Probabilistic cellular automata and competition across tropic levels
This thesis investigates a resource driven probabilistic cellular automata (PCA) model of plant competition in terms of local interactions, spatial distributions, and invasion. The model also incorporates herbivores and carnivores and examines their effect on plant populations and community structure. Comparisons are drawn between the model, field studies and other mathematical models. Chapter 1 provides a background of relevant concepts from plants and animal ecology, details a number of mathematical models used in this field and describes the model relevant models and results in the literature. It concludes with a comparison of the features of the most germane models and field studies. Chapter 2 primarily focuses on plants, argues for the model we have chosen, recaptures previous results which are similar to some natural phenomena, and makes a preliminary investigation of community behaviour and disturbance. It then describes the effect of introducing biomass for plants on species behaviour, and their spatial distributions. Chapter 3 deals with competition between different species, and aspects of invasion. Coexistence between functionally different plants can occur, join count statistics and measures for patch location on the torus are developed and applied. Chapter 4 derives a generalised probabilistic model for ruderal monocultures, finds numerical solutions for these and investigates models for vegetatively growing species of plants. Chapter 5 examines the population effects of herbivory (i.e. importance of spatial correlation of disturbance) and analogies to competitor-stress tolerator-ruderal (CSR) primary plant types, as well as plant successional rates and factors affecting community composition. Equilibrium species composition corresponded to CSR theory when plant immigration was introduced. Chapter 6 investigates the basic effects of carnivory, and discusses parallels between probabilistic cellular automata and field studies.