Simple Model of Large Scale Organization in Evolution

TL;DR

This paper introduces a mathematical model for large-scale biological organization, demonstrating how species form genera with size distributions and extinction patterns that align with empirical paleontological data.

Contribution

It presents a simple, analytically tractable model capturing key features of evolutionary dynamics and genus size distributions.

Findings

Genus sizes grow linearly with age.

Extinction events follow a power-law distribution.

Model results match paleontological data.

Abstract

A mathematical model of interacting species filling ecological niches left by the extinction of others is introduced. Species organize themselves into genera of all sizes. The size of a genus on average grows linearly with its age, confirming a general relation between Age and Area proposed by Willis. The ecology exhibits punctuated equilibrium. Analytic and numerical results show that the probability distribution of genera sizes, genera lifetimes, and extinction event sizes are the same power law $P(x) \sim 1/x^2$, consistent with paleontological data.