Multi-species functional response models are required to model the predation of generalist preda- tors, which consume more than one prey species. In chapter 2, a new model for the multi-species functional response is presented. This model can describe generalist predators that exhibit func- tional responses of Holling type II to some of their prey and of type III to other prey. In chapter 3, I review some of the theoretical distinctions between Bayesian and frequentist statistics and show how Bayesian statistics are particularly well-suited for the fitting of functional response models because uncertainty can be represented comprehensively. In chapters 4 and 5, the multi- species functional response model is fitted to field data on two generalist predators: the hen harrier Circus cyaneus and the harp seal Phoca groenlandica. I am not aware of any previous Bayesian model of the multi-species functional response that has been fitted to field data. The hen harrier's functional response fitted in chapter 4 is strongly sigmoidal to the densities of red grouse Lagopus lagopus scoticus, but no type III shape was detected in the response to the two main prey species, field vole Microtus agrestis and meadow pipit Anthus pratensis. The impact of using Bayesian or frequentist models on the resulting functional response is discussed. In chapter 5, no functional response could be fitted to the data on harp seal predation. Possible reasons are discussed, including poor data quality or a lack of relevance of the available data for informing a behavioural functional response model. I conclude with a comparison of the role that functional responses play in behavioural, population and community ecology and emphasise the need for further research into unifying these different approaches to understanding predation with particular reference to predator movement. In an appendix, I evaluate the possibility of using a functional response for inferring the abun- dances of prey species from performance indicators of generalist predators feeding on these prey. I argue that this approach may be futile in general, because a generalist predator's energy intake does not depend on the density of any single of its prey, so that the possibly unknown densities of all prey need to be taken into account.

This study considers the dynamical interaction of two predatory carnivores (Lions (Panthera leo) and Spotted Hyaenas (Crocuta crocuta)) and three of their common prey (Buffalo (Syncerus caffer), Warthog (Phacochoerus africanus) and Kudu (Tragelaphus strepsiceros)). The dependence on spatial structure of species’ interaction stimulated the author to formulate reaction-diffusion models to explain the dynamics of predator-prey relationships in ecology. These models were used to predict and explain the effect of threshold populations, predator additional food and prey refuge on the general species’ dynamics. Vital parameters that model additional food to predators, prey refuge and population thresholds were given due attention in the analyses. The stability of a predator-prey model for an ecosystem faced with a prey out-flux which is analogous to and modelled as an Allee effect was investigated. The results highlight the bounds for the conversion efficiency of prey biomass to predator biomass (fertility gain) for which stability of the three species ecosystem model can be attained. Global stability analysis results showed that the prey (warthog) population density should exceed the sum of its carrying capacity and threshold value minus its equilibrium value i.e., W >(Kw + $) −W . This result shows that the warthog’s equilibrium population density is bounded above by population thresholds, i.e., W < (Kw+$). Besides showing the occurrence under parameter space of the so-called paradox of enrichment, early indicators of chaos can also be deduced. In addition, numerical results revealed stable oscillatory behaviour and stable spirals of the species as predator fertility rate, mortality rate and prey threshold were varied. The stabilising effect of prey refuge due to variations in predator fertility and proportion of prey in the refuge was studied. Formulation and analysis of a robust mathematical model for two predators having an overlapping dietary niche were also done. The Beddington-DeAngelis functional and numerical responses which are relevant in addressing the Principle of Competitive Exclusion as species interact were incorporated in the model. The stabilizing effect of additional food in relation to the relative diffusivity D, and wave number k, was investigated. Stability, dissipativity, permanence, persistence and periodicity of the model were studied using the routine and limit cycle perturbation methods. The periodic solutions (b 1 and b 3), which influence the dispersal rate (') of the interacting species, have been shown to be controlled by the wave number. For stability, and in order to overcome predator natural mortality, the nutritional value of predator additional food has been shown to be of high quality that can enhance predator fertility gain. The threshold relationships between various ecosystem parameters and the carrying capacity of the game park for the prey species were also deduced to ensure ecosystem persistence. Besides revealing irregular periodic travelling wave behaviour due to predator interference, numerical results also show oscillatory temporal dynamics resulting from additional food supplements combined with high predation rates.

Erratum pages inserted onto front end papers. / Bibliography: leaves 226-244. / vi, 244 leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / This thesis developed mathematical models of commercially exploited fish populations, addressing the question of how to harvest a predator-prey metapopulation. Optimal harvesting strategies are found using dynamic programming and Lagrange multipliers. Rules about harvesting source/sink populations, more/less vulnerable prey subpopulations and more/less efficient predator subpopulations are explored. Strategies for harvesting critical prey subpopulations are suggested. / Thesis (Ph.D.)--University of Adelaide, Dept. of Applied Mathematics, 2000?

Severe declines in the number of some songbirds over the last 40 years have caused heated debate amongst interested parties. Many factors have been suggested as possible causes for these declines, including an increase in the abundance and distribution of an avian predator, the Eurasian sparrowhawk Accipiter nisus. To test for evidence for a predator effect on the abundance of its prey, we analyse data on 10 species visiting garden bird feeding stations monitored by the British Trust for Ornithology in relation to the abundance of sparrowhawks. We apply Bayesian hierarchical models to data relating to averaged maximum weekly counts from a garden bird monitoring survey. These data are essentially continuous, bounded below by zero, but for many species show a marked spike at zero that many standard distributions would not be able to account for. We use the Tweedie distributions, which for certain areas of parameter space relate to continuous nonnegative distributions with a discrete probability mass at zero, and are hence able to deal with the shape of the empirical distributions of the data. The methods developed in this thesis begin by modelling single prey species independently with an avian predator as a covariate, using MCMC methods to explore parameter and model spaces. This model is then extended to a multiple-prey species model, testing for interactions between species as well as synchrony in their response to environmental factors and unobserved variation. Finally we use a relatively new methodological framework, namely the SPDE approach in the INLA framework, to fit a multi-species spatio-temporal model to the ecological data. The results from the analyses are consistent with the hypothesis that sparrowhawks are suppressing the numbers of some species of birds visiting garden feeding stations. Only the species most susceptible to sparrowhawk predation seem to be affected.