Population density and lifetime of a self-avoiding and annihilating random walker across a square lattice

Abstract

Much work has been done and is being done in modelling various macroecological patterns which persist in different ecological systems. This century, there has been an increase in the use of variations of random walks to design and compare ecological models. In this study, an uncorrelated and isotropic random walk is restricted to be non-intersecting or self-avoiding annihilating. The self-avoidance of the walk was designed to represent resource usage while the annihilation to represent the death process. Each new step of the walker, on the other hand, represents a birthing process. The walk was simulated across a 4 x 4 or 16-node lattice. It was found that prior to extinction time, a steady state in population is achieved and that there is increased frequency of occupation along the lattice edges with the corner sites being most occupied. These observations were correlated–explaining that the stagnation of population growth was a result of walker trapping at the corners which increased occupancy in those sites. Comparison of the model to natural ecological systems and the expanding of the model to various species and lattice sizes are recommended to further the study.