Spatiotemporal dynamics and the principle of competitive exclusion in community

Giricheva E.E., Abakumov A.I.
 pdf (9973K)  / List of references

Execution or violation of the principle of competitive exclusion in communities is the subject of many studies. The principle of competitive exclusion means that coexistence of species in community is impossible if the number of species exceeds the number of controlling mutually independent factors. At that time there are many examples displaying the violations of this principle in the natural systems. The explanations for this paradox vary from inexact identification of the set of factors to various types of spatial and temporal heterogeneities. One of the factors breaking the principle of competitive exclusion is intraspecific competition. This study holds the model of community with two species and one influencing factor with density-dependent mortality and spatial heterogeneity. For such models possibility of the existence of stable equilibrium is proved in case of spatial homogeneity and negative effect of the species on the factor. Our purpose is analysis of possible variants of dynamics of the system with spatial heterogeneity under the various directions of the species effect on the influencing factor. Numerical analysis showed that there is stable coexistence of the species agreed with homogenous spatial distributions of the species if the species effects on the influencing factor are negative. Density-dependent mortality and spatial heterogeneity lead to violation of the principle of competitive exclusion when equilibriums are Turing unstable. In this case stable spatial heterogeneous patterns can arise. It is shown that Turing instability is possible if at least one of the species effects is positive. Model nonlinearity and spatial heterogeneity cause violation of the principle of competitive exclusion in terms of both stable spatial homogenous states and quasistable spatial heterogeneous patterns.

Keywords: community, species composition, mathematical model, factor, Turing instability
Citation in English: Giricheva E.E., Abakumov A.I. Spatiotemporal dynamics and the principle of competitive exclusion in community // Computer Research and Modeling, 2017, vol. 9, no. 5, pp. 815-824
Citation in English: Giricheva E.E., Abakumov A.I. Spatiotemporal dynamics and the principle of competitive exclusion in community // Computer Research and Modeling, 2017, vol. 9, no. 5, pp. 815-824
DOI: 10.20537/2076-7633-2017-9-5-815-824
URL: http://crm-en.ics.org.ru/journal/article/2625/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.
Views (last year): 11.

Indexed in Scopus

Full-text version of the journal is also available on the web site of the scientific electronic library eLIBRARY.RU

The journal is included in the Russian Science Citation Index

The journal is included in the RSCI

International Interdisciplinary Conference "Mathematics. Computing. Education"

Copyright © 2009–2024 Institute of Computer Science