Numerical Analysis of Ordinary Differential Equations of Ecological Competing Species Across Diverse Environments

Abstract

In a geographical region, species have their range margins (i.e., the geographic boundaries where species can be found). Several species distribution models have shown that environmental factors (i.e., abiotic factors) and species interactions (i.e., biotic interactions) are responsible for shaping the distributions of species. Yet, most of the models often focus on one of these factors and ignore their joint effects. Consequently, predicting which species will exist and at what range margins is a challenge in ecology. Thus, in this paper, the combined influences of these ecological factors on multi-species community structures are studied. An ordinary differential equations (ODE) model is employed to study multi-species competition interactions across diverse environments. The model is numerically analysed for the range margins of the species and threshold values of competition strength which leads to the presence-absence of species. It is observed that the range margins are influenced by competition between species combined with environmental factors and the threshold values of competition strength correspond to transcritical bifurcation. Depending on the species’ competition strengths, the model exhibits coexistence and exclusion of species, mediated by weak and aggressive biotic interactions, respectively. It is observed that ecologically similar species competitively affect each other more than dissimilar species.