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In the analysis of movement patterns of animals, stochastic processes play an important role, providing us with a variety of tools to examine, model and simulate their behaviour. In this thesis we focus on the foraging of specific animals - bumblebees - and analyse experimental data to understand the influence of changes in the bumblebees’ environment on their search flights. Starting with a discussion of main classes of stochastic models useful for the description of foraging animals, we then look at a multitude of environmental factors influencing the dynamics of animals in their search for food. With this background we examine flight data of foraging bumblebees obtained from a laboratory experiment by stochastic analyses. The main point of interest of this analysis is the description, modelling and understanding of the data with respect to the influence of predatory threats on the bumblebee’s foraging search flights. After this detail-oriented view on interactions of bumblebees with food sources and predators in the experimental data, we develop a generalized reorientation model. By extracting the necessary information from the data, we arrive at a generalized correlated random walk foraging model for bumblebee flights, which we discuss and compare to the experimental data via simulations. We finish with a discussion of anomalous fluctuation relations and some results on spectral densities of autocorrelation functions. While this part is not directly related to the analysis of foraging, it concerns a closely related class of stochastic processes described by Langevin equations with non- trivial autocorrelation functions analyse experimental data to understand the influence of changes in the bumblebees’ environment on their search flights. Starting with a discussion of main classes of stochastic models useful for the description of foraging animals, we then look at a multitude of environmental factors influencing the dynamics of animals in their search for food. With this background we examine flight data of foraging bumblebees obtained from a laboratory experiment by stochastic analyses. The main point of interest of this analysis is the description, modelling and understanding of the data with respect to the influence of predatory threats on the bumblebee’s foraging search flights. After this detail-oriented view on interactions of bumblebees with food sources and predators in the experimental data, we develop a generalized reorientation model. By extracting the necessary information from the data, we arrive at a generalized correlated random walk foraging model for bumblebee flights, which we discuss and compare to the experimental data via simulations. We finish with a discussion of anomalous fluctuation relations and some results on spectral densities of autocorrelation functions. While this part is not directly related to the analysis of foraging, it concerns a closely related class of stochastic processes described by Langevin equations with nontrivial autocorrelation functions.

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Individual niche variation is increasingly being demonstrated in animal populations in a wide variety of species and taxa. Niche variation among individuals has important implications for the ecology, evolution and management of animal populations and is a subject of increasing interest. However, despite its widespread occurrence the causes and consequences of individual niche variation remain poorly understood. In this thesis I use the European badger (Meles meles), a well studied species of high ecological interest, as a model system to investigate individual niche variation. In order to achieve this I combine information on individual foraging niches derived via stable isotope analysis (SIA) of badger vibrissae with detailed life history and ecological data from a long-term study population to investigate the incidence, cause and consequence of individual niche variation within badger social groups. First I use the biomarker Rhodamine B to investigate vibrissae growth rates and patterns in badgers and demonstrate that the isotopic composition of a single vibrissa likely reflects diet over several months (Chapter 2). Next I explore the use of SIA as a tool to investigate badger diet, by comparing isotopic patterns to seasonal changes in diet measured using faecal analysis (Chapter 3). My results provide validation that SIA is powerful tool for investigating foraging variation in this species, and suggest that within badger populations substantial dietary variation may occur among individuals. Further investigation of isotopic variation Indicates that individuals within social groups differ markedly and consistently in their isotopic signature, independent of age and sex effects and that in some instances these differences are remarkably consistent across year (Chapter 4).This suggesting long term individual specialisation (Chapter 4). I find that the degree of this individual specialisation, and the relationship between specialisation and body condition is influenced by competition for resources (Chapter 5). Social groups with higher levels of competition exhibit greater specialisation and specialised individuals within these highly competitive environments are in better condition. Finally, I discuss the implications of these results for individual niche variation, for the application of SIA to study this behaviour and for badger ecology generally (Chapter 6). I also outline future directions for further research.

This thesis considers the importance of adding stochasticity to models of optimal foraging behaviour. The problem is divided into two elements, risk and information, which are treated separately. Part One: Risk. The theoretical and empirical results concerning animal preferences in risky situations are reviewed. Animals are known to show both risk-averse and risk-prone preferences over food reward. It is shown, theoretically, that a simple optimality model mimimizing the probability of death due to starvation accounts for at least some of the observed patterns of preference. The model is generalized to consider preference from arbitrary combinations of mean and variance. Three limitations of the model are treated in detail, that is the importance of starvation by "ruin", mind-changing about risk preferences, and energetic carry-over are discussed. The implications and limitations of these models are outlined. Part Two: Information. The theoretical literature is reviewed, and the problem of information is divided into three elements. A simple model of environmental tracking is studied. The model suggests that there is a trade-off between sensitivity to change and the costs of sampling. The model is tested using great tits (Parus major) foraging in an aviary. The trend in sampling was as predicted, but the birds were less sensitive to change than predicted. The problem of patch sampling is critically discussed. The value of sampling is defined, and this definition is used to compare the assumptions of previous models. Three such problems are treated: the importance of variance in the mixing distribution of patch sub-types; the importance of alternative and unambiguous patch types; and the importance of patch depression. It is concluded that previous models have often over-valued sampling. A simple and natural model of partial patch recognition is considered, and is shown to have empirical support. Implications and limitations of these models of information are discussed.

Archaeological research has provided evidence of change in the settlement and subsistence practices of human groups inhabiting the Great Plains throughout the Holocene. A substantial part of this reorganization appears to be tied to concurrent changes affecting local bison populations, a species upon which these groups were uniquely dependant. Although bison are thought to have been strongly affected by the severe climates of the Mid-Holocene, there is an absence of appropriate models from which to interpret data in the archaeological and paleontological records. Nevertheless, new techniques are allowing for the determination of ecological information directly from prehistoric remains. This study uses stable isotope ratios (813C, 8'SN, 8D) in bone collagen to examine the dietary ecology of bison in Southern Saskatchewan during eight distinct time periods spanning the last 9,000 years. Stable isotopes of hydrogen and nitrogen in the tissues of animals relate to aspects of local climate, while stable-carbon isotope values reflect dietary choices. When employed in a comparative fashion, these sources may be used to construct simple models of foraging behaviour.<p> The environmental data developed from this investigation appear to correlate generally with patterns predicted by conventional models of Holocene climate. Nevertheless, at least one period of unexpectedly moderate temperature was identified from a context dating to the and Mid-Holocene. The ecological impact of such an episode may have been significant. In addition, the results of this study suggest that bison diet has a complex relationship with local climate. Changes in plant distribution resulting from variations of temperature and precipitation appear to have less of an impact upon bison consumption patterns than do climatically induced changes in the nutritional quality of vegetation. Nevertheless, during specific time periods characterized by similar climatic regimes, their relative consumption of certain forage species (C3 and C4 plants) does not appear to have been consistent. Such a discrepancy may reflect adaptive differences between bison from distinct time periods, or alternatively, the effects of a climatic difference undetectable by isotopic means. In either case, it would appear that bison of the past may have been subject to significant nutritional stresses that could have caused them to behave in fundamentally different ways from modern populations.