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. 3
–5, the logarithm of the size-corrected rate of neutral molecular evolution, ln(foM1/4), 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 (
= 0.67 eV; 95% CI, 0.26–1.07 eV). Thus, after controlling for variation in foraminifera size, the 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 sea-surface temperature data for all taxa, the slope of the relationship between ln(foM1/4) 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 (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 (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, 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 (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 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 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. 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, 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 ( = 0.78 eV; 95% CI, 0.62–0.96 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 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 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 x 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 x 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 bo
3/4/vo 1023 J based on estimates for bo 2.8 x 107 W g–3/4 (17), vo 5.6 x 10–20 species·individual–1·sec–1 (see Appendix 5), and the geometric mean of the foraminifera mass estimates in Appendix 1, 5.7 x 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 individual-level variables (Eqs. 2 and 3) combine with spatially explicit population-level processes to determine the temperature-dependence 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. 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 Jm. 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 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).
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