Latitudinal gradients of biodiversity and macroevolutionary dynamics are prominent yet poorly understood.

• Abstract
• Model Development
• Results and Discussion
• Methods
• Acknowledgements
• References
• Figures

Biology Articles » Biodiversity » Kinetic effects of temperature on rates of genetic divergence and speciation » Model Development

Model Development

- Kinetic effects of temperature on rates of genetic divergence and speciation

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 temperature-dependence of mass-specific metabolic rate, (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_oM^–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 x 10^–19 J), and k is the Boltzmann constant (8.62 x 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, (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 _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 0–30°C from the poles to the equator (e^–E/k303/e^–E/k273 = 15-fold from 273–303 K). Because g and are both governed by , 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 per-generation basis, dD/d (substitutions·nucleotide^–1·generation^–1), such that

where f₀ 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. 2f₀ >> 8f₊J_ss. 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. 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 population-level 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_sg (D_s⁺)(1/8f₊J_ss) is independent of temperature when Assumptions 1 and 2 are upheld. Given that t_sg 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, D_s (substitutions nucleotide^–1), should be independent of temperature as well:

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 D_s⁺ and D_s, 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 (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 population-level 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 species-extinction 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, (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 (km²), 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 size-J_s populations are genetically diverging from each other at any given time and hence that V_m is higher.