Multiple extinction routes in stochastic population models

TL;DR

This paper analyzes multiple extinction pathways in stochastic predator-prey models, predicting the most probable extinction routes and proposing a simplified three-state model for population dynamics.

Contribution

It introduces a framework to compare extinction routes and predicts the dominant pathway in stochastic multi-population systems.

Findings

Predominant extinction route depends on initial conditions and parameters.

A three-state master equation effectively models coexistence and extinction probabilities.

Predicted most likely extinction path aligns with stochastic simulations.

Abstract

Isolated populations ultimately go extinct because of the intrinsic noise of elementary processes. In multi-population systems extinction of a population may occur via more than one route. We investigate this generic situation in a simple predator-prey (or infected-susceptible) model. The predator and prey populations may coexist for a long time but ultimately both go extinct. In the first extinction route the predators go extinct first, whereas the prey thrive for a long time and then also go extinct. In the second route the prey go extinct first causing a rapid extinction of the predators. Assuming large sub-population sizes in the coexistence state, we compare the probabilities of each of the two extinction routes and predict the most likely path of the sub-populations to extinction. We also suggest an effective three-state master equation for the probabilities to observe the coexistence state, the predator-free state and the empty state.