Evolutionary Model of Species Body Mass Diversification

We present a quantitative model for the biological evolution of species body masses within large groups of related species, e.g., terrestrial mammals, in which body mass $M$ evolves according to branching (speciation), multiplicative diffusion, and an extinction probability that increases logarithmically with mass. We describe this evolution in terms of a convection-diffusion-reaction equation for $\ln M$. The steady-state behavior is in good agreement with empirical data on recent terrestrial mammals, and the time-dependent behavior also agrees with data on extinct mammal species between 95–50 Myr ago.

Figure 1

Steady-state solution of the model for the species body mass distribution and suitably binned empirical data for 4002 recent terrestrial mammals (shown as a normalized histogram with 50 logarithmically spaced bins).

Figure 2

Data on species body mass for 569 North American terrestrial mammals [16] from 95–50 Myr ago. Each horizontal segment represents a species, and end points denote its first and last appearance in the fossil record. The superimposed curve shows the average of $\ln M$ for these species (smoothed with an exponential kernel).

Figure 3

A comparison of our model predictions (dashed line) from Eq. (5) and the mass distributions of extinct North American mammal species (solid line) in nine consecutive time ranges. (To get reasonable results with sparse empirical data, we smooth the distributions with a Gaussian kernel.)

Figure 4

Estimated relation between model time to historical time, indicating that the broadening of the mammalian species mass distribution began approximately 10 Myr before the KP boundary when nonavian dinosaurs became extinct.