Steady-state analysis of structured population models

Diekmann O, Gyllenberg M, & Metz JAJ (2003). Steady-state analysis of structured population models. Theoretical Population Biology 63 (4): 309-338. DOI:10.1016/S0040-5809(02)00058-8.

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Abstract

Our systematic formulation of nonlinear population models is based on the notion of the environmental condition. The defining property of the environmental condition is that individuals are independent of one another (and hence equations are linear) when this condition is prescribed (in principle as an arbitrary function of time, but when focussing on steady states we shall restrict to constant functions). The steady-state problem has two components: (i) the environmental condition should be such that the existing populations do neither grow nor decline; (ii) a feedback consistency condition relating the environmental condition to the community/population size and composition should hold. In this paper we develop, justify and analyse basic formalism under the assumption that individuals can be born in only finitely many possible states and that the environmental condition is fully characterized by finitely many numbers. The theory is illustrated by many examples. In addition to various simple toy models introduced for explanation purposes, these include a detailed elaboration of a cannibalism model and a general treatment of how genetic and physiological structure should be combined in a single model.

Item Type: Article
Uncontrolled Keywords: Population dynamics; Physiological structure; Nonlinear; Feedback via the environment; Deterministic at population level; Cannibalism; Finitely many states at birth; Population genetics; Adaptive dynamics; Competitive exclusion
Research Programs: Adaptive Dynamics Network (ADN)
Bibliographic Reference: Theoretical Population Biology; 63(4):309-338 (June 2003) (Published online 26 March 2003)
Depositing User: IIASA Import
Date Deposited: 15 Jan 2016 02:15
Last Modified: 25 Feb 2016 09:28
URI: http://pure.iiasa.ac.at/6827

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