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Kinetic Effects of Temperature on Rates of Genetic Divergence and Speciation Andrew P

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Kinetic Effects of Temperature on Rates of Genetic Divergence and Speciation Andrew P 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 dy- dependence of mass-specific metabolic rate, B៮ (J⅐secϪ1⅐gϪ1) namics are prominent yet poorly understood. We derive a model (12–14): that quantifies the role of kinetic energy in generating biodiver- Ϫ1/4 ϪE/kT ϪE/kT sity. The model predicts that rates of genetic divergence and B៮ ϭ B͞M ϭ boM e ϭ Boe , [1] speciation are both governed by metabolic rate and therefore Ϫ1 show the same exponential temperature dependence (activation where B is individual metabolic rate (J sec ), M is body mass (g), ؋ 10؊19 J). Predictions are T is absolute temperature (K), Bo is a normalization parameter 1.602 ؍ energy of Ϸ0.65 eV; 1 eV Ϫ1 Ϫ1 supported by global datasets from planktonic foraminifera for independent of temperature (J⅐sec ⅐g ) that varies with body Ϫ1/4 rates of DNA evolution and speciation spanning 30 million years. size as Bo ϭ boM (12), and bo is a normalization parameter As predicted by the model, rates of speciation increase toward the independent of body size and temperature that varies among tropics even after controlling for the greater ocean coverage at taxonomic and functional groups (12, 17). The Boltzmann– ϪE/kT tropical latitudes. Our model and results indicate that individual Arrhenius factor, e , characterizes the exponential effect of metabolic rate is a primary determinant of evolutionary rates: temperature on metabolic rate, where E is the average activation Ϸ1013 J of energy flux per gram of tissue generates one substitu- energy of the respiratory complex (Ϸ0.65 eV; 1 eV ϭ 1.602 ϫ Ϫ19 Ϫ5 Ϫ1 tion per nucleotide in the nuclear genome, and Ϸ1023 J of energy 10 J), and k is the Boltzmann constant (8.62 ϫ 10 eV K ). flux per population generates a new species of foraminifera. This Boltzmann–Arrhenius factor has been shown to describe the temperature dependence of metabolic rate for a broad allopatric speciation ͉ biodiversity ͉ macroevolution ͉ metabolic theory assortment of organisms in recent work (12) and in much earlier of ecology ͉ molecular clock 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 secϪ1), and he latitudinal increase in biodiversity from the poles to the the mutation rate, ␣ (mutations⅐nucleotideϪ1⅐secϪ1), both show equator is the most pervasive feature of biogeography. For T this same temperature dependence (12–14): two centuries, since the time of von Humboldt, Darwin, and Wallace, scientists have proposed hypotheses to explain this ϪE/kT g ϭ goB៮ ϭ goBoe [2] pattern. New species arise through the evolution of genetic differences among populations from a common ancestral lineage and (1–4). Many hypotheses therefore attribute the latitudinal biodi- ϪE/kT versity gradient to a gradient in speciation rates caused by some ␣ ϭ ␣oB៮ ϭ ␣oBoe , [3] independent variable, such as earth surface area or solar energy input (5–7). Some fossil data suggest that speciation rates do where go is the number of generations per joule of energy flux Ϫ1 indeed increase toward the tropics (8–10), but these findings through a gram of tissue (generations⅐J ⅐g), and ␣o is the remain open to debate due in part to our limited understanding number of mutations per nucleotide per joule of energy flux Ϫ1 Ϫ1 of the factors that control macroevolutionary dynamics. through a gram of tissue (mutations⅐nucleotide ⅐J ⅐g). Eqs. 2 Recent advances toward a metabolic theory of ecology (11) and 3 predict a 15-fold increase in the rates of individual turnover provide new opportunities for assessing the factors that control and mutation over the temperature range 0–30°C from the poles ϪE/k303 ϪE/k273 speciation rates. This recent work indicates that two fundamen- to the equator (e ͞e ϭ 15-fold from 273–303 K). tal variables influencing the tempo of evolution, the generation Because g and ␣ are both governed by B៮ , the number of time, and the mutation rate (3) are both direct consequences of mutations per nucleotide per generation, biological metabolism (12–14). Here we combine these recent ␣ ϭ ␣͞g ϭ ␣ ͞g ϰ e0/kT, [4] insights from metabolic theory with the theory of population ␶ o o genetics to derive a model that predicts how environmental is independent of temperature. temperature, through its effects on individual metabolic rates Speciation entails genetic divergence among populations from (Eqs. 1–4), influences rates of genetic divergence among popu- a common ancestral lineage, resulting in reproductive isolation lations (Eqs. 5–7) and rates of speciation in communities (Eqs. (2, 4). The theory of population genetics characterizes the rate 8 and 9). We evaluate the model by using data from planktonic of increase in the total genetic divergence, D (substitutions foraminifera, because this group has extensive DNA sequence nucleotideϪ1), between two reproductively isolated diploid pop- data for evaluating population-level predictions on genetic di- vergence combined with an exceptionally complete fossil record for evaluating community-level predictions on speciation rates. Conflict of interest statement: No conflicts declared. Freely available online through the PNAS open access option. Model Development Abbreviations: CI, confidence interval; FO, first occurrence; Ma, mega-annum; SSU rDNA, The two individual-level variables constraining the evolutionary small subunit rRNA-encoding DNA. rate of a population, the generation time, and the mutation rate †To whom correspondence may be addressed. E-mail: [email protected] or jhbrown@ (3) are both direct consequences of biological metabolism (15, unm.edu. 16). They are both governed by the body size- and temperature- © 2006 by The National Academy of Sciences of the USA 9130–9135 ͉ PNAS ͉ June 13, 2006 ͉ vol. 103 ͉ no. 24 www.pnas.org͞cgi͞doi͞10.1073͞pnas.0603587103 ulations, both of size Js, on a per-generation basis, dD͞d␶ The germ-line replication rate is largely controlled by the (substitutions⅐nucleotideϪ1⅐generationϪ1), such that individual turnover rate, g. Eqs. 6 and 7 therefore still apply if the genetic mechanism of speciation does not involve mutations of ϩ dD͞d␶ ϭ dD0͞d␶ ϩ dDϩ͞d␶ Ϸ 2f0␣␶ ϩ 8fϩJss␣␶ Ϸ 2f0␣␶, single nucleotides, which govern Ds and Ds, but instead involves some other form of mutation that occurs during germ-line [5a] replication, e.g., chromosomal transversions (4). Assumption 3 is that, over global temperature gradients, where f0 and fϩ are the respective fractions of mutations that are time-averaged rates of genetic divergence are constrained by selectively neutral (s ϭ 0) and beneficial (s Ͼ 0), Do and Dϩ are the respective contributions of neutral and beneficial mutations mutation rates and generation times of individuals, which govern to the total genetic divergence D, and 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 dD0͞d␶ ϭ ͑4Js f0␣␶͒͑1͞2Js͒ ϭ 2f0␣␶ [5b] variation about the predicted temperature trends through their and effects on population-level variables (Js and s in Eq. 6). Assump- tion 3 implies that genetic divergence mechanisms are globally Ϫ2s Ϫ4Jss dDϩ͞d␶ ϭ ͑4Js fϩ␣␶͒͑͑1 Ϫ e ͒͑͞1 Ϫ e ͒͒ Ϸ 8fϩJss␣␶ ubiquitous. This assumption is consistent with empirical obser- vations that morphospecies of planktonic foraminifera are ca- [5c] pable of global dispersal (20) yet comprise populations that are the respective rates of fixation of neutral and beneficial exhibit significant levels of divergence among polar to tropical mutations in the populations (3). Deleterious mutations (s Ͻ 0) oceanic provinces (21–24). Together these two observations have only a negligible chance of fixation due to purifying indicate that natural selection powerfully constrains effective selection (3) and are therefore excluded. Fixation rates increase rates of gene flow among foraminifera populations (25) and thereby facilitates genetic divergence among populations in with population size for beneficial mutations (Eq. 5c) but are relation to environmental gradients at all latitudes. independent of population size for neutral mutations (Eq. 5b). Assumptions 1–3 predict that the per capita speciation rate for According to the neutral theory of molecular evolution (3), the an entire ‘‘metacommunity’’ of individuals involved in species- 5a overall rate of genetic divergence (Eq. ) should also be extinction dynamics (26), v (species⅐individualϪ1⅐secϪ1), should approximately independent of population size, because the scale inversely with the time to speciation, ts (Eq. 6), and should number of neutral mutations far exceeds the number of bene- therefore increase exponentially with temperature in the same ficial ones, i.e. 2f0 ϾϾ 8fϩJss. Gene flow among populations, way as individual metabolic rate, B៮ (Eq. 1), characterized by the per-generation probability of individual ϪE/kT migration (3), is not explicitly modeled. Eq. 5 therefore applies v ϭ voe ϰ ͑1͞ts͒ ϰ B៮ , [8] to allopatric speciation (19), which is widely regarded as the most common mode of speciation (4). where vo is the speciation rate per individual per unit time Ϫ Ϫ Combining Eqs. 1–4 from the metabolic theory with Eq. 5 (species⅐individual 1⅐sec 1). Expressing speciation on a per cap- from population genetics theory, we can derive an analytical ita basis in Eq. 8 is consistent with Assumption 2 in that the sizes model of speciation by making three simplifying assumptions.
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