A MODEL FOR TROPHIC INTERACTION

TLDR

A nonlinear feeding rate function that incorporates feeding saturation and intraspecific consumer interference is used to model material or energy transfer between trophic levels, and it aligns with recent experimental data on feeding rates. The study aims to analyze the mathematical implications of a trophic interaction model using this nonlinear feeding rate function. The authors conduct equilibrium and stability analyses on the model. The analyses reveal that increasing maximum feeding rate can, under certain circumstances, reduce consumer populations, that mutual interference among consumers is a major stabilizing factor, and that realistic consumer‑resource models can be globally stable without obeying Kolmogorov's criteria.

Abstract

A nonlinear function general enough to include the effects of feeding saturation and intraspecific consumer interference is used to represent the transfer of material or energy from one trophic level to another. The function agrees with some recent experimental data on feeding rates. A model using this feeding rate function is subjected to equilibrium and stability analyses to ascertain its mathematical implications. The analyses lead to several observations; for example, increases in maximum feeding rate may, under certain circum- stances, result in decreases in consumer population and mutual interference between consumers is a major stabilizing factor in a nonlinear system. The analyses also suggest that realistic classes of consumer-resource models exist which do not obey Kolmogorov's Criteria but are nevertheless globally stable.