that brain-body allometry is restrained to a stable scaling
relationship across species and that any deviation from this slope is due to selection on brain size. Using the largest
fossil and extant dataset yet assembled, we find that shifts in allometric slope underpin major transitions in mam-
malian evolution and are often primarily characterized by marked changes in body size. Our results reveal that the
largest-brained mammals achieved large relative brain sizes by highly divergent paths. These findings prompt a
reevaluation of the traditional paradigm of relative brain size and open new opportunities to improve our under-
standing of the genetic and developmental mechanisms that influence brain size.
INTRODUCTION
The brain is directly responsible for governing an animal’s interac-
tions with its environment. As such, the brain is often considered to
flexibly respond to selection in changing environments (1–3). Brain
size is, however, also commonly accepted to be restrained by ener-
getic requirements that are considered universal across all verte-
brates (4,5). This apparent paradox highlights that brain size is one
of the most salient traits for understanding the fundamental balance
between adaptability and constraint in evolution. Despite this im-
portance, crucial aspects related to the timing, pattern, and drivers
that underlie modern phenotypic diversity in brain size remain
undescribed.
It has long been recognized that brain size scales with body size
following a standard linear allometric power law (6). The scaling
coefficient (slope) of this allometry is assumed to be relatively stable
across vertebrate classes and orders (most often estimated as be-
tween 2/3 and 3/4) (7) and is thought to reflect universal energetic
growth constraints (4,5). Largely because of methodological limita-
tions in phylogenetic comparative statistics, this working hypo-
thesis has received little scrutiny. Previous studies have therefore
mostly been limited to comparing residual variation along a stable
slope [i.e., mean relative brain size or encephalization quotient
(EQ), quantified through differences in the intercept of the evolu-
tionary allometry] (7,8). There is, however, evidence to suggest that
changes in the slope (quantifying changes in brain-body covaria-
tion) may constitute an important additional source of comparative
variation (9–12).
Identifying the points at which evolutionary shifts in brain-body
covariation occur is of paramount importance to understanding the
selection pressures that may be operating. Whereas shifts in inter-
cept address changes in mean among traits, shifts in slope address
changes in variation among traits (e.g., stabilizing selection restrains
variation, divergent selection allows for variation) (13). Failing to
account for the possibility that trait covariation may differ among
groups of species could potentially hide crucial sources of variation
that contribute to explaining phenotypic diversity. Moreover, evo-
lutionary allometries (allometries quantified across species) are de-
termined by ontogenetic and static allometries (across developmental
time in the same individual and individuals of the same species,
respectively) and thus are indicative of the genetic and developmen-
tal mechanisms that regulate growth (14). Consequently, more de-
tailed information on the allometric patterns that characterize the
brain-body relationship across evolutionary time will provide new
opportunities to investigate the nature of the processes that shape
those patterns. Last, the occurrence of shifts in slope would indicate
that comparisons of relative brain size (and EQ) are only valid among
groups with a similar slope. The ubiquitous approach of quantify-
ing only residual variation along a stable slope may therefore lead to
biased results and incorrect interpretations.
Birds and mammals are of particular interest in this context be-
cause they both independently evolved relatively larger brains than
1Department of Anthropology, Stony Brook University, Stony Brook, NY 11794, USA.
2Division of Anthropology, American Museum of Natural History, New York,
NY 10024, USA. 3Interdepartmental Doctoral Program in Anthropological Science s,
Stony Brook University, Stony Brook, NY 11794, USA. 4Department of Psychologi-
cal and Brain Sciences Johns Hopkins University, Baltimore, MD 21218, USA. 5Division
of Paleontology, American Museum of Natural History, New York, NY 10024, USA.
6NYIT College of Osteopathic Medicine, Old Westbury, NY 11568, USA. 7United
States National Museum, Smithsonian Institution, Washington, DC 20560, USA.
8Department of Migration, Max-Planck Institute of Animal Behavior, 78315 Radolfzell,
Germany. 9Department of Biology, University of Konstanz, 78464 Konstanz, Germany.
10Ecosystems and Environment Research Centre, School of Science, Engineering
and Environment, University of Salford, Manchester M5 4WX, UK. 11Division of Bio-
logical Anthropology, University of Cambridge, Cambridge CB2 3QG, UK. 12Behav-
ioral Ecology Research Group, Anglia Ruskin University, Cambridge CB1 1PT, UK.
13Department of Cognitive Biology, University of Vienna, Vienna 1090, Austria.
14Department of Anatomical Sciences, Stony Brook University, Stony Brook, NY
11794, USA. 15Department of Anthropology, Hunter College, New York, NY 10065,
USA. 16PhD Program in Anthropology, Graduate Center of the City University of
New York, 365 Fifth Avenue, New York, NY 10016, USA. 17New York Consortium in Evo-
lutionary Primatology, New York, NY 10065, USA. 18Department of Life Sciences, Nat-
ural History Museum, London SW7 5BD, UK. 19Department of Neuroscience,
University of Lethbridge, Lethbridge, AB T1K-3M4, Canada. 20Association Vahatra,
BP 3972, Antananarivo 101, Madagascar. 21Bruce Museum, Greenwich, CT 06830, USA.
22Department of Ornithology, American Museum of Natural History, New York, NY
10024, USA. 23Division of Science and Education, Field Museum of Natural History,
Chicago, IL 60605, USA. 24Department of Paleobiology, Smithsonian Institution,
Washington, DC 20013, USA. 25School of Anatomical Sciences, Faculty of Health
Sciences, University of the Witwatersrand, Johannesburg, South Africa. 26Turkana
Basin Institute, Stony Brook University, Stony Brook, NY 11794, USA. 27Campbell
Geology Museum, Clemson University, Clemson, SC 29634, USA. 28Department of
Anthropology, University College London, London WC1H 0BW, UK. 29College of
Science and Engineering, Flinders University, Bedford Park, SA 5042, Australia.
*Corresponding author. Email: jeroen.smaers@stonybrook.edu
Copyright © 2021
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rights reserved;
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American Association
for the Advancement
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NonCommercial
License 4.0 (CC BY-NC).
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other vertebrate classes (7). This innovation was likely facilitated by
an easing of the phenotypic integration between brain size and body
size (15). Such decoupling leads to increased variation available to
selection, which, in turn, is expected to heighten flexibility in re-
sponse to selection (16). Recent work has shown that shifts in slope
are paramount to explaining the brain’s evolutionary diversification
in birds (12), demonstrating that the selective response to increased
variation is not restricted solely to changes in mean relative brain
size but may also play out in terms of changes in brain-body covari-
ation. In mammals, shifts in brain-body covariation have been sug-
gested to occur in primates (9), carnivorans (17), marsupials, (18),
and among mammalian orders (11). However, it has remained un-
clear where and when such shifts occur throughout mammalian
evolution and how they contribute to explaining variation in the
brain-body relationship.
Several methodological innovations (19,20), in conjunction with
ever-increasing data availability, make it possible to test the widely
held assumption that the slope of brain-body allometry is stable in
mammals. Here, we use bivariate Bayesian multipeak Ornstein-
Uhlenbeck (OU) modeling (19,21) in combination with phyloge-
netic analysis of covariance (20) to identify changes in both slope
and intercept of the evolutionary allometry of the brain-body
relationship in mammals. We apply these methods to the largest
taxonomic sampling to date, comprising 107 extinct species and
1311 extant species spanning 21 orders (table S1; we quantify size
in terms of mass for both brain and body). Our approach allows us
to identify where and when allometric shifts occur in mammalian
evolution and whether these shifts are driven primarily by changes
in brain or body size. Our results provide new insight into the types
of selection that have shaped extant diversity and open new oppor-
tunities for research into the underlying mechanisms.
RESULTS
Allometric patterning through time
Across more than 1400 species, mammalian brain-body allometry
comprises 30 distinct grades (F21,2=29.02, P<0.001; L.Ratio=525.68,
P< 0.001, AIC=488, AICѡ > 0.999; Figs. 1 and 2,Table1, and
table S2). The ancestral mammalian grade has a slope of 0.51 and is
retained by several early radiating orders (golden moles and ten-
recs, elephant shrews, dugongs and manatees, hyraxes, sloths, and
armadillos), as well as by tree shrews, hares and rabbits, squirrels,
flying lemurs, and tarsiers (Fig.1). Shifts in slope are common (of
29 grade shifts, 16 include a shift in slope) and characterize both
early and late diversification. Most early slope shifts occurred near
the Cretaceous-Paleogene boundary (K-Pg; ~66 million years (Ma)
ago; Fig.1), and all indicate a shift toward a higher slope. This tem-
poral clustering suggests that changes in the relative growth trajec-
tory of brain and body size were fundamental for mammalian
diversification in the wake of the K-Pg mass extinction. This aligns
with a pattern recently observed in birds (12), suggesting that eco-
logical radiation and subsequent niche expansion following the
K-Pg mass extinction played a major role in shaping the trajectories
by which both birds and mammals became the largest-brained ver-
tebrate classes.
Shifts in slope (both increases and decreases) were also crucial in
later diversifications, with one prime example being anthropoid
primates (Fig.1). Stem and early crown anthropoids retained the ancestral
mammalian condition until shortly after the Paleogene-Neogene
boundary (~23Ma ago), after which several significant shifts oc-
curred rapidly (Table1 and table S2). These shifts from the ances-
tral grade (slope: b=0.51) resulted in new slopes for colobines
(b=0.67), cercopithecines (b =0.43), lesser apes (b= 0.32), great
apes (b= 0.23), hominins (b=1.10), and callitrichines (b =0.58).
Other shifts in slope near the Paleogene-Neogene boundary oc-
curred in bears and pinnipeds (Fig.1; Table1 and table S2), which
are noteworthy for having the largest downward shifts in slope in
the sample: from b = 0.58 in other carnivorans to b = 0.39 and
b=0.23, respectively. See the Supplementary Results for a complete
description of allometric repatterning across clades.
DISCUSSION
Different evolutionary trajectories for the
largest-brained mammals
Five mammalian groups (elephants, great apes, hominins, toothed
whales, and delphinids) attained their position at the top of the
bivariate brain-body space (Fig. 2) by following an unexpectedly
diverse range of trajectories. Elephants represent the simplest case,
as they evolved directly from the ancestral mammalian grade and
achieved large relative brain size by vastly increasing their body size
while increasing brain size even more rapidly (table S3). In toothed
whales and delphinids, relative brain size increased in a stepwise
manner. The first intercept shift occurred in the stem fereuungu-
lates, which follow a trajectory similar to (although less pronounced
than) that in elephants, by increasing brain size more than body
size. This was followed by an intercept shift in stem toothed whales,
which decreased brain and body size relative to stem cetaceans, with
body size decreasing more rapidly than brain size (uncertainty sur-
rounding this scenario exists and is a function of the interpretation
of the fossil record; see the Supplementary Results). Delphinids
show a third intercept shift driven by body size decrease and brain
size increase relative to other toothed whales. The evolutionary tra-
jectory of great apes and hominins was the most complex, starting
with two consecutive downward shifts in slope (while increasing
both brain and body size) in stem apes and stem great apes, fol-
lowed by the most marked increase in slope observed in this study,
in hominins (from b=0.23 to b=1.10). Delphinids and hominins,
which converge at the apex of the brain-body space, are the only
two grades with negative brain-body correlations, that is, brain size
increased while body size decreased (table S3). All five of the mam-
mal groups with the largest brain size may have originated in the
Neogene. This remarkable diversity in evolutionary trajectories and
late attainment of peak relative brain size parallels patterns in birds
in which the largest-brained taxa (parrots and corvids) attained
large brain sizes during the Neogene via very different trajectories
(12). These parallel patterns between birds and mammals suggest
that, similar to the K-Pg transition, the Paleogene-Neogene transition
may have created conditions ripe for ecological radiations and niche
expansions that affected brain size evolution.
Similar evolutionary trajectories for the
smallest-brained mammals
In contrast to relatively large-brained clades, species that lie near
the bottom of the brain-body space are consistently characterized
by a shift toward a higher slope and a lower intercept. Such shifts
occur in afrosoricids (b=0.66), hystricomorph rodents (b=0.66),
myomorph and castorimorph rodents (b=0.57), bats (b=0.66),
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eulipotyphlans (b=0.62), and marsupials (b = 0.58); all of which
derive directly from the ancestral mammalian grade (b=0.51)
(Table1). Bats, eulipotyphlans, and afrosoricids converge on the
same grade (i.e., same intercept and slope) as the myomorph and
castorimorph rodents and marsupials. These allometric changes are
mostly explained by a disproportionally higher decrease in mean brain
size relative to body size and a lower variance in body size relative to
brain size (tables S3 to S5). This suggests that body size becomes
more restrained than brain size at smaller body sizes, permitting
smaller animals to evolve disproportionately small brain sizes.
The higher evolutionary flexibility of mean brain size relative to
mean body size is apparent across all mammals, with stem toothed
whales being a notable exception (table S3). This contrasts with
birds, where pronounced changes in mean body size compared with
mean brain size are common (12). This effect may be rooted in the
scalability of mammalian neocortical architecture. While the mammalian
neocortex (dorsal pallium) is organized as an outer layer of neurons
surrounding scalable white matter, the bird dorsal pallium is orga-
nized in a nuclear manner that might limit its scalability (22).
Divergent versus stabilizing selection in brain and/
or body size
A detailed account of changes in evolutionary allometry across deep
time provides opportunities for understanding the types of selec-
tion operating in certain taxa. A crucial aspect in this regard are
putative differences in the cross-species variance of a trait among
groups. Although variance has long been considered crucial to un-
derstanding the types of selection operating in certain taxa (13) and
Fig. 1. Time-calibrated phylogeny of mammals with branch colors corresponding to the 30 significantly different allometric grades identified in this study
(Table 1). The ancestral mammalian grade is indicated in gray, with warmer colors (green and red) assigned to higher-slope grades, and colder colors (blue and purple)
to lower-slope grades. For each grade, a lighter color hue indicates grades with a lower intercept, and a darker hue indicates grades with a higher intercept (Table 1). Ar-
rows indicate changes in mean body size (white arrows) or mean brain size (black arrows) resulting in grade shifts, with double arrows indicating one of these variables is
changing faster than the other after considering allometry. Triangles indicate changes in cross-species trait variance in body size (white triangles) or brain size (black tri-
angles), with normal triangles indicating increase in mean variance and inverted triangles indicating decrease in mean variance (tables S3 to S5). The equality sign (=)
indicates no discernible change in brain size variance. See data S2 for individual species labels. Illustration by J. Lázaro.
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to play a principal role in driving shifts in allometric slope between
grades (fig. S1), it was undescribed by previous research. Several
patterns revealed by our analyses (table S5) demonstrate how
changes in the cross-species variance of a trait between groups af-
fect shifts in slope and may reveal possible selective pressures.
Stem cercopithecoids derived from the ancestral mammalian
grade by disproportionately increasing mean brain size relative to
mean body size and disproportionately decreasing body size vari-
ance relative to brain size variance (tables S3 to S5). This pattern
resulted in an increase in slope (from b=0.51 to b=0.67; Fig.1 and
Table 1). Within cercopithecoids, cercopithecines (baboons, ma-
caques, and relatives) diverged toward a lower slope (b=0.43)
through a moderate increase in mean brain and body size (~1.28 times
greater mean), a strong increase in body size variance (3.45 times
greater), and a stabilization of brain size variance (1.16 times greater).
Brain size of cercopithecines thus varies across a much wider range
of body size than other cercopithecoids (i.e., colobines), suggesting
more divergent selection on body size (scenario displayed in fig. S1B).
Considering the effects of locomotion on body size (23), and the fact
that cercopithecines include both arboreal and terrestrial species while
colobines are predominantly arboreal, this allometric repatterning
is likely associated with their differences inlocomotor diversity.
A similar scenario plays out in pinnipeds, which underwent a
significant decrease in slope compared with other carnivorans (from
b = 0.58 in carnivorans to b = 0.23), primarily due to decreased
brain size variance relative to body size variance (table S5). Body
size in pinnipeds thus varies widely compared with other carniv-
orans given their range of brain sizes (table S5). This suggests diver-
gent selection on body size, most likely influenced by the transition
to a semiaquatic niche (24).
A contrasting scenario is provided by great apes and hominins,
which have extremely different slopes. Great apes have the lowest
slope in the sample (b = 0.23, which they share with pinnipeds),
whereas hominins have the highest slope (b=1.10). Although both
mean brain size and mean body size are similar across these two
nested grades, the variance in hominin brain size is 6.45 times greater
than in great apes, while the variance in body size is only 1.58 times
greater. In this case, a major shift in variance occurred in brain size
while body size remained mostly static, suggesting divergent selection
on brain size (scenario displayed in fig. S1C) and more stabilizing
selection on body size (likely associated with the shift to bipedality
in hominins).
Allometric shifts do not always represent shifts in cognition
Variation in relative brain size is traditionally associated with cog-
nitive capacities and behavioral flexibility, but this notion has rested
on several fundamental assumptions. First, it has been assumed that
the slope of the brain-body relationship is stable across species and
that deviations from this allometry reflect selection on brain size. As
a result, numerous studies geared toward explaining the evolution
of relative brain size have focused on the evolution of brain size and
cognition (25,26). Our results do not support this assumption. Evo-
lutionary shifts in brain-body allometry commonly included changes
in slope and were often driven by changes in body size. Rather than
focusing on residual deviation from a common slope, the emphasis
should be on the allometric shifts themselves. In addition, address-
ing factors that are not directly tied to brain size or cognition likely
plays an important role. Some selective pressures that play a key
role in species diversification are more directly tied to body size
than brain size.
A prime example is locomotion. Known to influence body size
and energetic expenditure [e.g., high cost of flying in bats (27)], ma-
jor transitions inlocomotion allow for a redistribution of energetic
allocation to growth, thereby providing opportunities for allometric
Fig. 2. pGLS regressions for each of the grades. The ancestral mammalian grade is indicated in each display to provide an evolutionary context. Numbers indicate the
value of the slope for each grade. Colors and silhouettes are as in Fig. 1.
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repatterning. This is also apparent in birds, where relative brain size
is associated with flight style and complexity (28). Our analyses
confirm the influence of locomotion on brain-body allometry in
mammals by demonstrating that many major transitions inloco-
motion coincide with allometric repatterning events. For example,
the evolution of flight in bats coincides with an allometric shift in
intercept and slope (AIC=69.339; AICѡ < 0.001) that is charac-
terized by decreased body size variance, suggesting strong con-
straints on body size due to the highly specialized and energetically
demanding locomotion in this group. The transition from the
mammalian ancestral grade to terrestrial cursorial locomotion in
fereuungulates (AIC=46.051; AICѡ < 0.001) coincides with a dis-
proportionate increase in mean brain size to body size. The transition
to a semiaquatic niche in pinnipeds (AIC=31.527; AICѡ < 0.001)
coincides with disproportionate decrease in brain size variance rel-
ative to body size variance. Notably, the initial transition to an aquatic
niche in cetaceans is not linked to a shift in brain-body allometry,
although later shifts to higher mean brain size do occur in toothed
whales and delphinids. This makes whales a compelling counter ex-
ample, despite being largely freed from size constraints and reach-
ing the largest size of any vertebrates, baleen whales retain the same
brain-body allometry as their terrestrial cetartiodactylan relatives.
Within primates, allometric shifts coincide with increased commit-
ment to terrestriality in cercopithecines (AIC=81.709; AICѡ <
0.001). The origins of the great ape grade coincide with a decreased
slope (AIC=14.632; AICѡ < 0.005) and is associated with a
Table 1. Phylogenetic generalized least-squares parameters for all grades identified in the analysis. Grade numbers (1 to 6) indicate groups of clades with
significantly different slopes (clades with the same grade number indicate slopes that are not significantly different from each other). Within each grade with a
similar slope, grade letters indicate clades with a significantly different intercept. b and a refer to the values for the slope and intercept. “Lower” and “Upper”
refer to the lower and upper bounds of the 95% confidence intervals. Note that some grades with low sample size are not listed here because they did not
include a significant shift in slope (only a significant shift in intercept). These grades include elephants (n = 8), Cebus (n = 6), Atelinae (n = 8), Saki/Uakari (n = 4),
Daubentonia (n = 1), Tragulina (n = 4), and pangolin (n = 1). These grades are, however, listed in table S3, which analyzes their mean brain and body sizes.
NW, New World; OW, Old World.
Slope Intercept
Grade Clade n b SE Lower Upper aSE Lower Upper
1A Pinnipeds 32 0.226 0.080 0.064 0.389 3.001 1.045 0.872 5.130
1B Stem great apes 7 0.229 0.061 0.085 0.373 3.520 0.657 1.967 5.073
2A Stem apes 9 0.377 0.159 0.018 0.736 1.394 1.475 −1.944 4.731
2A Ursids 10 0.323 0.077 0.151 0.496 1.922 0.801 0.137 3.707
2A Cercopithecines 56 0.426 0.033 0.360 0.493 0.675 0.312 0.050 1.301
3A Ancestral 130 0.510 0.021 0.469 0.551 −1.588 0.357 −2.293 −0.882
3B Stem NW monkeys 16 0.402 0.051 0.294 0.510 0.309 0.383 −0.503 1.121
3B Stem
fereuungulates 100 0.542 0.020 0.501 0.582 −1.028 0.295 −1.612 −0.443
3D Stem-toothed
whales*31 0.468 0.035 0.396 0.540 1.093 0.436 0.204 1.982
3E Delphinids 16 0.533 0.046 0.435 0.631 0.847 0.550 −0.320 2.013
4A Dunnarts 15 0.545 0.092 0.349 0.741 −2.645 0.251 −3.180 −2.111
4B Castorimorphs/
myomorphs 180 0.567 0.014 0.538 0.595 −2.226 0.130 −2.482 −1.969
4B Stem marsupials 150 0.580 0.018 0.544 0.615 −2.140 0.174 −2.484 −1.797
4C Strepsirrhines 56 0.577 0.031 0.514 0.639 −1.403 0.267 −1.938 −0.869
4C Callitrichines 16 0.578 0.059 0.452 0.704 −1.279 0.361 −2.044 −0.515
4C Stem carnivorans 178 0.577 0.019 0.539 0.614 −1.666 0.204 −2.068 −1.264
4D Stem
cercopithecoids°29 0.671 0.074 0.520 0.822 −1.676 0.673 −3.052 −0.300
5A Eulipotyphlans 48 0.618 0.029 0.560 0.676 −2.712 0.158 −3.030 −2.394
5A Stem bats 217 0.672 0.015 0.642 0.701 −2.834 0.068 −2.968 −2.700
5A Afrosoricids 13 0.659 0.072 0.503 0.815 −3.010 0.369 −3.808 −2.213
5B Hystricomorphs 19 0.663 0.047 0.565 0.760 −2.674 0.357 −3.421 −1.926
5B OW fruit bats 47 0.665 0.016 0.633 0.697 −2.366 0.071 −2.510 −2.223
6A Hominins 11 1.097 0.164 0.736 1.458 −5.304 1.722 −9.095 −1.514
*“Stem toothed whales” refer to stem and crown nondelphinid toothed whales. °“Stem cercopithecoids” consists of the extinct species Victoriapithecus and
crown colobines.
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substantially larger increase in body size variance compared with
brain size variance. This may similarly have been associated with
increased reliance on orthograde behaviors related to terrestriali-
ty (29). The transition to bipedalism in hominins coincides with a
marked increase in slope (AIC=58.527, AICѡ < 0.001) that is
characterized by higher brain size variance relative to body size
variance.
Other factors that likely influence the brain-body allometry pri-
marily through changes in body mass include, but are not limited
to, sexual size dimorphism, diving depth in aquatic niches (30),
antipredator defensive mechanisms (31), and energetic strategies to
maintain homeostasis (possibly contributing to explaining the allo-
metric shifts in the convergent eulipotyphlans and afrosoricids)
(32). Overall, the general alignment of allometric shifts with major
transitions inlocomotion (table S2) and concomitant selection on
body size (e.g., small body size in a volant niche, large body size in
terrestrial and aquatic niches) suggests that the evolutionary repat-
terning of the brain-body relationship reflects an adaptive profile
that extends beyond selection on brain size alone (33). The over-
whelming focus on brain size and cognition in the literature there-
fore should be reconsidered.
A second fundamental assumption is that brain-body allometry
reflects the maintenance of basic autonomic, and sensory functions
and allometric deviations therefore reflect cognition (34). This in
turn relies on the assumption that there is little variation in the rel-
ative volumes of brain regions and that larger brains are mostly
scaled up small brains (35). If true, the only target for explanation
would be the (allometrically adjusted) brain-to-body ratio, irrespec-
tive of how changes in body size alter allometric patterning. This
assumption has, however, already been disproven by numerous
multivariate studies of brain region sizes (36,37). A poignant com-
parison in this context is that between the polar bear (Ursus maritimus)
and the California sea lion (Zalophus californianus). Although these
two species have a similar mean body size, the brain size of the polar
bear is twice that of the California sea lion. Consequently, the polar
bear exhibits a much higher (four times higher) relative brain size.
However, the California sea lion has 3.6 times more volume devoted
to brain regions that are associated with higher cognition relative to
regions associated with basic autonomic and sensory functions
(38). This is likely associated with vocal learning and other cogni-
tive skills in the California sea lion (39). Although cognitive tests in
polar bears are generally lacking, this example indicates that relative
brain size alone may not be a sufficient proxy for the amount of
brain tissue that is allocated to higher cognition (33).
This example further illustrates the potentially confounding
effects of assuming a stable slope across all species. As mentioned,
pinnipeds display the lowest slope among mammals, a pattern that
is most likely driven by divergent selection on body size. Given that
pinnipeds are large mammals, such a low slope inevitably results in
low relative brain size when considering a common slope (the com-
mon slope is higher than that observed in pinnipeds alone). Attrib-
uting this low relative brain size to selection on brain size and
cognition obscures the trajectory that resulted in their low relative
brain size (namely, most predominantly selection on body size, not
brain size). Overall, assuming a stable slope across all species im-
plies that selection on body size is comparable across species—an
assumption that is difficult to uphold given the wide variety of niches
that mammals inhabit and the fundamental role that body size plays
in ecological and evolutionary processes.
In general, these results indicate that the brain-body relationship
reveals more than just selection on brain size. Therefore, relative
brain size may not always be a valid proxy of cognition. The same
argument applies to the widely used EQ measure (8), which is also
quantified using deviations from a stable slope. A possible way to
improve the comparative study of cognition is to compare different
brain regions. Whereas comparisons among brain regions associated
with different functions would reveal neurobehavioral specializa-
tions (36,38), comparisons among brain regions from different de-
velopmental precursors would highlight changes in growth allocation
(10). Such remapping factors ensure validity by using hypotheses
that are based on established neuroanatomical and neuroscientific
principles (40). Comparisons among brain regions also have the po-
tential to reveal which patterns of brain region evolution explain
brain size evolution (41) and whether such patterns of brain region
evolution can be tied to cognition (38). Such analyses are essential
because the evolution of brain size may not always be in line with
the evolution of brain regions (or other neuroanatomical features)
that are associated with higher cognition. The association between
increased brain size and increased complexity is assuredly strong
(42), but crucial exceptions to this trend suggest that much may be
left to discover on this topic. For example, whereas some archaeo-
cetes (fossil stem cetaceans) had brains that are larger than toothed
whales (data S2), their brains have relatively smaller cerebral hemi-
spheres compared with toothed whales (43). Early cetacean brain
evolution may thus have comprised two different trajectories: in-
creased brain size with low complexity in archaeocetes, and stable
or decreased brain size with high complexity in toothed whales. In
this example, complexity does not match absolute brain size, al-
though it does match with relative brain size as toothed whales have
a higher relative brain size. In the above described comparison of
the polar bear and the California sea lion (38), however, complexity
does not match either absolute or relative brain size (or EQ). Both
these empirical cases confirm that deviations from the general asso-
ciation between brain size and complexity occur and may be a source
of future discovery. Such trends are of paramount importance to
the study of cognition and can only be revealed through compari-
sons among brain regions (or other neuroanatomical features).
Allometric shifts reveal comparative differences
in adaptive profile
The primary importance of identifying evolutionary allometric
shifts lies in the fact that they provide fundamental information on
both the patterns and the processes that shape extant variation. Be-
cause evolutionary allometries are determined by ontogenetic and
population-level allometries, they can be considered as macroevo-
lutionary signatures of changes in the microevolutionary mechanisms
that regulate growth (14). Accurate identification of macroevolu-
tionary shifts thus provides crucial information on the mechanisms
that shape comparative differences in adaptive profile.
The potential of this approach is arguably best exemplified by
humans, where a shift to bipedality allowed for a redistribution of
energy from locomotion to reproduction and brain growth (44).
This redistribution of energy to the brain effected changes in the
mechanisms of its growth, for example, delayed expression of genes
associated with synaptic development (45) and neotenic changes in
mRNA expression (46) for those brain regions that explain human
brain size expansion (36,41). In turn, these developmental changes
caused an evolutionary allometric shift that is characterized by a
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significantly higher ratio of brain variance to body variance, which
indicates divergent selection on brain size (causing an increase in
slope; see Figs.1 and 2 and table S5).
Humans represent an evolutionary allometric shift that is driven
primarily by changes in brain size. We observed other allometric
repatterning events driven primarily by brain size in elephants, Old
World fruit bats, toothed whales, and delphinids. In other clades
evolutionary allometric shifts may be primarily driven by selection
for body size (e.g., cercopithecines, great apes, and pinnipeds). In all
cases, these allometric shifts occur at transitions into a new niche
and/or changes in energetic requirements or energetic availability
and further involve redistribution of growth allocation, shifts in the
genetic and developmental mechanisms that regulate growth, and
allometric repatterning.
Although the mechanisms underlying different types of allomet ric
shifts are not yet fully understood, we emphasize that accurate identifi-
cation of these shifts is a necessary first step toward reaching this goal.
Contrary to the traditional paradigm of relative brain size, we show
that allometric shifts can be characterized by changes in slope and may
be caused by changes in both brain and/or body size. This prompts a
reevaluation of the conventional concept of a grade shift as only rep-
resenting changes in intercept and reveals that a full understanding of
the evolution of brain size relative to body size requires the consider-
ation of effects that extend beyond selection on brain size alone.
Implications for the use of “relative brain size”
Relative brain size and the related EQ measure are one of the most
widely used measures in comparative biology and have played a
fundamental role in developing several core theories in the life sci-
ences (4,47). Here, we demonstrate that the way in which relative
brain size and EQ are traditionally quantified (using deviations
from a stable slope) may result in erroneous inferences on which
taxa increased or decreased brain size and hampers a deeper under-
standing of the patterns and types of selection that explain changes
in brain size (and body size). In other words, our results demon-
strate that the traditional statistical measures of relative brain size
and EQ do not always validly capture variation in brain size. We
demonstrate that a more nuanced approach to quantifying varia-
tion of brain size relative to body size (quantifying changes in both
the intercept and the slope of the evolutionary allometry, combined
with investigating univariate patterns of change in brain and/or
body size that underpin these bivariate changes in intercept and
slope) provides new insights and opens new opportunities for im-
proving our understanding of the patterns and processes that char-
acterize brain size evolution.
In general, our results do not contradict the notion that variation
in brain size is associated with cognition. Our results rather demon-
strate that the traditional measures of relative brain size and EQ do
not always validly capture variation in brain size. This result cau-
tions against the unequivocal use of relative brain size or EQ to
quantify or study cognition. We argue that the evolution of cogni-
tion is more validly represented by comparisons among brain re-
gions (or other neuroanatomical features). Such comparisons have
the potential to identify which patterns of brain region evolution
explain brain size evolution and therefore reveal more precise and
relevant information regarding the evolution of cognition (38,41).
This does not render the study of brain size relative to body size
useless. On the contrary, it reframes this trait more broadly to rep-
resent comparative differences in adaptive profile, thereby accounting
for the complexity and diversity of the underlying processes and ul-
timately encapsulating aspects beyond cognition and brain size.
MATERIALS AND METHODS
Data
Data on brain and body size (both quantified as mass) were gleaned
from the literature (table S1 and data S2). Comparisons between
techniques using brain tissue mass data and endocranial volume
data from the skulls of fossil species have been validated in multiple
published studies (48,49), and endocranial volume has been proven
a reliable proxy estimate of brain size of both mammalian and non-
mammalian taxa (11). The phylogeny is a consensus tree derived by
Smaers etal. (38) from the mammalian supertree compiled by
Faurby etal. (50). Fossil placement was done according to the liter-
ature (table S1) and is detailed in data S2.
Identifying shifts in allometric patterning
Methods are similar to those reported in previous work (12). We
estimated differences in slope and intercept of the brain-to-body
relationship directly from the data using a Bayesian multiregime
OU modeling approach (19). The OU model assumes that the evo-
lution of a continuous trait “X” along a branch over time increment
“t” is quantified as dX(t)=[ − X(t)]dt+dB(t) (51). Relative to
the standard Brownian motion (BM) model [dX(t)=dB(t)], the
OU model adds parameters that estimate mean trait value () and
the rate at which changes in mean values are observed (). The in-
clusion of these additional parameters allows an appropriate differ-
entiation between changes in the mean ( and ) and variance ()
of a trait over time and thus renders the OU model framework more
appropriate than BM for modeling changes in the direction of trait
evolution. Here, we used a bivariate implementation of OU model-
ing that is explicitly geared toward estimating shifts in slope and
intercept of evolutionary allometries by using reversible-jump Mar-
kov chain Monte Carlo (MCMC) machinery (21) (“OUrjMCMC”).
We implemented this approach by combining 10 parallel chains of
2 million iterations each with a burn-in proportion of 0.3. We al-
lowed only one shift per branch, and the total number of shifts was
constrained by means of a conditional Poisson prior with a mean
equal to 2.5% of the total number of branches in the tree and a max-
imum number of shifts equal to 5%. Starting points for MCMC
chains were set by randomly drawing a number of shifts from the
prior distribution and assigning these shifts to branches randomly
drawn from the phylogeny with a probability proportional to the
size of the clade descended from that branch. The MCMC was ini-
tialized without any birth-death proposals for the first 10,000 gener-
ations to improve the fit of the model. The output of this procedure
generates an estimate of a best-fit allometric model with posterior
probabilities assigned to each shift in slope and/or intercept.
In part due to difficulties in parameter estimation intrinsic to
OU modeling (52), the bivariate OUrjMCMC output may include
false positives and/or false negatives (21). To identify false nega-
tives, we ran a univariate OU model estimation procedure (19) on
the residuals of each grade to detect shifts in mean. If such shifts in
mean were detected, they were added as shifts in intercept to the
allometric model (no such shifts were detected for these data). To
identify false positives, the allometric model was translated to a
least-squares framework and used in a confirmatory analysis using
phylogenetic analysis of covariance (“pANCOVA”) (20). Although
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pANCOVA uses a different evolutionary process than OU modeling
(i.e., BM instead of OU), it is expected that grade membership as esti-
mated by the OU modeling is confirmed using least-squares analysis.
Because BM assumes fewer statistical parameters, pANCOVA can be
considered as a conservative confirmatory test of the significance of
grade membership as estimated by OU modeling. All reported results
are those that were confirmed by pANCOVA (Table1 and table S2).
Assessing differential changes in mean brain and/
or body size
To assess whether changes in the brain-to-body allometry were
driven primarily by mean brain size or body size, phylogenetic
means for both brain size and body size were calculated for each of
the allometric grades identified by the allometric patterning analy-
sis. Phylogenetic means were calculated following standard phylo-
genetic generalized least-squares procedures (20).
Patterns of mean brain/body size increase/decrease were evalu-
ated by comparing mean differences in brain size and body size be-
tween ancestral and descendant grades (or “derived grades”; note
that we, here, consider “descendant” and “derived” as equivalent
terms) (table S3). The ratio of the difference in ancestral-to-descendant
mean brain size to the difference in ancestral-to-descendant
mean body size (
¯
brain
_
¯
body
; log scale) was considered as an indication of
the proportionality of ancestral-to-descendant change in mean
brain size relative to mean body size. The scaling coefficient of the
brain-to-body relationship of the ancestral grade was used as the
expected proportionality of this ratio. The upper bound of the 95%
confidence interval of the scaling coefficient of the ancestral grade
was used as the cutoff to infer that the change in mean size observed
from ancestral-to-descendant grade is characterized by more change
in mean brain size than body size. To account for the fact that gen-
eralized least-squares procedures minimize residual error for the
dependent variable, we inverse this procedure when evaluating
changes in mean body size. For body size, we thus considered the
proportion
(
¯
body
_
¯
brain
)
relative to the scaling coefficient of the ancestral
body-to-brain relationship (table S4). Although we consider the
use of the body-to-brain relationship for evaluating body size to be
more rigorous than also using the brain-to-body relationship for
these purposes, we emphasize that the results are largely unaffected
by this choice (i.e., the same results regarding disproportionate
brain/body increase/decrease are attained when using the brain-
to-body relationship to evaluate both brain size and body size).
More change in mean brain size than mean body size is inferred
when
(
¯
brain
_
¯
body
)
is higher than the upper bound of the ancestral brain-
to-body expectation and
(
¯
body
_
¯
brain
)
is lower than the upper bound body-
to-brain expectation. In Fig.1, this scenario is indicated as two
arrows for mean brain size and one arrow for mean body size. More
change in mean body size than mean brain size is inferred when
(
¯
brain
_
¯
body
)
is lower than the upper bound of the ancestral brain-to-body
expectation and
(
¯
body
_
¯
brain
)
is higher than the upper bound body-to-
brain expectation. In Fig.1, this scenario is indicated as one arrow for
mean brain size and two arrows for mean body size (which is the case
only for toothed whales). In pinnipeds, the observed proportion lies
above the upper bound of both the ancestral brain-to-body and body-
to-brain relationship. This is therefore indicated as two arrows for
brain size and two for body size (both indicating an increase in size).
For example, stem cercopithecoid primates (consisting of the
fossil Victoriapithecus and extant colobines) derive directly from
the mammalian ancestral grade (Fig.1). This gives this grade an
expected change in mean brain size relative to change in mean body
size of 0.47 with a maximum expectation of 0.55 (table S3). The
mammalian ancestral grade has a mean brain size of 1.92 and a
mean body size of 6.92 (log scale). The stem cercopithecoid/colo-
bine grade has a mean brain size of 4.40 and a mean body size of
9.04. The difference in mean brain size from the mammalian ances-
tral grade to the colobine grade is +2.48; that of body size is +2.12.
The ratio
(
¯
brain
_
¯
body
)
is thus 1.17, which is 0.62 points above the up-
per bound brain-to-body expectation (table S3). The ratio
(
¯
body
_
¯
brain
)
is
0.86, which is 0.88 below the upper bound of the body-to-brain ex-
pectation (table S4). Colobines thus indicate more change in mean
brain size relative to change in mean body size than expected from
their ancestral grade.
Stem toothed whales are the only grade in the sample that indi-
cates more change in mean body size than change in mean brain
size. Relative to stem cetaceans (archaeocetes), stem toothed whales
decrease in size (although note the uncertainties inherent in this
inference discussed in the Supplementary Results). Archaeocetes
have a mean brain size of 7.25 and a mean body size of 15.03. Stem
toothed whales have a mean brain size of 6.67 and a mean body size
of 11.90. The differences in mean brain and mean body size from
archaeocetes to stem toothed whales are thus −0.58 and−3.13, re-
spectively. The confidence interval of the slope for the ancestral grade
of stem toothed whales is 0.50:0.58. The ratio
(
¯
brain
_
¯
body
)
is 0.19, which
0.39 below the upper bound of the brain-to-body relationship.
The ratio
(
¯
body
_
¯
brain
)
is 5.39, which 3.65 above the upper bound of the
body-to-brain relationship. Therefore, it is inferred that stem toothed
whales indicated more change in mean body size than change in
mean brain size than allometrically expected given their ancestral
grade (specifically, more decrease in mean body size than decrease
in mean brain size).
It should be noted that this procedure is valid only in the case of
a positive brain-to-body correlation. This assumption is not upheld
in delphinids and hominins, who demonstrate a decrease in body size
and an increase in brain size (table S3). It is, however, evident that
selection favors increased brain size relative to body size in these cases.
Assessing differential changes in the variance of brain and/
or body size
Patterns of changes in the variance of brain size and body size
among grades were evaluated by comparing the differences in variances
in brain size and body size between ancestral and descendant grades
[phylogenetic variance was calculated following standard phylogenetic
generalized least-squares procedures (20)]. The change in ancestral-
to-descendant body size variance is expected to be 1:1 for all grades,
as this would maintain the proportionality of scaling differences from
ancestral-to-descendant grades. If this ratio is >1, then changes in
body size variance are greater than changes in brain size variance. If
this ratio is <1, then changes in brain size variance are greater than
changes in body size variance. Results are presented in table S5.
SUPPLEMENTARY MATERIALS
Supplementary material for this article is available at http://advances.sciencemag.org/cgi/
content/full/7/18/eabe2101/DC1
View/request a protocol for this paper from Bio-protocol.
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Acknowledgments: We thank E. R. Seiffert for the useful comments and discussion, and
K. W. S. Ashwell for sharing marsupial data. We further thank J. Lázaro for making Fig. 1.
Funding: J.B.S. was funded by the National Science Foundation (grant 80692). A.M.B. was
funded by the National Science Foundation (grant DEB 1801224). A.G. was funded by the
European Research Council (H2020 ERC-Stg-637171). C.S.M. was supported by the
Gerstner Fellowship and the Gerstner Family Foundation, the Kalbfleisch Fellowship, and
the Richard Gilder Graduate School of the American Museum of Natural History. V.W. was
funded by the Australian Research Council Discovery Grant (DP170103227). D.d.V. was
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supported by funds from the Natural Environment Research Council (NERC NE/
T000341/1). Author contributions: J.B.S., D.K.N.D., K.S., R.S.R., and D.R.H. gleaned data
from the literature. D.R.H., B.B., J.G.F., C.C.G., A.G., W.L.J., P.R.M., and C.S.M. assisted with
phylogenetic placement of extinct species. J.B.S., R.S.R., and D.R.H. performed the
statistical analyses. J.B.S. wrote the first draft. All authors read and edited the paper.
Competing interests: The authors declare that they have no competing interests. Data
and materials availability: All data needed to evaluate the conclusions in the paper are
present in the paper and/or the Supplementary Materials. Additional data related to this
paper may be requested from the authors.
Submitted 6 August 2020
Accepted 10 March 2021
Published 28 April 2021
10.1126/sciadv.abe2101
Citation: J. B. Smaers, R. S. Rothman, D. R. Hudson, A. M. Balanoff, B. Beatty, D. K. N. Dechmann,
D. de Vries, J. C. Dunn, J. G. Fleagle, C. C. Gilbert, A. Goswami, A. N. Iwaniuk, W. L. Jungers,
M. Kerney, D. T. Ksepka, P. R. Manger, C. S. Mongle, F. J. Rohlf, N. A. Smith, C. Soligo, V. Weisbecker,
K. Safi, The evolution of mammalian brain size. Sci. Adv. 7, eabe2101 (2021).
on April 28, 2021http://advances.sciencemag.org/Downloaded from
The evolution of mammalian brain size
Rohlf, N. A. Smith, C. Soligo, V. Weisbecker and K. Safi
Fleagle, C. C. Gilbert, A. Goswami, A. N. Iwaniuk, W. L. Jungers, M. Kerney, D. T. Ksepka, P. R. Manger, C. S. Mongle, F. J.
J. B. Smaers, R. S. Rothman, D. R. Hudson, A. M. Balanoff, B. Beatty, D. K. N. Dechmann, D. de Vries, J. C. Dunn, J. G.
DOI: 10.1126/sciadv.abe2101
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