Sharp seasonal threshold property for cooperative population dynamics with concave nonlinearities

TL;DR

This paper investigates the existence of a critical duration of unfavorable seasons in periodic biological populations with concave nonlinearities, establishing conditions for a sharp threshold between population persistence and extinction.

Contribution

It provides sufficient conditions for the sharp seasonal threshold property in monotone differential models with concave nonlinearities, extending previous results to higher dimensions.

Findings

Existence of a critical unfavorable season duration for population extinction

Conditions ensuring the sharp seasonal threshold property in any dimension

Application to a two-dimensional insect population model

Abstract

We consider a biological population whose environment varies periodically in time, exhibiting two very different "seasons" : one is favorable and the other one is unfavorable. For monotone differential models with concave nonlinearities, we address the following question: the system's period being fixed, under what conditions does there exist a critical duration for the unfavorable season? By "critical duration" we mean that above some threshold, the population cannot sustain and extincts, while below this threshold, the system converges to a unique periodic and positive solution. We term this a "sharp seasonal threshold property" (SSTP, for short). Building upon a previous result, we obtain sufficient conditions for SSTP in any dimension and apply our criterion to a two-dimensional model featuring juvenile and adult populations of insects.