Effects of stochastic population fluctuations in two models of biological macroevolution

TL;DR

This paper investigates how stochastic population fluctuations influence long-term evolutionary dynamics in two macroevolution models, revealing that noise can induce intermittent behavior and 1/f fluctuations, affecting diversity and population sizes.

Contribution

It introduces stochastic noise into macroevolution models and analyzes their impact on diversity, population sizes, and spectral properties, highlighting the significance of fluctuations.

Findings

Strong noise induces intermittent behavior and 1/f fluctuations.

Different models exhibit distinct spectral densities in noiseless limit.

Stochastic fluctuations significantly affect long-term evolutionary dynamics.

Abstract

Two mathematical models of macroevolution are studied. These models have population dynamics at the species level, and mutations and extinction of species are also included. The population dynamics are updated by difference equations with stochastic noise terms that characterize population fluctuations. The effects of the stochastic population fluctuations on diversity and total population sizes on evolutionary time scales are studied. In one model, species can make either predator-prey, mutualistic, or competitive interactions, while the other model allows only predator-prey interactions. When the noise in the population dynamics is strong enough, both models show intermittent behavior and their power spectral densities show approximate $1/f$ fluctuations. In the noiseless limit, the two models have different power spectral densities. For the predator-prey model, $1/f^2$ fluctuations appears, indicating random-walk like behavior, while the other model still shows $1/f$ noise. These results indicate that stochastic population fluctuations may significantly affect long-time evolutionary dynamics.