Stability Analysis of Competing Insect Species for a Single ResourceReport as inadecuate




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Journal of Applied Mathematics - Volume 2014 2014, Article ID 285350, 14 pages -

Research Article

African Insect Science for Food and Health icipe, P.O. Box 30772-00100, Nairobi, Kenya

Department of Mathematics, University of Dar es Salaam, P.O. Box 35062, Dar es Salaam, Tanzania

CHIESA Project, African Insect Science for Food and Health icipe, P.O. Box 30772-00100, Nairobi, Kenya

Unité de Recherche IRD 072, Laboratoire Evolution, Génomes et Spéciation, UPR 9034, 22 CNRS, 91198 Gif-Yvette, France

Université Paris-Sud 11, 91405 Orsay, France

Received 22 February 2014; Accepted 12 June 2014; Published 6 July 2014

Academic Editor: Carlos Conca

Copyright © 2014 Sizah Mwalusepo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The models explore the effects of resource and temperature on competition between insect species. A system of differential equations is proposed and analysed qualitatively using stability theory. A local study of the models is performed around axial, planar, and interior equilibrium points to successively estimate the effect of i one species interacting with a resource, ii two competing species for a single resource, and iii three competing species for a single resource. The local stability analysis of the equilibrium is discussed using Routh-Hurwitz criteria. Numerical simulation of the models is performed to investigate the sensitivity of certain key parameters. The models are used to predict population dynamics in the selected cases studied. The results show that when a single species interacts with a resource, the species will be able to establish and sustain a stable population. However, in competing situation, it is observed that the combinations of three parameters half-saturation, growth rate, and mortality rate determine which species wins for any given resource. Moreover, our results indicate that each species is the superior competitor for the resource for the range of temperature for which it has the lowest equilibrium resource.





Author: Sizah Mwalusepo, Henri E. Z. Tonnang, Estomih S. Massawe, Tino Johansson, and Bruno Pierre Le Ru

Source: https://www.hindawi.com/



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