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Kinetic effects of temperature on rates of genetic divergence and speciation

Contributed by James H. Brown, May 2, 2006
Abstract
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: ≈10^{13} J of energy flux per gram of tissue generates one substitution per nucleotide in the nuclear genome, and ≈10^{23} J of energy flux per population generates a new species of foraminifera.
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 (1–4). 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 (5–7). Some fossil data suggest that speciation rates do indeed increase toward the tropics (8–10), 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 (12–14). 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. 1 – 4 ), influences rates of genetic divergence among populations (Eqs. 5 – 7 ) 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 populationlevel predictions on genetic divergence combined with an exceptionally complete fossil record for evaluating communitylevel predictions on speciation rates.
Model Development
The two individuallevel 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 massspecific metabolic rate, B̄(J·sec^{−1}·g^{−1}) (12–14):
where B is individual metabolic rate (J sec^{−1}), M is body mass (g), T is absolute temperature (K), B_{o} is a normalization parameter independent of temperature (J·sec^{−1}·g^{−1}) that varies with body size as B_{o} = b_{o}M ^{−1/4} (12), and b_{o} is a normalization parameter independent of body size and temperature that varies among taxonomic and functional groups (12, 17). The Boltzmann–Arrhenius 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 Boltzmann–Arrhenius 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, α (mutations·nucleotide^{−1}·sec^{−1}), both show this same temperature dependence (12–14):
and
where g_{o} is the number of generations per joule of energy flux through a gram of tissue (generations·J^{−1}·g), and α _{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 15fold increase in the rates of individual turnover and mutation over the temperature range 0–30°C from the poles to the equator (e ^{−E/k303}/e ^{−E/k273} = 15fold from 273–303 K). Because g and α are both governed by B̄, the number of mutations per nucleotide per generation,
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 populations, both of size J_{s} , on a pergeneration basis, dD/dτ (substitutions·nucleotide^{−1}·generation^{−1}), such that
where f _{0} and f _{+} are the respective fractions of mutations that are selectively neutral (s = 0) and beneficial (s > 0), D_{o} and D _{+} are the respective contributions of neutral and beneficial mutations to the total genetic divergence D, and
and
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. 2f _{0} ≫ 8f _{+} J_{s}s. Gene flow among populations, characterized by the pergeneration 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. 1 – 4 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, D _{s} ^{+}, 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 D _{s} ^{+} ∝ e ^{0/kT}. Assumption 2 is that the populationlevel variables influencing genetic divergence rates are independent of temperature (i.e., J_{s} ∝ e ^{0/kT} and s ∝ e ^{0/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, t_{s} (sec), should decline exponentially with increasing temperature in the same way as the individual generation time, 1/g,
because the number of generations required for speciation to occur, t_{s}g ≈ (D _{s} ^{+})(1/8f _{+} J_{s}sα_{τ}) is independent of temperature when Assumptions 1 and 2 are upheld. Given that t_{s}g is independent of temperature and that the number of mutations per nucleotide per generation is also independent of temperature (α_{τ} in Eq. 4 ), the total genetic divergence between incipient species, D_{s} (substitutions nucleotide^{−1}), should be independent of temperature as well:
The germline 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 D _{s} ^{+} and D_{s} , but instead involves some other form of mutation that occurs during germline replication, e.g., chromosomal transversions (4).
Assumption 3 is that, over global temperature gradients, timeaveraged rates of genetic divergence are constrained by mutation rates and generation times of individuals, which govern speciation times for diverging populations (t_{s} 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 populationlevel variables (J_{s} 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 (21–24). 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 1–3 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, t_{s} (Eq. 6 ), and should therefore increase exponentially with temperature in the same way as individual metabolic rate, B̄ (Eq. 1 ),
where v_{o} 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, J_{s} , 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, V_{m} (species sec^{−1}), should increase linearly with total metacommunity abundance, J_{m} ,
and therefore with metacommunity area, A_{m} (km^{2}), and with metacommunity abundance per unit area, J_{A} = J_{m} /A_{m} . These predictions follow directly from the model assumptions: Increases in J_{m} imply that greater numbers of sizeJ_{s} populations are genetically diverging from each other at any given time and hence that V_{m} is higher.
Results and Discussion
We begin by evaluating the predicted temperature dependence of mutation rates, α (Eq. 3 ), by using a global compilation of small subunit ribosomal rRNAencoding 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. 3 – 5 , the logarithm of the sizecorrected rate of neutral molecular evolution, ln(f_{o} αM ^{1/4}), is a linear function of ocean temperature, 1/kT (r^{2} = 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 (x̄ = 0.67 eV; 95% CI, 0.26–1.07 eV). Thus, after controlling for variation in foraminifera size, the temperaturedependence 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 seasurface temperature data for shallowdwelling taxa and temperatures at 200m depth for deeperdwelling 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(f_{o} αM ^{1/4}) and 1/kT still yields a 95% CI for E that includes the predicted value of 0.65 eV (0.04–1.45 eV), but the correlation is weaker (r^{2} = 0.18 versus 0.34 for the model in Fig. 1). This finding supports the hypothesis that deeperdwelling taxa exhibit lower sizecorrected 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 warmerbodied endotherms than for ectothermic animals of similar size (14, 16) and that relative rates of nuclear DNA evolution increase with environmental temperature for plants (27–29). 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 ≈35–40°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, D_{s} 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 (21–24, 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 D _{s} ^{+}, J_{s} , 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, V_{m} (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 timeaveraged rate of speciation is significantly higher in the tropics (Fig. 3 A, equalarea latitudinal bands 2 and 3) than in the temperate zones (Fig 3 A, bands 1 and 4), even after controlling for sampling effort and for the greater habitat area at tropical latitudes (Fig. 3 B; 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 (r ^{2} = 0.97; P = 0.01; Fig. 3 B), which have been estimated by using a robust paleotemperature calibration (33) to control for the ≈8°C decline in highlatitude ocean temperatures 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 temperaturedependent changes in the per capita speciation rate, v (Eq. 8 ), and in total community abundance per unit area, J_{A} (Eq. 9 ), because only ocean area, A_{m} , is held constant for the metacommunitylevel rates depicted in Fig. 3 B.
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 (J_{s} ), the intensity of natural selection (s), and/or metacommunity abundance (J_{A} ) (Eqs. 5 – 9 ).
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, J_{A} (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 (x̄ = 0.78 eV; 95% CI, 0.62–0.96 eV). Thus, after controlling for variation in foraminifera community abundance across latitudes, the temperaturedependence 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 individuallevel 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 Boltzmann–Arrhenius 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 D_{s} , 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 × 10^{13} 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 × 10^{13} 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 b_{o}M̅ ^{3/4}/v_{o} ≈ 10^{23} J based on estimates for b_{o} ≈ 2.8 × 10^{7} W g^{−3/4} (17), v_{o} ≈ 5.6 × 10^{−20} species·individual^{−1}·sec^{−1} (see Appendix 5), and the geometric mean of the foraminifera mass estimates in Appendix 1, M̅ ≈ 5.7 × 10^{−5} g. This is an enormous quantity of energy; it exceeds global net primary production for an entire year (≈10^{21} J) (38) and current annual fossil fuel consumption by all of humanity (≈10^{20} 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 individuallevel 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 populationlevel 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 longstanding 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. 5 – 9 ). 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 J_{m} . Synthesizing our energetically and genetically based model of speciation (Eqs. 1 – 9 ) 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 massdependence 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 f_{o} α = D/2Γ (following Eq. 5 ), where Γ is the time since divergence. To account for the greater contribution of the warmerbodied taxon to f_{o} α, we characterize the overall habitat temperature for each taxon pair depicted in Fig. 1 by using the Boltzmann average,
where T _{1} and T _{2} 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 seasurface temperatures for shallowdwelling taxa and temperatures at 200m depth for deeperdwelling 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 Boltzmannaveraged 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. 3 B was analyzed by using morphospecieslevel data in the Neptune database, a compilation of fossil samples from over 160 deepsea 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. 3 A) 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. 3 A) and to one of six 5Ma time intervals spanning the last 30 Ma. (ii) We selected a subset of 40 samples at random and without replacement from each equalarea 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 V_{m} . (v) We repeated steps ii–iv 100 times to generate the 95% CIs for V_{m} depicted in Fig. 3 B (Appendix 3).
Paleotemperature Data.
To obtain the estimates of average ocean temperature depicted in Fig. 3 B, 1̅/̅k̅T̅, we modeled variation in seasurface 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) − T _{0})sin^{2}(πL/180) + T _{0}, where P(t) is the seasurface temperature at the poles at time t, and T _{0} is the seasurface 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 T _{0} 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 1̅/̅k̅T̅ depicted in Fig. 3 B.
Estimating the per Capita Speciation Rate.
Evaluating the temperature dependence of the per capita speciation rate (Eq. 8 ) required explicitly accounting for temperaturedependent 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, J_{A} . We estimated the temperature dependence of the per capita speciation rate, characterized by E (Eq. 8 ), and the normalization parameter, v_{o} , by expressing the latitudinal distribution of FOs as a cumulative function of ocean area (Fig. 3 A), paleotemperature T(L, t), and metacommunity abundance (Appendix 5).
Estimating the Energy Required to Induce Mutations.
Following Eqs. 2 – 5 , the size and temperaturecorrected rate of molecular evolution, f_{o} αM ^{1/4} e^{E/kT} , is equal to f _{0}α _{o}b_{o} . For primates, we obtain an estimate of 2.5 × 10^{13} J·g^{−1}·substitutions^{−1}·nucleotide for 1/f _{0}α _{o} by using an estimate of b_{o} ≈ 3.9 × 10^{8} W g^{−3/4} for endotherms (17) and the geometric mean of the estimates of f_{o} αM ^{1/4} e^{E/kT} in ref. 14 for the globin gene (≈4.9 × 10^{10} substitutions·nucleotide^{−1}·10^{−8} yr·g^{1/4}). For planktonic foraminifera, we obtain an estimate of 1.8 × 10^{13} J·g^{−1}·substitutions^{−1}·nucleotide for 1/f _{0}α_{o} by using an estimate of b_{o} ≈ 2.8 × 10^{7} W g^{−3/4} for unicells (17) and the geometric mean of the estimates of f_{o} αM ^{1/4} e^{E/kT} for the data depicted in Fig. 1 (≈5.0 × 10^{9} substitutions·nucleotide^{−1}·10^{−8} yr·g^{1/4}).
Acknowledgments
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 DEB0072909, and the University of California, Santa Barbara. V.M.S. was supported by National Institutes of Health Grant 1 P50 GM6876302 through the Bauer Center for Genomics Research.
Footnotes
 ^{†}To whom correspondence may be addressed. Email: drewa{at}nceas.ucsb.edu or jhbrown{at}unm.edu

Author contributions: A.P.A., J.F.G., and J.H.B. designed research; A.P.A. and J.F.G. performed research; A.P.A. and V.M.S. contributed new reagents/analytic tools; A.P.A. analyzed data; and A.P.A., J.F.G., V.M.S., and J.H.B. wrote the paper.

Conflict of interest statement: No conflicts declared.
 Abbreviations:
 CI,
 confidence interval;
 FO,
 first occurrence;
 Ma,
 megaannum;
 SSU rDNA,
 small subunit rRNAencoding DNA.
Abbreviations:

Freely available online through the PNAS open access option.
 © 2006 by The National Academy of Sciences of the USA
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