seasonal influence on age-structured invasive species with yearly generation

TL;DR

This study models how seasonal reproductive cycles and age structure affect the invasion speed of species, revealing that delays and seasonal timing significantly influence propagation dynamics.

Contribution

It introduces a reaction-diffusion model with seasonal delays and nonlocal responses, providing new insights into invasion speeds in age-structured, seasonal environments.

Findings

Time delay reduces invasion speed.

Season without juveniles is optimal to slow invasion.

Invasion speed increases with the square root of diffusion rate.

Abstract

How do seasonal successions influence the propagation dynamics of an age-structured invasive species? We investigate this problem by considering the scenario that the offsprings are reproduced in spring and then reach maturation in fall within the same year. For this purpose, a reaction-diffusion system is proposed, with yearly periodic time delay and spatially nonlocal response caused by the periodic developmental process. By appealing to the recently developed dynamical system theories, we obtain the invasion speed $c^*$ and its coincidence with the minimal speed of time periodic traveling waves. The characterizations of $c^*$ suggest that (i) time delay decreases the speed and its periodicity may further do so; (ii) the optimal time to slow down the invasion is the season without juveniles; (iii) the speed increases to infinity with the same order as the square root of the diffusion rate.