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Metabolic Rate Calibrates the Molecular Clock: Reconciling Molecular and Fossil Estimates of Evolutionary Divergence

Observations that rates of molecular evolution vary widely within and among lineages have cast doubts upon the existence of a single molecular clock. Differences in the timing of evolutionary events estimated from genetic and fossil evidence have raised further questions about the existence of molecular clocks and their use. Here we present a model of nucleotide substitution that combines new theory on metabolic rate with the now classic neutral theory of molecular evolution. The model quantitatively predicts rate heterogeneity, and reconciles differences in molecular- and fossil-estimated dates of evolutionary events. Model predictions are supported by extensive data from mitochondrial and nuclear genomes. By accounting for the effects of body size and temperature on metabolic rate, a single molecular clock explains heterogeneity in rates of nucleotide substitution in different genes, taxa, and thermal environments. This model suggests that there is indeed a general molecular clock, as originally proposed by Zuckerkandl and Pauling, but that it ticks at a constant substitution rate per unit mass-specific metabolic energy rather than per unit time. More generally, the model suggests that body size and temperature combine to control the overall rate of evolution through their effects on metabolism.


Introduction
Variation in rates of nucleotide substitution has been correlated with metabolic rate (1) , generation time (9) and environmental temperature (10). We currently lack a mechanistic understanding of the factors responsible for these observed patterns and for rate heterogeneity in general. Here we propose a mechanistic model that predicts heterogeneity in rates of molecular evolution by combining principles of allometry and biochemical kinetics with Kimura's neutral theory of evolution. This model may also provide insights into macroevolutionary patterns including rates of speciation, patterns of biodiversity, and evolutionary relationships among organisms (11).

The Model
Metabolic rate is the rate at which energy and materials are taken up from the environment and used for maintenance, growth, and reproduction. It ultimately governs most biological rate processes, including the three generally thought to control mutation rate -generation time, cell division rate, and free radical production rate (1,6,9,12).
Mass-specific metabolic rate (B) varies with body size, M, and temperature, T, as where b o is a coefficient independent of mass and temperature (6). The body size term, M -1/4 , has its origins in the fractal-like geometry of biological exchange surfaces and distribution networks (5). The Boltzmann factor, e -E/kT , underlies the temperaturedependence of metabolic rate, where E is the activation energy of the rate-limiting biochemical reactions of metabolism (~0.6-0.7 eV, ref. (6)), k is Boltzmann's constant (8.62 x 10 -5 eV K -1 ), and T is absolute temperature (K). Eq. 1 explains most of the variation in the metabolic rates of plants, animals, and microbes (6).
When combined with assumptions of the neutral theory (13), Eq. 1 can also be used to characterize rates of molecular evolution. The first assumption is that molecular 4 evolution is due primarily to neutral mutations that randomly drift to fixation in a population, resulting in nucleotide substitutions (13). This assumption is consistent with theory and data demonstrating that deleterious mutations have only a negligible chance of becoming fixed in a population because of purifying selection (14), and that favorable mutations occur very rarely (15). Under this assumption, the rate of nucleotide substitution is equal to the neutral mutation rate and is independent of population size (13). The second assumption is that point mutations, and therefore substitutions, occur at a rate proportional to B. This is because most mutations are due to free radicals or replication errors, and rates of free radical production and cell division are both consequences of metabolism. Together, these two assumptions imply that the nucleotide substitution rate α, defined as the number of substitutions per site per unit time, varies with body size and temperature as where f is the proportion of point mutations that are selectively neutral, and ν is the number of point mutations per site per unit of metabolic energy expended by a unit mass of tissue (g mutations site -1 J -1 ). Thus, the product fν is the neutral mutation rate per unit mass-specific metabolic energy and -following Kimura's neutral theory -the substitution rate. If the body size and temperature-dependence of substitution rate is controlled by B, then fv is predicted to be a constant independent of M and T.
Consequently, Eq. 2 predicts the existence of a molecular clock that "ticks" at a constant rate per unit mass-specific metabolic energy rather than per unit time. On average, a 5 certain quantity of metabolic energy transformation within a given mass of tissue causes a substitution in a given gene regardless of body size, temperature, or taxon. Equation 2 therefore predicts a 100,000-fold increase in substitution rates across the biological size range (~10 8 g whales to ~10 -12 g microbes), and a 40-fold increase in substitution rates across the biological temperature range (~ 0°-40°C).
Rearranging terms in Eq. 2 and taking logarithms yields: where C = ln(fνb o ).

Model Predictions
Equations 3 and 4 lead to three explicit predictions. First, the logarithm of mass-corrected substitution rates should be linear functions of 1/kT with a slope of approximately -0.60 to -0.70 eV (Eq. 3), reflecting the activation energy of aerobic metabolism, E. Second, the logarithm of temperature-corrected substitution rates should be linear functions of lnM with slopes of approximately -1/4 (Eq. 4), reflecting the allometric scaling of massspecific metabolic rate (5). Third, if these first two predictions hold then, for a given gene, the number of substitutions per site per unit mass-specific metabolic energy, fν, should be approximately invariant across taxa. 6

Calculation of substitution rates
Estimated rates of mitochondrial and nuclear DNA divergence, D, were compiled for animals representing all major taxonomic groups (e.g., invertebrates, fish, amphibians, reptiles, birds, and mammals) listed in Appendices 1 and 2, respectively. protein-coding DNA sequences from 5,669 nuclear genes and 326 mammal species (Appendix 2). Times of divergence, τ in Mya, were independently estimated using paleontological data (e.g., fossil records, geological events), and varied from 0.  Mya for mitochondrial data, and 5.5-56.5 Mya for nuclear data (Appendices 1-2).
Substitution rates were then calculated as α = D/2τ. While not all sources used the same mathematical model to estimate D in mitochondrial genomes, variation due to differences in methodology (17) is small compared to the predicted effects of body size and temperature.

Body size and temperature estimates
The formula for estimating substitution rate (α = D/2τ) is actually an average for two descendent lineages over the time period τ that may differ in body mass. To account for differences in body mass between the two descendant lineages, we take the "quarterpower average", which controls for the greater influence of the smaller lineage on the calculated substitution rate (Appendix 3). Body temperatures of endothermic birds and mammals were estimated from the literature and varied between ~35-40ºC. Body temperatures of ectotherms were estimated as the mean annual ambient temperature where the organisms presently occur. This assumes that extant ectotherms are approximately in thermal equilibrium with their environment, and that they occur in a similar thermal environment as their ancestors.

Assessing independent effects of body mass and temperature
Body mass is positively correlated with body temperature in the data considered here because the largest animals we considered are all endothermic. It is therefore necessary to assess the independent effects of mass and temperature on substitution rates.
We do so for each molecular clock shown in Figs. 1a-d and 2a-d using a multiple linear regression model of the form: ln(α) = a*(1/kT) + b*ln( M) + c, where 1/kT and ln(M) are the independent variables and ln(α) is the dependent variable. Fitting linear models of this form, and then performing a Type III analysis of variance (ANOVA) on the resulting models, we find that the P-values for both the body mass and temperature terms are both statistically significant (P < 0.01) for all models except the cytochrome-b model of overall substitution rate. We use Type III ANOVA rather than Type I because the hypotheses tested did not depend on the ordering of effects in the models.
Estimating divergence dates 8 We estimated divergence times using all of the substitution rate data listed in Appendix 2, and fit an ordinary least-squares regression model of the form D*M -1/4 = 0.029τ, where D is the divergence between pairs of mammalian taxa (16), M is the quarter-power average of mass in g (see below), and τ is the fossil-estimated divergence date in Mya (Appendix 2). Clock-estimated dates of divergence, τ, were then calculated using this model for 3 pairs of taxa based on their respective values of D and M.

Results and Discussion
Data support each of the model's three predictions. First, the logarithm of masscorrected substitution rate is a linear function of inverse absolute temperature for all four molecular clocks (Fig. 1a-d). The linear regression models account for 54-65% of the variation in substitution rates among diverse organisms, including endotherms (body temperatures of ~35-40°C), and ectotherms from a broad range of thermal environments (~0-30°C). The slopes of these lines are all close to the predicted value of -0.66 eV (Table 1, see Methods). Thus, nucleotide substitution rates are strongly temperaturedependent contrary to recent reports (2), and, this dependence is predicted by our model using the average activation energy of metabolism. Second, log-log plots of temperature-  Table 1).
Substitution rates therefore show the same M -1/4 allometric scaling as mass-specific metabolic rate, B. Third, both endotherms and ectotherms (vertebrates and invertebrates) fall on the same lines in these relationships, supporting the prediction that fν is approximately invariant across taxa for a given gene. These results build on previous 9 work showing correlations of substitution rate to body size by showing that all animals fall on a single line that is predicted by our model. Note that this model quantifies the combined effects of body size and temperature. Analyses that consider only one of these variables separately explain much less of the observed variation in substitution rates (Table 2).
Still further support for the predicted mass-dependence of molecular evolution (prediction 2) comes from analysis of an extensive new data set on rates of synonymous substitutions in mammalian nuclear genomes (Appendix 2, see Methods). A log-log plot of substitution rate versus body mass for these data also gives a straight line with a slope close to the predicted value of -1/4 (-0.21, 95% C.I.: -0.18 to -0.23; Fig. 3).
The fact that the model predic ts empirically observed substitution rates supports the hypothesis that there is a direct relationship between the rate of energy transformation Differences in the fitted intercepts, and therefore fv, among genes, genomes, and types of substitutions may reflect the influence of other factors in addition to body size and temperature. For examp le, f is known to vary from near 1 for synonymous codon sites and non-coding regions to near 0 for non-synonymous sites, and v differs between mitochondrial and nuclear genomes (17). The model can incorporate these and other possible sources of variation. In Table 1, the fitted intercepts for mtDNA, rRNA, and cytb are all approximately 26.5. The intercept for cyt-b transversions is lower (25.15), and that for silent nuclear substitutions is lower still (23.70). These differences are consistent with current theory and data finding lower rates of transversions than transitions, and lower overall rates of mutation in nuclear than in mitochondrial genomes (17). Mya). Our model helps to reconcile these discrepancies by incorporating the effects of body size ( Fig. 4; we corrected only for mass, because mammals have similar body temperatures). Note that when comparing pairs of taxa that differ substantially in body size, it is necessary to take the "quarter-power average" of mass to account for the greater influence of the smaller taxon (see Appendix 3). Indeed, an unexpected consequence of this work is a possible explanation for the inevitable dominance of smaller organisms in the evolutionary process. As a second example, we show that the "hominoid slowdown hypothesis", which proposed that rates of molecular evolution have slowed in hominoids since their split from Old World monkeys (18), might also be explained from this work.

Based on differences in average body mass between extant hominoids (50 kg) and Old
World monkeys (7 kg), our model predicts a ~0.6-fold slowdown (= (7 kg/50 kg) 1/4 ), close to the estimated 0.7 (ref. (18)). For the third example, we show how differences in temperature may account for the nearly four-fold discrepancy between a molecular and geological estimate of the age of notothenioid antarctic fishes (19) (11 vs. 38 Mya).
Assuming that the temperate-zone ectotherms used to calibrate the clock occurred at ~15°C, whereas the notothenioid fishes occurred at ~0°C, our model appears to reconcile this discrepancy (e -E/k(273+15) /e -E/k(273+0) ≈ 4). These three examples illustrate how calibrating molecular clocks for body size and temperature may provide important new insights into evolutionary history. Because plants and microbes show the same body sizeand temperature-dependence for metabolic rate as animals (6), it will be interesting to see if Eq. 2 applies to these organisms.
These results may also have broader implications for understanding the factors controlling the overall rate of evolution. The central role of metabolic rate in controlling biological rate processes implies that a molecular clock also governs evolutionary processes that occur at higher levels of biological organization where the neutral molecular theory does not apply. The rate and direction of phenotypic evolution is ultimately dependent on the somewhat unpredictable action of natural selection.
However, the overall rate of evolution is ultimately constrained by the turnover rate of individuals in populations, as reflected in generation time, and the genetic variation among individuals, as reflected in mutation rate (7,14). Both of these rates are proportional to metabolic rate, so Eq. 1 may also predict the effects of body size and temperature on overall rates of genotypic and phenotypic change. Such predictions would 12 be consistent with general macroevolutionary patterns showing that most higher taxonomic groups originate in the tropics (20), that speciatio n rates increase from the poles to the equator (21,22), that biodiversity is highest in the tropics (11), and that smaller organisms evolve faster and are more diverse than larger organisms (23).