Effective carrying capacity and analytical solution of a particular case of the Richards-like two-species population dynamics model

TL;DR

This paper analytically solves a generalized two-species population model for amensalism and commensalism, revealing the relationship between effective carrying capacity and extrinsic growth factors, especially in the Gompertz model.

Contribution

It provides an analytical solution for specific ecological interactions in a generalized two-species model and clarifies the link between carrying capacity and growth factors.

Findings

Analytical solutions for amensalism and commensalism models.

Equivalence between effective carrying capacity and extrinsic growth factor in the Gompertz model.

Insights into sigmoid growth curves and population dynamics.

Abstract

We consider a generalized two-species population dynamic model and analytically solve it for the amensalism and commensalism ecological interactions. These two-species models can be simplified to a one-species model with a time dependent extrinsic growth factor. With a one-species model with an effective carrying capacity one is able to retrieve the steady state solutions of the previous one-species model. The equivalence obtained between the effective carrying capacity and the extrinsic growth factor is complete only for a particular case, the Gompertz model. Here we unveil important aspects of sigmoid growth curves, which are relevant to growth processes and population dynamics.