How many species have mass M?

TL;DR

This paper introduces an analytical model explaining the distribution of species by body mass, accounting for evolutionary and extinction dynamics, and validates it with extensive data on mammals and birds.

Contribution

It presents a simplified cladogenetic diffusion model that predicts species mass distributions and explains the asymmetry observed in empirical data.

Findings

Model accurately fits mammal and bird mass data

Tradeoff between Cope's rule and extinction risk is essential

Predictions made about evolution of avian species masses

Abstract

Within large taxonomic assemblages, the number of species with adult body mass M is characterized by a broad but asymmetric distribution, with the largest mass being orders of magnitude larger than the typical mass. This canonical shape can be explained by cladogenetic diffusion that is bounded below by a hard limit on viable species mass and above by extinction risks that increase weakly with mass. Here we introduce and analytically solve a simplified cladogenetic diffusion model. When appropriately parameterized, the diffusion-reaction equation predicts mass distributions that are in good agreement with data on 4002 terrestrial mammal from the late Quaternary and 8617 extant bird species. Under this model, we show that a specific tradeoff between the strength of within-lineage drift toward larger masses (Cope's rule) and the increased risk of extinction from increased mass is necessary to produce realistic mass distributions for both taxa. We then make several predictions about the evolution of avian species masses.