Combined effect of successive competition periods on population dynamics

TL;DR

This paper models how successive competition periods with different resource competition types affect population dynamics, revealing complex interactions and stability outcomes depending on competition order.

Contribution

It introduces a mathematical framework using transition matrices to analyze the combined effects of successive competition types on populations.

Findings

Results depend on the order of competition types, especially for scramble and contest.

Stability properties of population models are influenced by the sequence of competition periods.

The framework extends to more than two successive competition periods.

Abstract

This study investigates the effect of competition between individuals on population dynamics when they compete for different resources during different seasons or during different growth stages. Individuals are assumed to compete for a single resource during each of these periods according to one of the following competition types: scramble, contest, or an intermediate between the two. The effect of two successive competition periods is determined to be expressed by simple relations on products of two "transition matrices" for various sets of competition types for the two periods. In particular, for the scramble and contest competition combination, results vary widely depending on the order of the two competition types. Furthermore, the stability properties of derived population models as well as the effect of more than two successive competition periods are discussed.