How to Cite: Behera, N., Ashok, P., Singh, M. M., Kumar, M. K., Kumbha, S., Shukla, G., & Saxena, S. (2022). Implementation of the lattice model in the coexistence of species and its potential consequences on environment. International Journal of Health Sciences, 6(S5), 1106–1128. https://doi.org/10.53730/ijhs.v6nS5.8831 International Journal of Health Sciences ISSN 2550-6978 E-ISSN 2550-696X © 2022. Manuscript submitted: 18 March 2022, Manuscript revised: 9 April 2022, Accepted for publication: 27 May 2022 1106 Implementation of the lattice model in the coexistence of species and its potential consequences on environment Narayan Behera Center for Ecological Research, Kyoto University, Otsuka, Kamitanakami-Hirano, Otsu, Shiga 520-2113, Japan and SVYASA University, Jigani, Anekal, Bengaluru, India- 560105 Corresponding author email: nbehera321@gmail.com 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 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