Discrete-time dynamics of structured populations via Feller kernels

Horst R. Thieme

doi:10.3934/dcdsb.2021082

Article Contents

2022, Volume 27, Issue 2: 1091-1119. Doi: 10.3934/dcdsb.2021082

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Discrete-time dynamics of structured populations via Feller kernels

Horst R. Thieme

School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287-1804, USA

Received: August 2020

Revised: January 2021

Early access: March 2021

Published: February 2022

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Abstract

Feller kernels are a concise means to formalize individual structural transitions in a structured discrete-time population model. An iteroparous populations (in which generations overlap) is considered where different kernels model the structural transitions for neonates and for older individuals. Other Feller kernels are used to model competition between individuals. The spectral radius of a suitable Feller kernel is established as basic turnover number that acts as threshold between population extinction and population persistence. If the basic turnover number exceeds one, the population shows various degrees of persistence that depend on the irreducibility and other properties of the transition kernels.

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Mathematics Subject Classification: Primary: 92D25, 47B65, 47G10, 47H07, 47J25; Secondary: 28C15, 47N60.

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