Computational Approaches to Predator-Prey and Food Web Modelling

Abstract

This thesis considers multiple approaches to the development of mathematical and computational models of food web assembly and simulation. In particular, we study three models of increasing complexity, scope and realism. The first approach concerns simple two-dimensional discrete models representative of a system incorporating both mutation and predation. This conceptual model demonstrates the establishment of a stable two-species ecosystem from a single initial species by means of mutation. It is amenable to mathematical analysis, and we study the population dynamics including hyperchaos and a Neimark-Sacker bifurcation. Second, we undertake a computational study on ten predator phenotypes and ten prey phenotypes arranged on coupled map lattices, with the prey species able to mutate amongst their nearest-neighbours. Whilst the dimensions of the systems under consideration have increased, the number of species and their relationships remain predetermined. Results indicate that the distribution of competition amongst prey is of little significance, provided that intraspecific is stronger than interspecific, and that it is preferable for a predator to adopt a foraging strategy that scales linearly with prey populations if it is the only predator phenotype. In an environment of multiple predator phenotypes, extreme feeding strategies are optimal. In the third case, we reproduce the Webworld model of food web assembly that combines ecological processes with dynamics on the network structure through extinctions and speciation events. We show that the model supports a link-species relationship of 9 neither constant link-density or connectance, and new properties are calculated including clustering coefficients and stability in the sense of community robustness. Finally, we extend this model to a spatially-explicit variant, which features migration of populations between multiple local sites. We study the effects of different schemes and rates of movement on local and global properties of the metacommunity, and consider the distinctions between systems of coupled homogeneous and heterogeneous local environments.

Date of Award	Oct 2018
Original language	English
Supervisor	Mark Mc Cartney (Supervisor) & David Glass (Supervisor)