Effect of crowdedness in coexistence and production

Abstract

Sublinear power law patterns of 3/4 scale are observed widely in prey-predator and biomass-production relations [1]. It has been conjectured that it is a phenomenon driven by a crowdedness effect. However, the physical dynamics behind it is not well understood. In this thesis, we will introduce an age-dependant model consistent with the sublinear pattern. A discrete Lotka-Volterra model in a two dimensional domain is described using the model and its numerical simulations are compared to the classic Lotka-Volterra equations. Finally, crowdedness effects in this model are simulated and analyzed. This thesis aims to describe some underlying mechanisms to density dependant effects in biology, as well as showing advantages of using discrete models in computational biology.