www.sciencemag.org/cgi/content/full/330/6008/1216/DC1
Supporting Online Material for
The Evolution of Maximum Body Size of Terrestrial Mammals
Felisa A. Smith,* Alison G. Boyer, James H. Brown, Daniel P. Costa, Tamar Dayan, S. K.
Morgan Ernest, Alistair R. Evans, Mikael Fortelius, John L. Gittleman, Marcus J.
Hamilton, Larisa E. Harding, Kari Lintulaakso, S. Kathleen Lyons, Christy McCain,
Jordan G. Okie, Juha J. Saarinen, Richard M. Sibly, Patrick R. Stephens, Jessica Theodor,
Mark D. Uhen
*To whom correspondence should be addressed. E-mail: [email protected]
Published 26 November 2010, Science 330, 1216 (2010)
DOI: 10.1126/science1194830
This PDF file includes:
Materials and Methods
Figs. S1 to S5
Tables S1 to S3
References
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Supplemental Online Material
A. Collection of Data
Body mass of extinct species was obtained in a variety of ways. For some species, estimates were
directly available from the primary or secondary literature or from online databases (S1, S2). These were
used preferentially. For other species, body mass was estimated from molar or limb measurements in the
literature, unpublished compilations provided by authorities, extracted from online databases or measured
directly from museum specimens. In particular, dimensions of molars provide a robust basis for estimating
body mass for both fossil and modern mammals (S3). From molar and/or limb measurements, body mass
was estimated using ordinal or family specific allometric regressions based on extant taxa. Because we
were only interested in the largest mammals, our data are not comprehensive but focused on the largest
families and/or genera within each order. We confined our current analysis to terrestrial mammals. Fossil
ages were standardized using the midpoint for each Cenozoic sub-epoch on the Gradstein geological time
scale (S4).
B. Influence of sampling
To investigate the influence of taphonomy on our results, we determined the likelihood of finding the
largest specimens in an assemblage as a function of sampling effort. Using 91 modern mammal
assemblages across Africa where all mammals and their body masses were known (NCEAS Absolut6; S5),
we performed a series of sampling experiments. First, we randomly selected 1-12 of these modern
localities, from which we secondarily performed a random draw of mammal species in the local fauna. In
this second step, we began with 5% of the assemblage and increased sampling up to 50%. The
maximum body mass recovered and associated statistical metrics (i.e., minimum, 1 quartile, mean,
median, and 3 quartile of the maximum) were computed for each draw. We performed 10,000
iterations at each step from 5-50% using 1-step increments until we had sampled 12 of all the modern
African localities (fig. S1). Our results indicated that including even 10% of all sites on the continent
produced nearly 100% probability of recovering the largest mammals at each locality. Likely, this is
because the largest mammals on a continent typically have very large geographic distributions, occur in
multiple sites and hence are more likely to be recovered. Although we used modern mammal
communities to model the likelihood of recovering the largest species from fossil assemblages, our results
suggest our sampling protocol is likely to be quite robust.
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C. Characterizing trajectory of maximum body mass
Statistical characterization of the trajectory of maximum size evolution was complicated both by time
averaging (data were binned by sub-epoch), which introduced additional measurement error on the
independent axis, and determination of the “origin” or starting point. We chose the K/Pg as the
temporal starting point and the maximum body size in the latest Cretaceous sample as the initial size.
This explicitly assumes that the increase in size was triggered by the ecological release due to the mass
extinction event. All data were log-transformed prior to analysis. Different model fits were performed as
described in the text; the Gompertz yielded the lowest AICc values (Table 1; fig. S2).
To examine the relationship between herbivore maximum body mass and that of carnivores, both
correlation analyses and a linear regression were performed. We found that carnivore maximum body
mass closely tracked that of herbivores, although they reached asymptotes differing by an order of
magnitude (fig. S4). It is unclear what this relationship implies about interactions between these trophic
groups. Does carnivore body mass track or drive herbivore evolution? Or are both responding in a
similar way to another factor and are reaching different plateaus because of physiological constraints
imposed by their dietary strategy? Pearson Correlation (on log-transformed data) = 0.819; df=15; p
<0.000.
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D. Influence of species diversity
We examined the potential influence of diversity on morphological evolution in several ways. First we
examined the relationship between the generic diversity of mammals in North America to the maximum
body mass of mammals by sub-epoch. We focused on North America because the diversity data for
North America are the best-sampled and best-reported among all of the continents in the Paleobiology
Database (S6). Diversity estimates were extracted from the Paleobiology Database (S1) using the rangethrough option to determine the diversity for each interval of time. We regressed North American generic
diversity as a function of log maximum body mass by sub-epoch. The linear regression was positive, but
non-significant and accounted for very little of the variation in the data (y = 17.97 log mass + 44.36; P
> 0.28, R = 0.084). Because the maximum body mass appears to plateau in the middle to late Eocene,
we tested the relationship between diversity and maximum mass separately for the increasing part of the
curve (prior to 35 Ma) and for the plateau (after 35 Ma) separately. The relationship was positive but
non-significant for the increasing part of the curve (y= 42.781*log mass + 6.247; P > 0.12, R = 0.53).
The relationship between diversity and body mass in the plateau was negative, but non-significant and
accounted for very little of the variation in the data (y=-102.425*log mass + 480.98; P > 0.38, R =
0.124).
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Second, for each lineage, and for mammals overall, generic diversity was regressed against maximum
generic mass for each sub-epoch. We found no general relationship; there was no tendency for mammals
to be larger when they were more diverse.
Finally, we examined species diversity globally. The adaptive radiation following the K/Pg extinction event
clearly led to an increase in global mammal taxonomic richness, S. We fit an exponential model to the
data such that
, where s0 is the initial taxonomic richness at the time of the K/Pg extinction
and is the rate of increase. Because maximum body size follows a saturating function with time, the
relationship between maximum body size and taxonomic richness is also a saturating function that can be
obtained by substituting the taxonomic diversification equation into the Gompertz equation, giving,
where
and
. Because taxonomic richness
continues to increase throughout the Cenozoic whereas maximum body mass asymptotes, maximum body
mass must necessarily become increasingly independent of taxonomic richness as maximum body mass
approaches an upper limit. We fit this adjusted model with the free parameters ,
, . This model
provided a significant characterization of the relationship between log M and taxonomic richness (R =
0.81, table S2, fig. S3).
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We compared our model to the power law,
, of Trammer (S7, S8). Trammer proposed the
model to characterize the evolution of taxonomic richness and maximum body size in exponentially
diversifying clades. His model assumes continued exponential growth in maximum body mass, which is
clearly not the case in Cenozoic mammals. Indeed, we found that our model had a significantly lower
AICc value than the power law (table S2).
E. Analysis of Abiotic factors
We compared the overall global trajectory of terrestrial body mass with three potential drivers proposed
in the literature: terrestrial land area (S9), percent atmospheric oxygen concentration (S10) and
environmental temperature (S11). Environmental temperature was estimated from measurements of ! O
adjusted (‰) in parts per thousand. Because the abiotic data were generally recorded at a much finescale temporal scale than our corresponding mass estimates, we averaged values falling within each subepoch to obtain a single datum (table S1). To check how different data manipulation influenced our
analyses, we also binned data into standardized bins of 5 Ma and 10 Ma; bins any smaller or larger than
these values failed to capture the variation in our dataset. Results were almost identical to the Gradstein
binning method we employ in the main text. In fact, by standardizing the bin width, regression
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coefficients were slightly improved over those reported in the paper, while the parameter estimates
remained unchanged.
Abiotic data were analyzed against the maximum global body mass for the entire Cenozoic in a variety of
ways. First, we employed linear regression of log transformed body mass against each binned abiotic
factor (table S3). We excluded values for the Mesozoic because the lack of sites and poor preservation
meant data were sparse. We had little confidence that we had actually captured the largest mammals
present. We also excluded data for the early and late Holocene (=modern) because the temporal scale
was several orders of magnitude shorter than other epochs. All abiotic values yielded highly significant
results, with R values ranging from 0.61 to 0.85 (table S3). However, when we constrained the analysis
to the last 42.9 Ma (eliminating the initial exponential phase), atmospheric oxygen concentration was no
longer significant; indeed, the R value dropped to 0.06. This was not an artifact leading from reduced
sample size; both temperature and land are remained highly significant (table S3). We also ran a multiple
regression using a stepwise procedure. In this analysis, temperature was the significant factor and land
area dropped out. However, when the procedure was reversed (e.g., land area was entered first), both
factors were significantly related to maximum body mass. This was true for the entire data and for only
the last 42.9 Ma. Further analysis was hampered both by the limited extent of our data and the strong
co-linearity among variables (Pearson correlation between land area and temperature = 0.904, P<0.000,
df=15). Hence, currently we are unable to decouple the influence of temperature and land area.
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To examine the potential influence of land area on contemporary mammals, we collected information on
the largest mammal that occupied various islands, continents and major ocean basins. Body mass and
occupancy for continents and ocean basins were derived from an updated version of MoM v4.0 (S12);
island area and occupancy were taken from an updated version of Dahl (S13). Data were log-transformed
and a linear regression was conducted (fig. S4).
Supplemental References
S1. http://www.paleodb.org/cgi-bin/bridge.pl
S2. M. Fortelius (coordinator), Neogene of the Old World Database of Fossil Mammals (NOW), University
of Helsinki; http://www.helsinki.fi/science/now/.
S3. J.D. Damuth, B.J. MacFadden, Body size in mammalian paleobiology: estimation and biological
implications(Cambridge Univer. Press, Cambridge, Cambridge, 1990).
S4. F.M. Gradstein, J. G. Ogg, A. G. Smith, A Geologic Time Scale 2004 (Cambridge Univer. Press,
Cambridge, Cambridge, 2004).
S5. unpublished dataset version 6 (“Absolut6” 2009), cf. Damuth, J., M. Fortelius, P. Andrews, C.
Badgley, E.A. Hadly, S. Hixon, C. Janis, R.H. Madden, K. Reed, F.A. Smith, J.Theodor, J.A. Van Dam, B.
Van Valkenburgh, L. Werdelin (National Center for Ecological Analysis and Synthesis (NCEAS)
workshop on Mammalian Communities, organized by John Damuth, 2001).
S6. J. Alroy, Science 280, 731 (1998).
S7. J.Trammer, Evol. Ecol. Res. 4, 147 (2002).
S8. J. Trammer, Evolution 59, 941 (2005).
S9. A.G. Smith, D.G. Smith, B.M. Funnell. Atlas of Mesozoic and Cenozoic coastlines (Cambridge Univer.
Press, Cambridge, Cambridge, 1994).
S10. P.G. Falkowski M.E. Katz, A.J. Milligan, K. Fennel, B.S. Cramer, M.P. Aubry, R.A. Berner, M.J. Novacek,
W.M. Zapol, Science 309, 2202 (2005).
S11. J.C. Zachos, G.R. Dickens, R.E. Zeebe, Nature 451, 279 (2008).
S12. F.A. Smith, S.K. Lyons, S.K.M. Ernest, K.E. Jones, D.M. Kaufman, T. Dayan, P.A. Marquet, J.H. Brown,
J.P. Haskell. Ecology 84, 3402 (2003).
S13. A.L. Dahl, Island Directory (UNEP Regional Seas Directories and Bibliographies No. 35. UNEP, Nairobi,
1991).
S14. http://islands.unep.ch/isldir.htm
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table S1. Maximum body mass globally and for each continent and abiotic factors over the Cenozoic. Estimated terrestrial land area from (S9);
oxygen isotope values from (S11); atmospheric oxygen concentration from (S10). O-isotope adjustments: CIB (+0.64), NUT (+0.45) as described in
(S11). For some older sub-epochs, and for South America, in particular, body mass is likely underestimated. Some epochs have a limited rock record
and limited data are available.
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Table S2. Statistical details of species diversity analyses. The exponential fit has the form
Model
Parameters
AICc
r
34.12
0.57
0.002
24.0
0.81
<0.001
2
p-value
Diversity over time
Exponential
Body size-diversity
Saturating function
,
,
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table S3. Linear regressions of maximum mammalian global body mass versus globally averaged abiotic factors
over the Cenozoic. Body mass was log transformed prior to analysis. As might be expected, temperature and
land area were significantly correlated (Pearson correlation =0.904), complicating interpretations. Slope and
intercept are not reported for non-significant relationships.
Slope
(+/- std
error)
Intercept
(+/- std
error)
N
Paleocene through
Pleistocene
Middle Eocene through
Pleistocene
Paleocene through
Pleistocene
Middle Eocene through
Pleistocene
Paleocene through
Pleistocene
0.612 (0.140)
2.347 (0.312)
14
0.61
0.001
0.214 (0.064)
3.497 (0.167)
10
0.58
0.01
0.090 (0.011)
-9.546 (1.549)
14
0.85
0.001
0.033 (0.012)
-0.901 (1.743)
10
0.50
0.02
0.373 (0.073)
-4.15 (1.515)
14
0.69
0.001
Middle Eocene through
Pleistocene
----
----
10
0.06
0.498
Factor
Temporal interval
Temperature
Temperature
Land Area
Land Area
Atmospheric
oxygen
concentration
Atmospheric
oxygen
concentration
R value P value
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figure S1. Statistical moments of maximum mass (g) of species sampled from modern assemblages of
mammals in Africa. Each graph represents the number of the total sites sampled, while the horizontal axis
represents the percent of sampled species per site, and mass (g) is depicted on the vertical axis.
Statistical moments shown from 10,000 sampling iterations: minimum of maximum (red), 1 quartile of
maximum (yellow), median of maximum (green), mean of maximum (light blue), 3 quartile of maximum
(dark blue), and maximum of maximum (purple).
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figure S2. Maximum body size over the Cenozoic plotted against time. The K/Pg is represented by the
dotted line in each panel. A) Global mammals with both a Gompertz model (solid line) and power-law
(dashed gray line) fit; B) Africa; C) Eurasia; D) North America; E) Carnivores only. Panels A through D
represent herbivores, as these were always the largest mammals present on each continent after the K/Pg.
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F
B
figure S3. Influence of diversity on terrestrial mammal body size evolution. A) Species diversity as measured
by number of genera over the Cenozoic; B) log maximum body size against diversity (again measured by
number of genera). Data extracted from the Paleobiology database (S1) using the range-through option.
Panel A is fit by an exponential (Genera = 191.4 * e
; R = 0.56; p = 0.001); panel B is our saturating
function explained in the text (table S2).
0.014 * t
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figure S4. Ratio between herbivore and carnivore body mass over the Cenozoic. Note that ratio plateaus
at approximately 10 during the early Oligocene; value shown in red likely reflects the paucity of fossil
remains of larger carnivores from the late Miocene. Whether carnivore body mass drives or tracks herbivore
evolution is beyond the scope of our current analysis. Pearson correlation between log transformed carnivore
and herbivore body mass (kg) =0.819, P< 0.000, df =15.
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figure S5. Maximum body mass of contemporary mammals versus continental, insular or ocean basin area.
Data derived from the island directory (S13, S14) and an updated version of MOM v4.0 (S12). These data
suggest available habitat may limit the maximum size of mammals perhaps through energetic constraints on
the number of animals of large size that can be supported in the habitat. Equation (unstandardized
coefficient with standard error): Log Mass = 0.67 (0.043) Log Area + 2.016 (0.202), df = 55, R = 0.82, P
< 0.000).
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