Cope’s Rule and the Dynamics of Body Mass
Evolution in North American Fossil Mammals
John Alroy
Body mass estimates for 1534 North American fossil mammal species show that new
species are on average 9.1% larger than older species in the same genera. This within-
lineage effect is not a sampling bias. It persists throughout the Cenozoic, accounting for
the gradual overall increase in average mass (Cope’s rule). The effect is stronger for larger
mammals, being near zero for small mammals. This variation partially explains the
unwavering lower size limit and the gradually expanding mid-sized gap, but not the
sudden large increase in the upper size limit, at the Cretaceous-Tertiary boundary.
Shortly after Cope described the first im-
portant Paleocene faunas from North
America, he realized that the average size of
mammals has increased dramatically during
the Cenozoic (1). He attributed this pattern
to a tendency for new groups to evolve at
small sizes, combined with a persistent in-
nate drive toward larger size. The idea that
evolutionary increases in body size are com-
mon has been recast in more Darwinian
terms and termed “Cope’s rule.” Despite a
long history of research (2), most modern
studies have found little evidence to sup-
port this rule (3–5), dismissed it as context-
dependent (6), or explained it with the
statistical argument that means will rise
passively as a group founded by small spe-
cies diffuses through a bounded morpho-
space (7–12). Even actively driven trends
have been attributed to convergence on an
optimal body size, not to a general tendency
toward size increase (7, 8). Here I show that
there is an active within-lineage trend
in the fossil record of North American
mammals that is consistent with Cope’s
prediction.
Earlier studies of Cope’s rule have fo-
cused on short-term trends (3, 5, 8), ana-
lyzed small sets of species (3, 4, 6, 8), dis-
covered patterns to be sampling biases (9),
or failed to make direct comparisons of
potential ancestor-descendant species pairs
(5, 10, 11). However, direct comparisons
make it possible to distinguish within-lin-
eage processes (for example, selection) from
among-lineage processes (for example, dif-
ferential extinction or origination), two fac-
tors that have been conflated in earlier
analyses of the overall size ranges of indi-
vidual clades (5) or of clade-subclade pairs
(11).
I analyzed species ranging in age from
Campanian (late Cretaceous) to late Pleis-
tocene by using generic assignment and rel-
ative age as indicators of potential ancestor-
descendant relationships. This is not a very
robust phylogenetic method. But, as dis-
cussed below, it is highly conservative, sim-
ilar to more sophisticated methods that are
widely accepted, and based on seemingly
uncontroversial assumptions. Furthermore,
a specially designed bootstrapping test
shows that the main result could not have
been obtained unless the species-to-species
comparisons did contain a large amount of
phylogenetic signal.
Studying body mass trends requires not
just an approximate phylogeny but both
robust mass estimates and precise dates of
first and last appearance (Fig. 1). The mass
estimates were based on published lower
first molar (m
1
) measurements, which have
been related precisely to body mass in living
mammals (13–17). Data were available for
1534 species, represented by 15,281 mea-
sured specimens from 2875 fossil popula-
tions. The data encompass those of some
earlier studies (3, 6, 7, 11) but are at least an
order of magnitude more plentiful.
The appearance dates were based on a
recent time-scale analysis (18, 19)ofacom-
prehensive faunal database for North
American fossil mammals (18, 20, 21).
These data include 4015 taxonomic lists for
individual fossil localities, which have been
standardized taxonomically by referring to a
companion database that flags 2692 invalid
species names and 1197 invalid genus-spe-
cies combinations. The corrected lists doc-
ument occurrences of 3181 valid species.
Instead of using the traditional system of
North American land mammal ages, I con-
verted the raw data directly into numerical
age-range estimates by subjecting the lists
to multivariate ordination and calibrated
the results to numerical time using 152
independent estimates of geochronological
age (21).
For each new species, one potential an-
cestor was selected from the other species in
the same genus that appeared before it did.
If some of these older species were still
extant at this time, one was selected at
random; if not, then the older species that
last went extinct was selected. Like several
new methods that incorporate temporal in-
formation into phylogenetics (22), this pro-
cedure tends to minimize the number of
implied ghost lineages. In order to test for
trends, the difference in log body mass was
computed for each older-younger species
pair. This is similar to the widely used phy-
logenetic contrast procedure (23), in which
measured characters are transformed into
differences between putative sister species.
Admittedly, the proxy ancestor method
does not directly examine character data
and therefore is oversimplistic and error
prone. However, its assumptions are justi-
fied. First, because the mammalian fossil
record is well sampled, ancestor-descendant
species should be observed with great fre-
quency regardless of the assumed evolution-
ary model (24). Second, there is a correla-
tion of age rank and clade rank in many
mammalian groups (25): The relative ages
of fossil species do correspond with the
relative sequences of evolutionary splitting
implied by phylogenies. Third, errors in
identifying ancestor-descendant pairs will
push the average size difference toward zero,
which should obscure anything less than
the strongest within-lineage trends. There
are many possible errors: Older species
might be closely related but not directly
Department of Paleobiology, Smithsonian Institution,
MRC 121, Washington, DC 20560, USA.
Fig. 1. Temporal distribution of Cenozoic mam-
malian species across the body mass spectrum.
Age ranges were based on a multivariate ordina-
tion of faunal lists (18–21). Mass estimates were
computed with the use of published regression
coefficients for mass against m
1
length 3 width
[Carnivora, Insectivora, Primates, and Rodentia
(13)] or against m
1
length [Artiodactyla and Peris-
sodactyla (14)]. Coefficients for Primates were
also used for Plesiadapiformes (15); coefficients
for Carnivora were also used for Mesonychia (16).
Proboscidean m
1
’s are rarely described, and their
lower cheek teeth all are relatively large; mass
estimates based on m
2
area measurements and
the all-mammal regression for combined p
4
-m
2
area agreed with earlier literature (17). The all-
mammal m
1
area regression was used for all re-
maining mammals.
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ancestral to younger species (for example,
sister species); they might be only distantly
related if a genus is diverse or polyphyletic;
or they might be descendants, instead of
ancestors, if undersampling leads to incor-
rect estimation of the relative order of ap-
pearance. Finally, the algorithm is even
more conservative because it reduces sam-
ple sizes. Many genera are represented in
the mass estimate data set by only one
species and therefore cannot be studied. In
addition, at least one species must be the
oldest in each polytypic genus and therefore
cannot be matched to a still older species.
Despite these losses, 779 of the 1534 mea-
sured species (50.8%) were assigned a puta-
tive ancestor.
The basic pattern is overwhelming (Fig.
2). Newly appearing species are on average
0.0874 natural log units (9.1%) larger than
older congeneric species, a highly signifi-
cant difference according to two standard
tests and a nonparametric resampling anal-
ysis. The only clear-cut hypothesis that pre-
dicts such a pattern is the most narrow and
deterministic interpretation of Cope’s rule;
namely, that there are directional trends
within lineages. Alternative hypotheses
make no special predictions about average
differences in mass between taxonomically
paired species: neither increases in variance
by diffusion away from evolutionary bound-
aries nor differential origination and extinc-
tion among lineages have to do with with-
in-lineage patterns. One could argue that
the trend would be artifactual if taxono-
mists preferentially removed relatively
small and derived lineages from nominal
genera. But this bias is not obvious in the
literature, and the argument begs the ques-
tion of why taxonomists would not only do
this but at the same time retain relatively
large derived species in nominal genera.
The strong support for a within-lineage
effect raises several questions. First, average
body mass across the fauna increases dra-
matically during the Cenozoic; can this ef-
fect account for the trend by itself, or are
among-lineage effects such as differential
extinction also needed to explain it? A
simple calculation shows that it can. A
least-squares fit of time against mean size for
the Cenozoic data yields a slope of
0.0392 6 0.0037 ln g per million years
(My). The first appearances of the older
and younger species in each comparison
differ on average by 2.62 My, so the in-
crease of 0.0874 ln g per generation
amounts to an increase of 0.0334 ln g/My,
which is an insignificant 1.6 standard errors
lower than the observed slope.
A second question is whether the with-
in-lineage trend varies through time: It
might just be a feature of one unusual in-
terval, such as the immediate post–Creta-
ceous-Tertiary (K-T) boundary recovery
phase. To address this question I binned the
older-younger matches into 2.5-My inter-
vals throughout the Cenozoic (Fig. 3).
There is a weak, marginally significant cor-
relation between time and average size dif-
ference (Spearman’s r 5 0.342, t 5 1.784,
P , 0.10). However, this correlation is
positive; the effect’s strength actually in-
creased over time. Least-squares regression
predicts a mean size change of 12.7% dur-
ing the initial, early Paleocene radiation of
mammals, but 121.0% in the latest Pleis-
tocene. The average might have tracked
either the appearance of new taxonomic
groups with stronger biases or environmen-
tal changes that favored large sizes. Short-
term excursions from the trend are not con-
sistent, as shown by the lack of significant
serial correlation [Spearman’s r 5 0.132,
t 5 0.636, not significant (NS)]. These
results suggest that progressive increase in
size has been an important pattern through-
out much of mammalian history.
Despite the consistency of this evolu-
tionary bias, it does not account for all of
the major features of the body mass distri-
bution (Fig. 1). These are a constant lower
mass limit of about 2 ln units; a gradual
increase in the upper mass limit throughout
the Cenozoic; a rapid expansion in the up-
per, but not lower, mass limit immediately
after the K-T boundary; and the gradual
development of a gap in the middle part of
the size spectrum that begins in the Eocene
at about 46 million years ago (Ma).
Most of these patterns could be ex-
plained by the existence of two body mass
optima, each serving as a statistical point
attractor or equilibrium. Unlike purely un-
constrained distributions, distributions with
attractors eventually cease to expand.
Therefore, a preestablished small-sized equi-
librium might explain the invariant lower
size limit. Meanwhile, a second, larger op-
timum, combined with the observation that
there were no truly large mammals before
the K-T boundary, might explain why the
upper limit was not stable: There may not
have been enough time during the Cenozo-
ic for the distribution to expand and envel-
op the upper optimum.
Fig. 2. Frequency distribution of differences in
body mass between 779 matched pairs of young-
er and older species in the same genera. Dashed
line indicates zero difference. Younger species are
significantly larger, either according to a standard
t test (t 5 3.225, df 5 776, P , 0.01) or according
to a G test [442 of 779 (56.7%) are larger, with a
null expectation of 50%, G 5 14.782, df 5 1, P ,
0.005]. A more robust, nonparametric test shows
that the pattern is due to within-lineage trends
instead of an among-lineage trend. This involves
creating pseudo-matches of the younger species
to older ones drawn randomly with replacement
(bootstrapping). Totally random draws would gen-
erate unrealistically large temporal and body mass differences, because species are only placed in the
same genera if they appear at similar times and have similar sizes. Therefore, a conservative algorithm
was used as follows: (i) The differences in first appearance dates and the absolute differences in the
mass of matched species were counted (bin sizes were set at 0.1 My and 0.01 ln g). (ii) As candidate
older species were drawn randomly, the observed differences were subtracted from the two count
vectors. (iii) If either difference had a zero count, the counts were restored and the candidate species
was replaced. (iv) Once all younger species had been matched, the mean difference was computed. (v)
The procedure was iterated to create a null distribution. Because only absolute values of mass differ-
ences were held constant, the average differences could take on any value. For combinatoric reasons,
an average of 74.7 pairs per trial (9.6%) could not be matched. Even though the average differences in
mass for unmatched species pairs were high (0.118 ln g), the remaining matched pairs averaged
differences that were very close to the original value (0.084 versus 0.087 ln g). The bootstrapped species
pairs in 10,000 trials differed in mass by an average of 0.022 ln g, which is significantly less than 0.084
lng(P 5 0.0071).
Fig. 3. Trend in strength of the within-lineage
Cope’s rule effect through the Cenozoic. Here,
the data shown in Fig. 2 are binned into intervals
2.5 My long and averaged. Sample sizes range
from 12 to 79 older-younger species pairs per
interval, with an average of 29.1. Alternative bin
sizes of 1 to 10 My yield similar patterns. Creta-
ceous data are too sparse to allow reliable aver-
ages to be computed. The dashed line illustrates
the expected average change of zero if there is no
effect.
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Large-scale ecological studies of mostly
small-sized, extant North American mam-
mals do suggest that there is a body mass
optimum at about 100 g (26), which is close
to the average size of Cretaceous mammals
and in agreement with the lower half of the
temporal distribution (Fig. 1). We can test
for this optimum by regressing the differ-
ence in body mass between younger and
older species against the mass of the older
species (Fig. 4A). If a single optimum exists,
then relatively large older species will be
matched to smaller, younger species and
vice versa, thereby creating a negative cor-
relation. Assuming a linear, or Ornstein-
Uhlenbeck model (23), the ratio of the
resulting intercept and slope will define
the optimal mass; that is, the point at which
the expected change in mass is zero.
With the appropriate corrections for the
fact that the independent variable (mass of
the older species) appears also as part of the
dependent variable (the change in mass),
the predicted negative correlation is not
seen; instead, there is a significant positive
correlation (n 5 779; r 5 0.113; F 5 10.06;
df 5 1, 777; P , 0.005). Superficially, this
positive linear relation implies that body
mass continues to increase at an ever accel-
erating rate. A disequilibrium such as this
one is biologically unrealistic because there
must be biomechanical and physiological
limits to size. The dilemma could be solved
by showing that although the rate of in-
crease is rapid in the middle of the size
range, it falls to zero at very large sizes. Such
a dual-optimum dynamic should resemble a
quadratic or cubic function; both functions
can imply one stable and one unstable equi-
librium, but they differ fundamentally be-
cause only the quadratic could imply a sec-
ond stable equilibrium.
A quadratic fit does not significantly
improve on the original r value (r 5 0.115;
F 5 0.41; df 5 1, 776; NS) and neither does
a cubic fit (r 5 0.126; F 5 1.22; df 5 2,
775; NS). This result may be due to noise
in the proxy phylogeny or to undersam-
pling of the large lineages. But in any case,
both fits do imply that the rate of increase
is maximal in the middle of the distribu-
tion, and the 95% confidence intervals
cannot exclude near-zero rates at the ends
(Fig. 4B). The rate of increase is maximal
at 75.3 kg (predicted difference 5 0.233 ln
g). The function is so flat at the lower end
that for small mammals there is more of an
optimal zone than an optimal point; the
biologically required large mammal equi-
librium is so large that it is not statistically
clear-cut and apparently never was at-
tained during the Cenozoic. In any event,
either stability or an increase in size, but
not a decrease, is predicted for lineages of
almost any size.
Any of these equilibrium models could
partially account for the trend toward larger
size, the persistence of an unwavering lower
limit, and the gradual opening up of a gap in
the middle of the distribution. However,
they cannot account for the sudden expan-
sion of the distribution after the K-T mass
extinction event at 65 Ma. In the last mil-
lion years of the Cretaceous, 29 measured
species averaged 150 g. In the first million
years of the Cenozoic, 33 measured species
(27 of them new) averaged 1.01 kg. This
extraordinary shift of 1.91 ln units is un-
equaled elsewhere in the data set.
Would there have been a rapid shift if
the modern size-change function (Fig. 4B)
suddenly came into existence at the K-T
boundary? On the basis of the linear and
cubic equilibrium models, the expected
increase from 150 g is only either 0.035 or
0.006 ln units per first appearance. There-
fore, the Cretaceous fauna already was
solidly within the optimal zone of most
Cenozoic small mammals, and the size-
change dynamic does not explain the sud-
den shift by itself. Better explanations
might involve stochastic factors or short-
term changes in the underlying dynamic.
That the early Paleocene really was a very
unusual time is indicated by the phenom-
enal rates of origination seen then (21). In
any case, the data are compatible with the
idea that the extinction of large terrestrial
vertebrates such as dinosaurs at the K-T
boundary opened up the larger end of the
body size spectrum for occupation by
mammals.
Despite the clear evidence for nonran-
dom within-lineage evolution, the overall
trend in body size known as Cope’s rule
may reflect a balance of forces operating
both within and among lineages (27). Dif-
ferential turnover rates at small sizes may
help to explain the very sharp lower size
limit. Similarly, if higher rates of extinc-
tion or lower rates of origination (or both)
have suppressed the diversity of large
mammals, that might explain why the bi-
ologically required optimum at a large size
seems to be at or beyond the limit of the
observed size range. The situation would
be analogous to the hypothesized “taxon
cycle” in island communities (28), in
which newly arriving species evolve to-
ward niches that are opened up by the
extinction of older species. The analogy
would be particularly relevant if the exis-
tence of a large body mass optimum itself
were due not to functional constraints
but to character displacement pushing lin-
eages away from the center of the distri-
bution. Even if these speculations eventu-
ally are refuted, the extraordinary size bias
in the production of new mammalian spe-
cies throughout the Cenozoic will contin-
ue to demand explanation.
Fig. 4. Positive correlation between the mass of
older species in each matched pair and the differ-
ence in mass between the younger and older spe-
cies. Although not significantly better than a linear
fit, a cubic fit (thick solid line) implies a biologically
realistic falloff in the rate of size increase at very
large body sizes. Data are shown in (A); one point
at the 2.43, 14.56 coordinate falls outside the
plot’s limits. The same polynomial fit is shown in
(B), where the y axis has been expanded. The
relation implies evolutionary tendencies (arrows)
toward stable optima in body mass (solid circles)
and away from an unstable equilibrium (open cir-
cle); these points fall where the expected change
(thick line) equals zero (dashed line). The thick
arrow shows the trajectory implied by both linear
and cubic functions. The 95% confidence inter-
vals (thin solid lines) are based on 1000 bootstrap
replicates of the original data. Regressions are
corrected for the “regression to the mean” artifact;
that is, the spurious negative correlation between
any two variables y-x and x. Let s
x
equal the slope
of the regression of y-x on x,s
y
equal that of y-x on
y, and s
E
equal the slope of the Ornstein-Uhlen-
beck equilibrium function; and assume that the
data result from a summation of the linear regres-
sion to the mean and equilibrium functions. Be-
cause the value of the slope fixes the covariance,
correlation, and intercept, the desired coefficients
can be estimated by numerically solving for s
E
in
the easily derivable equation s
x
1 s
y
5 s
E
(s
E
1
2)/(s
E
1 1). For a polynomial regression, this is
done separately for each of the regressions of y-x on a power of x that is involved.
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18 December 1997; accepted 6 March 1998
Proteolytic Inactivation of MAP-Kinase-Kinase
by Anthrax Lethal Factor
Nicholas S. Duesbery, Craig P. Webb, Stephen H. Leppla,
Valery M. Gordon, Kurt R. Klimpel,* Terry D. Copeland,
Natalie G. Ahn, Marianne K. Oskarsson, Kenji Fukasawa,
Ken D. Paull, George F. Vande Woude†
Anthrax lethal toxin, produced by the bacterium Bacillus anthracis, is the major cause
of death in animals infected with anthrax. One component of this toxin, lethal factor (LF),
is suspected to be a metalloprotease, but no physiological substrates have been iden-
tified. Here it is shown that LF is a protease that cleaves the amino terminus of mitogen-
activated protein kinase kinases 1 and 2 (MAPKK1 and MAPKK2) and that this cleavage
inactivates MAPKK1 and inhibits the MAPK signal transduction pathway. The identifi-
cation of a cleavage site for LF may facilitate the development of LF inhibitors.
Anthrax toxin, produced by the bacterium
Bacillus anthracis, is composed of three pro-
teins: protective antigen (PA), edema fac-
tor (EF), and lethal factor (LF) (1). PA
binds to specific cell surface receptors and,
upon proteolytic activation to a 63-kD frag-
ment (PA63), forms a membrane channel
that mediates entry of EF and LF into the
cell (2). EF is an adenylate cyclase and
together with PA forms a toxin referred to
as edema toxin (3). LF and PA together
form a toxin referred to as lethal toxin.
Lethal toxin is the dominant virulence fac-
tor produced by B. anthracis and is the
major cause of death of infected animals
(4). Intravenous injection of lethal toxin
into rats causes death in as little as 38 min
(5), and addition of the toxin to mouse
macrophages in culture causes lysis within 2
hours (6). LF is a 776–amino acid protein
that contains a putative zinc-binding site
[HEFGF (7)] at residues 686 through 690,
which is characteristic of metalloproteases.
Mutation of the H or E residues inactivates
LF (8) and reduces its zinc-binding activity
(9). However, no physiological substrate
has been identified.
The National Cancer Institute main-
tains a database of antineoplastic drugs
that have been tested against a panel
of 60 human cancer cell lines [NCI’s
ADS (10)]. A screen of this database
aimed at identifying novel inhibitors of
the mitogen-activated protein kinase
(MAPK) signal transduction pathway,
an evolutionarily conserved pathway that
controls cell proliferation and differentia-
tion, revealed that anthrax LF had
an activity profile similar to that of
PD09859, a compound that selectively in-
hibits the MAPK pathway (11). We there-
fore examined the effect of LF on the
MAPK pathway.
In response to extracellular signals,
MAPK is phosphorylated and activated by
MAPK kinases 1 and 2 (MAPKK1 and
MAPKK2). In oocytes of the frog Xenopus
laevis, progesterone-stimulated synthesis of
Mos, a serine/threonine kinase, leads to ac-
tivation of the MAPK pathway, which is
essential for the activation of maturation-
promoting factor (that is, cyclin B/p34
cdc2
kinase) and the resumption of meiosis (mat-
uration) (12). Addition of PA and LF to
oocyte culture medium had no effect on
progesterone-induced oocyte maturation
(13). In contrast, injection of 1 ng of LF
into oocytes inhibited maturation by 50%
as judged by an assay of germinal vesicle
(nuclear envelope) breakdown (GVBD),
and GVBD was completely inhibited by 10
ng of LF (Table 1). Injection of LF Glu
687
3 Cys
687
(E687C), an inactive LF contain-
ing a single amino acid substitution in the
putative zinc-binding site (8), had no effect
on GVBD (Table 1). Because a decrease in
adenosine 39,59-monophosphate–depen-
dent protein kinase A activity is also re-
quired for oocyte maturation (12), there
was concern that low levels of EF may have
been present as a contaminant. However,
preparations of LF from strains of B. anthra-
cis deficient in the production of EF also
N. S. Duesbery, C. P. Webb, T. D. Copeland, M. K.
Oskarsson, G. F. Vande Woude, Advanced BioScience
Laboratories–Basic Research Program, National Cancer
Institute–Frederick Cancer Research and Development
Center, Post Office Box B, Frederick, MD 21702, USA.
S. H. Leppla, V. M. Gordon, K. R. Klimpel, National Insti-
tute of Dental Research–National Institutes of Health,
9000 Rockville Pike, Bethesda, MD 20892, USA.
N. G. Ahn, Department of Chemistry and Biochemistry,
Howard Hughes Medical Institute, University of Colorado,
Campus Box 215, Boulder, CO 80309, USA.
K. Fukasawa, Department of Cell Biology, University of
Cincinnati, College of Medicine, P.O. Box 670521, Cin-
cinnati, OH 45267, USA.
K. D. Paull, Division of Cancer Research, National Cancer
Institute, National Institutes of Health, Bethesda, MD
20892, USA.
*Present address: Biopraxis, Post Office Box 9100 –78,
San Diego, CA 92191, USA.
†To whom correspondence should be addressed.
SCIENCE
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VOL. 280
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1 MAY 1998
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www.sciencemag.org734
![Fig. 1. Temporal distribution of Cenozoic mammalian species across the body mass spectrum. Age ranges were based on a multivariate ordination of faunal lists (18–21). Mass estimates were computed with the use of published regression coefficients for mass against m1 length 3 width [Carnivora, Insectivora, Primates, and Rodentia (13)] or against m1 length [Artiodactyla and Perissodactyla (14)]. Coefficients for Primates were also used for Plesiadapiformes (15); coefficients for Carnivora were also used for Mesonychia (16). Proboscidean m1’s are rarely described, and their lower cheek teeth all are relatively large; mass estimates based on m2 area measurements and the all-mammal regression for combined p4-m2 area agreed with earlier literature (17 ). The allmammal m1 area regression was used for all remaining mammals.](/figures/fig-1-temporal-distribution-of-cenozoic-mammalian-species-1fje06ol.webp)