Implementation of the lattice model in the coexistence of species and its potential consequences on environment

Narayan Behera; Prashasti Ashok; M. M. Singh; M. Kartic Kumar; Satyanarayana Kumbha; Gaurav Shukla; Swasti Saxena

doi:10.53730/ijhs.v6nS5.8831

Authors

Narayan Behera
nbehera321@gmail.com
Center for Ecological Research, Kyoto University, Otsuka, Kamitanakami-Hirano, Otsu, Shiga 520-2113, Japan and SVYASA University, Jigani, Anekal, Bengaluru, India- 560105
Prashasti Ashok Department of Geology, Institute of Earth Sciences, Bundelkhand University, Jhansi, India-284128
M. M. Singh Department of Geology, Institute of Earth Sciences, Bundelkhand University, Jhansi, India-284128
M. Kartic Kumar Department of Geomatics Engineering, Wachemo University, Hossana, Ethiopia
Satyanarayana Kumbha Department of Mechanical Engineering, Jigjiga University, Jigjiga-1020 Ethiopia
Gaurav Shukla Department of Civil Engineering, School of Engineering & Technology, Maharishi University of Information Technology (MUIT), Lucknow, India- 226013
Swasti Saxena Sardar Vallabhbhai National Institute of Technology, Surat, India-395007

Keywords:

lattice models, the coexistence of species, Species biodiversity, Conservation, mean-field model, Spatial pattern, Global change

Abstract

The population dynamics of a system of two competing species have been investigated in the mean-field and lattice approximation. The two species are denoted by A and B. Each site of the square lattice is either occupied by an individual or vacant. The two species complete for vacant sites to reproduce. There is a reproduction only to the nearest neighbours. We consider the invasion of a rare species into a population composed of a resident species based on a pair – approximation method in which the dynamics of both average densities and nearest neighbour correlations are considered. The results are then compared with those obtained by the mean-field approximation. Whenspecies B contain intraspecific interaction term, invasion of the rare species A into resident species B becomes easier in lattice structured populations. But the rare species B invading species A is difficult in lattice models in comparison to mean-field approximation. The overall coexistence of species is enhanced in lattice models. These results were verified by simulation on a square lattice although the range of the enhancement of the species coexistence is reduced. This calls for the attention that pair-approximation is an oversimplification of the real situation.

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