Kinetic effects of temperature on rates of genetic
divergence and speciation
Andrew P. Allen*
, James F. Gillooly
, Van M. Savage§
, and James H. Brown
*National Center for Ecological Analysis and Synthesis, 735 State Street, Suite 300, Santa Barbara, CA 93101; Department of Zoology, University of Florida,
Gainesville, FL 32611; §Bauer Center for Genomics Research, Harvard University, Boston, MA 02138; and Department of Biology, University of New Mexico,
Albuquerque, NM 87131
Contributed by James H. Brown, May 2, 2006
Latitudinal gradients of biodiversity and macroevolutionary dynamics
are prominent yet poorly understood. We derive a model
that quantifies the role of kinetic energy in generating biodiversity.
The model predicts that rates of genetic divergence and
speciation are both governed by metabolic rate and therefore
show the same exponential temperature dependence (activation
energy of 0.65 eV; 1 eV 1.602 10 19 J). Predictions are
supported by global datasets from planktonic foraminifera for
rates of DNA evolution and speciation spanning 30 million years.
As predicted by the model, rates of speciation increase toward the
tropics even after controlling for the greater ocean coverage at
tropical latitudes. Our model and results indicate that individual
metabolic rate is a primary determinant of evolutionary rates:
1013 J of energy flux per gram of tissue generates one substitution
per nucleotide in the nuclear genome, and 1023 J of energy
flux per population generates a new species of foraminifera.
allopatric speciation biodiversity macroevolution metabolic theory
of ecology molecular clock
The latitudinal increase in biodiversity from the poles to the
equator is the most pervasive feature of biogeography. For
two centuries, since the time of von Humboldt, Darwin, and
Wallace, scientists have proposed hypotheses to explain this
pattern. New species arise through the evolution of genetic
differences among populations from a common ancestral lineage
(1­4). Many hypotheses therefore attribute the latitudinal biodiversity
gradient to a gradient in speciation rates caused by some
independent variable, such as earth surface area or solar energy
input (5­7). Some fossil data suggest that speciation rates do
indeed increase toward the tropics (8­10), but these findings
remain open to debate due in part to our limited understanding
of the factors that control macroevolutionary dynamics.
Recent advances toward a metabolic theory of ecology (11)
provide new opportunities for assessing the factors that control
speciation rates. This recent work indicates that two fundamental
variables influencing the tempo of evolution, the generation
time, and the mutation rate (3) are both direct consequences of
biological metabolism (12­14). Here we combine these recent
insights from metabolic theory with the theory of population
genetics to derive a model that predicts how environmental
temperature, through its effects on individual metabolic rates
(Eqs. 1­4), influences rates of genetic divergence among populations
(Eqs. 5­7) and rates of speciation in communities (Eqs.
8 and 9). We evaluate the model by using data from planktonic
foraminifera, because this group has extensive DNA sequence
data for evaluating population-level predictions on genetic divergence
combined with an exceptionally complete fossil record
for evaluating community-level predictions on speciation rates.
Model Development
The two individual-level variables constraining the evolutionary
rate of a population, the generation time, and the mutation rate
(3) are both direct consequences of biological metabolism (15,
16). They are both governed by the body size- and temperaturedependence
of mass-specific metabolic rate, B (J sec 1
g 1
)
(12­14):
B B M boM 1/4
e E/kT
Boe E/kT
, [1]
where B is individual metabolic rate (J sec 1
), M is body mass (g),
T is absolute temperature (K), Bo is a normalization parameter
independent of temperature (J sec 1
g 1
) that varies with body
size as Bo boM 1/4
(12), and bo is a normalization parameter
independent of body size and temperature that varies among
taxonomic and functional groups (12, 17). The BoltzmannArrhenius
factor, e E/kT
, characterizes the exponential effect of
temperature on metabolic rate, where E is the average activation
energy of the respiratory complex ( 0.65 eV; 1 eV 1.602
10 19
J), and k is the Boltzmann constant (8.62 10 5
eV K 1
).
This Boltzmann­Arrhenius factor has been shown to describe
the temperature dependence of metabolic rate for a broad
assortment of organisms in recent work (12) and in much earlier
work conducted near the beginning of the last century (18).
Recent work indicates that the generation time, expressed
here as the individual turnover rate, g (generations sec 1
), and
the mutation rate, (mutations nucleotide 1
sec 1
), both show
this same temperature dependence (12­14):
g goB goBoe E/kT
[2]
and
oB oBoe E/kT
, [3]
where go is the number of generations per joule of energy flux
through a gram of tissue (generations J 1
g), and o is the
number of mutations per nucleotide per joule of energy flux
through a gram of tissue (mutations nucleotide 1
J 1
g). Eqs. 2
and 3 predict a 15-fold increase in the rates of individual turnover
and mutation over the temperature range 0­30°C from the poles
to the equator (e E/k303
e E/k273
15-fold from 273­303 K).
Because g and are both governed by B, the number of
mutations per nucleotide per generation,
g o go e0/kT
, [4]
is independent of temperature.
Speciation entails genetic divergence among populations from
a common ancestral lineage, resulting in reproductive isolation
(2, 4). The theory of population genetics characterizes the rate
of increase in the total genetic divergence, D (substitutions
nucleotide 1
), between two reproductively isolated diploid popConflict
of interest statement: No conflicts declared.
Freely available online through the PNAS open access option.
Abbreviations: CI, confidence interval; FO, first occurrence; Ma, mega-annum; SSU rDNA,
small subunit rRNA-encoding DNA.
To whom correspondence may be addressed. E-mail: drewa@nceas.ucsb.edu or jhbrown@
unm.edu.
 2006 by The National Academy of Sciences of the USA
9130­9135 PNAS June 13, 2006 vol. 103 no. 24 www.pnas.org cgi doi 10.1073 pnas.0603587103
ulations, both of size Js, on a per-generation basis, dD d
(substitutions nucleotide 1
generation 1
), such that
dD d dD0 d dD d 2f0 8f Jss 2f0 ,
[5a]
where f0 and f are the respective fractions of mutations that are
selectively neutral (s 0) and beneficial (s 0), Do and D are
the respective contributions of neutral and beneficial mutations
to the total genetic divergence D, and
dD0 d 4Js f0 1 2Js 2f0 [5b]
and
dD d 4Js f 1 e 2s
1 e 4Jss
8f Jss
[5c]
are the respective rates of fixation of neutral and beneficial
mutations in the populations (3). Deleterious mutations (s 0)
have only a negligible chance of fixation due to purifying
selection (3) and are therefore excluded. Fixation rates increase
with population size for beneficial mutations (Eq. 5c) but are
independent of population size for neutral mutations (Eq. 5b).
According to the neutral theory of molecular evolution (3), the
overall rate of genetic divergence (Eq. 5a) should also be
approximately independent of population size, because the
number of neutral mutations far exceeds the number of beneficial
ones, i.e. 2f0 8f Jss. Gene flow among populations,
characterized by the per-generation probability of individual
migration (3), is not explicitly modeled. Eq. 5 therefore applies
to allopatric speciation (19), which is widely regarded as the most
common mode of speciation (4).
Combining Eqs. 1­4 from the metabolic theory with Eq. 5
from population genetics theory, we can derive an analytical
model of speciation by making three simplifying assumptions.
Assumption 1 is that the number of genetic changes required for
reproductive isolation to evolve is independent of temperature.
The genetic divergence between incipient taxa attributable to
beneficial mutations, Ds , can serve as a proxy for this quantity,
because empirical data indicate that the genes initially responsible
for the evolution of reproductive isolation are generally
under selection (4). Assumption 1 thus implies that Ds e0/kT
.
Assumption 2 is that the population-level variables influencing
genetic divergence rates are independent of temperature (i.e.,
Js e0/kT
and s e0/kT
in Eq. 5); these variables are governed by
ecological details of the particular speciation mechanism facilitating
genetic divergence (19). Together, Assumptions 1 and 2
predict that the time to speciation, ts (sec), should decline
exponentially with increasing temperature in the same way as the
individual generation time, 1 g,
ts 1 g Ds d dD
1 g Ds 1 8f Jss 1 goBo eE/kT
, [6]
because the number of generations required for speciation to
occur, tsg (Ds )(1 8f Jss ) is independent of temperature
when Assumptions 1 and 2 are upheld. Given that tsg is independent
of temperature and that the number of mutations per
nucleotide per generation is also independent of temperature (
in Eq. 4), the total genetic divergence between incipient species,
Ds (substitutions nucleotide 1
), should be independent of temperature
as well:
Ds tsg dD d tsg dDo d tsg 2f0 e0/kT
. [7]
The germ-line replication rate is largely controlled by the
individual turnover rate, g. Eqs. 6 and 7 therefore still apply if the
genetic mechanism of speciation does not involve mutations of
single nucleotides, which govern Ds and Ds, but instead involves
some other form of mutation that occurs during germ-line
replication, e.g., chromosomal transversions (4).
Assumption 3 is that, over global temperature gradients,
time-averaged rates of genetic divergence are constrained by
mutation rates and generation times of individuals, which govern
speciation times for diverging populations (ts in Eq. 6), and not
by spatial gradients in the ecological mechanisms that facilitate
genetic divergence. Ecological variables may, however, generate
variation about the predicted temperature trends through their
effects on population-level variables (Js and s in Eq. 6). Assumption
3 implies that genetic divergence mechanisms are globally
ubiquitous. This assumption is consistent with empirical observations
that morphospecies of planktonic foraminifera are capable
of global dispersal (20) yet comprise populations that
exhibit significant levels of divergence among polar to tropical
oceanic provinces (21­24). Together these two observations
indicate that natural selection powerfully constrains effective
rates of gene flow among foraminifera populations (25) and
thereby facilitates genetic divergence among populations in
relation to environmental gradients at all latitudes.
Assumptions 1­3 predict that the per capita speciation rate for
an entire ``metacommunity'' of individuals involved in speciesextinction
dynamics (26), v (species individual 1
sec 1
), should
scale inversely with the time to speciation, ts (Eq. 6), and should
therefore increase exponentially with temperature in the same
way as individual metabolic rate, B (Eq. 1),
v voe E/kT
1 ts B, [8]
where vo is the speciation rate per individual per unit time
(species individual 1
sec 1
). Expressing speciation on a per capita
basis in Eq. 8 is consistent with Assumption 2 in that the sizes
of genetically diverging populations, Js, are independent of
temperature and therefore independent of latitude. By expressing
speciation on a per capita basis, we can use Eq. 8 to predict
that the overall rate of speciation in the metacommunity, Vm
(species sec 1
), should increase linearly with total metacommunity
abundance, Jm,
Vm Jmv AmJAvoe E/kT
, [9]
and therefore with metacommunity area, Am (km2
), and with
metacommunity abundance per unit area, JA Jm Am. These
predictions follow directly from the model assumptions: Increases
in Jm imply that greater numbers of size-Js populations
are genetically diverging from each other at any given time and
hence that Vm is higher.
Results and Discussion
We begin by evaluating the predicted temperature dependence
of mutation rates, (Eq. 3), by using a global compilation of
small subunit ribosomal rRNA-encoding DNA (SSU rDNA)
data obtained by sequencing nuclear genomes of planktonic
foraminifera (see Appendix 1, which is published as supporting
information on the PNAS web site). These data encompass
evolutionary rates for 15 morphospecies whose geographic
ranges collectively span arctic to tropical waters.
As predicted by Eqs. 3­5, the logarithm of the size-corrected
rate of neutral molecular evolution, ln(fo M1/4
), is a linear
function of ocean temperature, 1 kT (r2
0.34; P 0.003; Fig.
1). Furthermore, the absolute value of the fitted slope yields a
95% confidence interval (CI) for E that closely matches the
predicted value of 0.65 eV (x 0.67 eV; 95% CI, 0.26­1.07 eV).
Thus, after controlling for variation in foraminifera size, the
Allen et al. PNAS June 13, 2006 vol. 103 no. 24 9131
EVOLUTION
temperature-dependence of nuclear DNA evolution matches the
prediction derived in Eq. 3 based on the activation energy of
individual metabolic rate. Importantly, we derive this relationship
by characterizing habitat temperatures by using sea-surface
temperature data for shallow-dwelling taxa and temperatures at
200-m depth for deeper-dwelling taxa (see Appendix 1). If,
instead, we characterize habitat temperatures by using seasurface
temperature data for all taxa, the slope of the relationship
between ln(fo M1/4
) and 1 kT still yields a 95% CI for E that
includes the predicted value of 0.65 eV (0.04­1.45 eV), but the
correlation is weaker (r2
0.18 versus 0.34 for the model in Fig.
1). This finding supports the hypothesis that deeper-dwelling
taxa exhibit lower size-corrected rates of molecular evolution as
a direct consequence of declines in habitat temperature with
increasing depth. Thus, it appears that thermal habitat preference
significantly influences rates of DNA evolution for this
group.
The results in Fig. 1 represent previously unrecognized and
direct evidence, based on well established fossil calibrations (see
Appendix 1), that absolute rates of DNA evolution increase
exponentially with environmental temperature in the same way
as individual metabolic rate. These results also serve to reinforce
and extend previous work indicating that absolute rates of
mitochondrial DNA evolution are higher for warmer-bodied
endotherms than for ectothermic animals of similar size (14, 16)
and that relative rates of nuclear DNA evolution increase with
environmental temperature for plants (27­29). Note that our
model predicts that rates of molecular evolution should increase
exponentially with environmental temperature for ectotherms
but not for endotherms, which maintain body temperatures of
35­40°C during active periods, regardless of ambient temperature.
Hence, our model and results do not contradict a study of
birds, which found ``no support for an effect of latitude on rate
of molecular evolution'' (30).
We evaluate the predicted temperature dependence for the
genetic divergence between incipient species, Ds in Eq. 7, by
using a global compilation of SSU rDNA data for 20 ``cryptic''
taxa (23) that have been identified within seven morphospecies
of planktonic foraminifera (see Appendix 2, which is published
as supporting information on the PNAS web site). These cryptic
taxa are ecologically distinct genotypes with different geographic
distributions (21­24, 31) and temperature optima (23). They are
therefore thought to represent incipient morphotaxa in the
relatively early stages of speciation (24).
Despite evidence indicating that rates of molecular evolution
increase exponentially with environmental temperature (Fig. 1),
the genetic divergence between incipient taxa is independent of
ocean temperature (Fig. 2; P 0.74), as predicted by Eq. 7.
These findings are consistent with Assumptions 1 and 2 of our
model that Ds , Js, and s are all independent of temperature. We
note, however, that the data depicted in Fig. 2 encompass taxon
pairs at various stages of divergence, not just the incipient stage,
which is fleeting and therefore difficult to observe (4).
We evaluate latitudinal gradients in rates of speciation at the
level of metacommunities, Vm (Eq. 9), by using fossil data
compiled in the Neptune database, which span the last 30 million
years (Ma) of macroevolution for planktonic foraminifera (32).
Our analysis involves assessing how the rate of first occurrence
(FO) of new morphospecies, which is a surrogate measure for the
speciation rate (10), varies across latitudes at the global scale.
When analyzing and interpreting these data, it is important to
recognize that each morphospecies may evolve to comprise
several distinct genotypes that occupy different thermal environments,
as shown in Fig. 2.
By using these fossil data, we show that the time-averaged rate
of speciation is significantly higher in the tropics (Fig. 3A,
equal-area latitudinal bands 2 and 3) than in the temperate zones
(Fig 3A, bands 1 and 4), even after controlling for sampling effort
and for the greater habitat area at tropical latitudes (Fig. 3B; and
see Appendix 3, which is published as supporting information on
the PNAS web site). Furthermore, this gradient in macroevolutionary
dynamics is significantly correlated with average ocean
temperatures (r2
0.97; P 0.01; Fig. 3B), which have been
estimated by using a robust paleotemperature calibration (33) to
control for the 8°C decline in high-latitude ocean temperatures
Fig. 1. Effect of ocean temperature, 1 kT, on the size-corrected rate of
neutral molecular evolution, ln(fo M1/4), for nuclear genomes of planktonic
foraminifera. The slope ( 0.67 eV) was fitted by using ordinary least-squares
regression and is close to the value of E 0.65 eV (95% CI, 0.26 to 1.07
eV), which was predicted based on the temperature dependence of individual
metabolic rate (Eq. 3). Refer to Appendix 1 for details on this global compilation
of SSU rDNA data.
Fig. 2. Effect of ocean temperature, 1 kT, on genetic divergence, ln(Ds), for
nuclear genomes of ecologically distinct genotypes within seven morphospecies
of planktonic foraminifera. The sample sizes in the legend refer to the
numbers of pairwise comparisons among populations comprising each morphospecies.
The data were weighted such that each morphospecies contributed
equally to the ordinary least-squares regression slope, which does not
differ from the predicted value of 0 (Eq. 7). This conclusion remains unchanged
if data points, rather than morphospecies, are weighted equally (P 0.10).
Refer to Appendix 2 for details on this global compilation of SSU rDNA data.
9132 www.pnas.org cgi doi 10.1073 pnas.0603587103 Allen et al.
over the past 30 Ma (see Appendix 4, which is published as
supporting information on the PNAS web site). According to our
model, this correlation reflects the combined effects of temperature-dependent
changes in the per capita speciation rate, v (Eq.
8), and in total community abundance per unit area, JA (Eq. 9),
because only ocean area, Am, is held constant for the metacommunity-level
rates depicted in Fig. 3B.
Importantly, the strength of this correlation may be sensitive
to the number and placement of latitudinal bands, because FO
events for ocean plankton are unevenly distributed across latitudes,
as shown in another study conducted with the Neptune
database (32). These findings are consistent with the hypothesis
that speciation events for marine taxa are often concentrated
along the margins of oceanographic currents, because these
currents facilitate divergent selection, genetic divergence, and
speciation (34, 35). In our model, oceanographic currents could
enhance speciation rates through their effects on population
subdivision (Js), the intensity of natural selection (s), and or
metacommunity abundance (JA) (Eqs. 5­9).
To control for any effects of spatial aggregation of FO events
on the estimated rates of macroevolution, we evaluate the
predicted temperature dependence of the per capita speciation
rate, v (Eq. 8), by using an alternative approach that explicitly
controls for latitudinal covariation in ocean area, temperature,
and metacommunity abundance per unit area, JA (Eq. 9),
without having to bin the FO data into arbitrary regions
(Appendix 5, which is published as supporting information on
the PNAS web site). By using this alternative approach, we
obtain a 95% CI for E that includes the predicted value of 0.65
eV (x 0.78 eV; 95% CI, 0.62­0.96 eV). Thus, after controlling
for variation in foraminifera community abundance across
latitudes, the temperature-dependence of speciation matches
the prediction derived in Eq. 8 based on the activation energy
of individual metabolic rate. These results support Assumption
3 of our model that variation in speciation rates across global
temperature gradients is largely controlled by the same individual-level
variables constraining rates of genetic divergence
among populations (i.e., generation times and mutation rates
in Eqs. 2 and 3).
The model and results presented here yield four insights into
the factors governing the origin and maintenance of biodiversity.
The first insight is that energy flux is a primary determinant of
evolutionary dynamics. Consequently, the rates of nucleotide
substitution (Fig. 1) and per capita speciation both vary exponentially
with temperature according to the same BoltzmannArrhenius
factor controlling individual metabolic rate (e E/kT
in
Eq. 1). The second insight is that the total genetic change
required to produce a new species, characterized by Ds, is
independent of temperature (Fig. 2) and therefore independent
of latitude and metabolic rate. Our model and results support the
hypothesis that the tropics are a ``cradle'' for biodiversity (10,
36), because a given amount of genetic change results in the same
degree of ecological and morphological differentiation, regardless
of the temperature regime, but takes exponentially less time
in a hotter environment (Eq. 6) due to shorter generation times
(Eq. 2) and higher mutation rates (Eq. 3). Consequently, ``effective''
evolutionary time per unit absolute time is greater at
tropical latitudes, as proposed by Rohde (37).
The third insight is that a fixed quantity of energy is required, on
average, to produce a given magnitude of evolutionary change. We
showed earlier that 2.5 1013
J of energy must be fluxed per gram
of tissue to induce one substitution per nucleotide in nuclear
genomes of primates (14). That estimate is remarkably close to the
value determined here of 1.8 1013
J g 1
for nuclear genomes of
foraminifera (see Methods). Similarly, a fixed but much larger
quantity of energy must be fluxed through a population to produce
a new morphospecies of foraminifera, independent of environmental
temperature and hence latitude. We estimate this quantity to be
boM3/4
vo 1023
J based on estimates for bo 2.8 107
W g 3/4
(17), vo 5.6 10 20
species individual 1
sec 1
(see Appendix 5),
and the geometric mean of the foraminifera mass estimates in
Appendix 1, M 5.7 10 5
g. This is an enormous quantity of
energy; it exceeds global net primary production for an entire year
( 1021
J) (38) and current annual fossil fuel consumption by all of
humanity ( 1020
J) (39). We expect this quantity to vary with the
mode of speciation and hence with taxon and environmental
setting, because the absolute rate of genetic divergence is a function
not only of individual-level variables governed by metabolic rate
(i.e., generation times and mutation rates) but also of gene flow,
effective population size, and the intensity of natural selection. This
example highlights the need to better understand how individuallevel
variables (Eqs. 2 and 3) combine with spatially explicit
Fig. 3. Both ecological and macroevolutionary variables exhibit pronounced variation from the poles to the equator. (A) Depicted are the latitudinal gradient
in contemporary mean annual sea-surface temperatures (48) (dashed line) and ocean surface area per 0.5° latitude (solid line; negative numbers correspond to
southern latitudes). Different shades are used to represent four equal-area latitudinal bands of 9.1 107 km2 ocean area each. (B) Depicted are the effects
of ocean temperature on time-averaged speciation rates over the past 30 Ma in each of the four equal-area latitudinal bands. The line was fitted by using ordinary
least-squares regression. Speciation rates were calculated based on the latitudinal distribution of 150 FO of foraminifera morphospecies by using the Neptune
database (32); 95% CIs (vertical lines) were generated, as described in Appendix 3, by using a randomization procedure that explicitly controls for the effects
of variation in sampling efforts on paleontological analyses. The average sea-surface temperature within each latitudinal band over the past 30 Ma was
estimated, as described in Appendix 4, by using a robust paleotemperature calibration (33).
Allen et al. PNAS June 13, 2006 vol. 103 no. 24 9133
EVOLUTION
population-level processes to determine the temperaturedependence
of speciation rates (Eq. 8).
The fourth insight is that habitat area is also an important
determinant of latitudinal gradients in speciation rates and
hence biodiversity, as suggested by Rosenzweig (6). In fact, our
model and results indicate that the predicted exponential effects
of temperature on speciation rates are only manifested after
controlling for habitat area and community abundance by
expressing speciation on a per capita basis (Eq. 8). This approach
runs counter to the long-standing tradition among evolutionary
biologists and paleontologists of expressing speciation on a per
species basis (species species 1
time 1
) (4). Nevertheless, it is
consistent with evolutionary theory, because speciation occurs at
the level of populations (Eqs. 5­9). It is also consistent with the
recently proposed neutral biodiversity theory (NBT) of Hubbell
(26), which predicts that the per capita speciation rate, v,
determines the number of species maintained in a metacommunity
of fixed abundance Jm. Synthesizing our energetically and
genetically based model of speciation (Eqs. 1­9) with NBT may
therefore yield a better understanding of why biodiversity increases
exponentially with environmental temperature in the
same way as individual metabolic rate for diverse groups of
terrestrial, aquatic, and marine ectotherms (7, 40, 41).
We conclude by noting that the theory developed here also
predicts that evolutionary rates vary as a power function with
body size according to the mass-dependence of individual metabolic
rate ( M 1/4
). This result has been shown for rates of
microevolution, i.e., nucleotide substitution (14), but has not yet
been demonstrated for rates of macroevolution. Extension of our
model may therefore yield insights into the combined effects of
body size and temperature on other prominent yet poorly
understood gradients in macroevolutionary dynamics (for examples,
see refs. 42 and 43).
Methods
Molecular Evolution Data. The SSU rDNA data in Fig. 1 were
compiled from the sources cited in Appendix 1. Our model
predicts that rates of molecular evolution increase exponentially
with temperature (Eq. 3), which implies that the warmer, more
rapidly evolving taxon makes a greater contribution to the
genetic divergence, D, and hence to the calculated rate of
molecular evolution fo D/2 (following Eq. 5), where is the
time since divergence. To account for the greater contribution
of the warmer-bodied taxon to fo , we characterize the overall
habitat temperature for each taxon pair depicted in Fig. 1 by
using the Boltzmann average,
T E E ln e E/kT1
e E/kT2
2 k,
where T1 and T2 are the habitat temperatures of the two taxa in
Kelvins. Habitat temperatures were independently estimated by
using a global compilation of contemporary community abundance
data collected from 1,265 sites around the world (44) in
conjunction with contemporary ocean temperature data (45).
Habitat temperatures were estimated by using sea-surface temperatures
for shallow-dwelling taxa and temperatures at 200-m
depth for deeper-dwelling taxa (Appendix 1).
Genetic Divergence Data. The SSU rDNA data in Fig. 2 were
compiled from the sources cited in Appendix 2. The habitat
temperature of each population was estimated from the spatial
location of sampling by using contemporary ocean temperature
data (45). The Boltzmann-averaged habitat temperature,
T E, was then calculated for each taxon pair depicted in the
figure.
FO Data. The latitudinal distribution of FOs of morphospecies in
Fig. 3B was analyzed by using morphospecies-level data in the
Neptune database, a compilation of fossil samples from over 160
deep-sea drilling holes around the world that have been dated to an
average precision of 1 Ma (32). We analyzed the Neptune data by
using the following procedure to simultaneously control for latitudinal
variation in area (Fig. 3A) and for the effects of sampling
effort on paleontological analyses (46): (i) We assigned each of
3,000 core samples to one of four latitudinal bands of equal ocean
surface area (Fig. 3A) and to one of six 5-Ma time intervals
spanning the last 30 Ma. (ii) We selected a subset of 40 samples at
random and without replacement from each equal-area latitudinal
band and time interval, yielding a data subset comprising 900
samples. (iii) We determined the band of FO for each morphospecies
of foraminifera arising through speciation over the past 30 Ma.
(iv) We tallied the total number of FOs in each band to obtain
estimates for Vm. (v) We repeated steps ii­iv 100 times to generate
the 95% CIs for Vm depicted in Fig. 3B (Appendix 3).
Paleotemperature Data. To obtain the estimates of average ocean
temperature depicted in Fig. 3B, 1 kT, we modeled variation in
sea-surface temperatures with respect to latitude, L ( 90° to 90°N),
and time, t, by using the heat equation on the surface of a sphere,
T(L, t) (P(t) T0)sin2
( L 180) T0, where P(t) is the seasurface
temperature at the poles at time t, and T0 is the sea-surface
temperature at the equator. The function P(t) was estimated in Fig.
2 of ref. 33 by using robust methods of paleotemperature calibration.
The parameter T0 was assumed to remain constant at 28°C
over the past 30 Ma based on available evidence (47). The function
T(L, t) was integrated over time and space, as described in Appendix
4, to yield the estimates of 1 kT depicted in Fig. 3B.
Estimating the per Capita Speciation Rate. Evaluating the temperature
dependence of the per capita speciation rate (Eq. 8)
required explicitly accounting for temperature-dependent
changes in foraminifera community abundance across latitudes.
To avoid difficulties associated with inferring live abundances of
foraminifera from shell accumulation rates, we characterized
this temperature dependence by using a global compilation of
plankton tow data (45) on foraminifer metacommunity abundance
per unit area, JA. We estimated the temperature dependence
of the per capita speciation rate, characterized by E (Eq.
8), and the normalization parameter, vo, by expressing the
latitudinal distribution of FOs as a cumulative function of ocean
area (Fig. 3A), paleotemperature T(L, t), and metacommunity
abundance (Appendix 5).
Estimating the Energy Required to Induce Mutations. Following Eqs.
2­5, the size- and temperature-corrected rate of molecular evolution,
fo M1/4
eE/kT
, is equal to f0 obo. For primates, we obtain an
estimate of 2.5 1013
J g 1
substitutions 1
nucleotide for 1 f0 o by
using an estimate of bo 3.9 108
W g 3/4
for endotherms (17) and
the geometric mean of the estimates of fo M1/4
eE/kT
in ref. 14 for the
globin gene ( 4.9 1010
substitutions nucleotide 1
10 8
yr g1/4
).
For planktonic foraminifera, we obtain an estimate of 1.8 1013
J g 1
substitutions 1
nucleotide for 1 f0 o by using an estimate of
bo 2.8 107
W g 3/4
for unicells (17) and the geometric mean of
the estimates of fo M1/4
eE/kT
for the data depicted in Fig. 1 ( 5.0
109
substitutions nucleotide 1
10 8
yr g1/4
).
We thank Fangliang He, Andrew Martin, Richard Norris, Klaus
Rohde, and John Wilkins for their insightful comments and suggestions.
A.P.A. was supported as a Postdoctoral Associate at the
National Center for Ecological Analysis and Synthesis, a center funded
by National Science Foundation Grant DEB-0072909, and the University
of California, Santa Barbara. V.M.S. was supported by National
Institutes of Health Grant 1 P50 GM68763-02 through the Bauer
Center for Genomics Research.
9134 www.pnas.org cgi doi 10.1073 pnas.0603587103 Allen et al.
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