Discreteness of populations enervates biodiversity in evolution

TL;DR

This paper demonstrates that the intrinsic fluctuations caused by the discreteness of populations lead to exponential decay in biodiversity, highlighting the importance of stochastic effects over deterministic models in ecological systems.

Contribution

It introduces a stochastic framework based on the children's rock-paper-scissors game to show how population discreteness causes biodiversity loss, extending physical dissipation concepts to ecology.

Findings

Biodiversity decays exponentially due to intrinsic fluctuations.

Discreteness-induced fluctuations can cause extinction in ecosystems.

The decay process is analogous to physical dissipation phenomena.

Abstract

Biodiversity widely observed in ecological systems is attributed to the dynamical balance among the competing species. The time-varying populations of the interacting species are often captured rather well by a set of deterministic replicator equations in the evolutionary game theory. However, intrinsic fluctuations arisen from the discreteness of populations lead to stochastic derivations from the smooth evolution trajectories. The role of these fluctuations is shown to be critical at causing extinction and deteriorating the biodiversity of ecosystem. We use children's rock-paper-scissors game to demonstrate how the intrinsic fluctuations arise from the discrete populations and why the biodiversity of the ecosystem decays exponentially, disregarding the detail parameters for competing mechanism and initial distributions. The dissipative trend in biodiversity can be analogized to the gradual erosion of kinetic energy of a moving particle due to air drag or fluid viscosity. The dissipation-fluctuation theorem in statistical physics seals the fate of these originally conserved quantities. This concept in physics can be generalized to scrutinize the errors that might be incurred in the ecological, biological, and quantitative economic modeling for which the ingredients are all discrete in number.