Abstract/Summary

The spatial-dynamics of animal movement behaviour are still under-studied and remain less understood than desired. Exploration of this phenomenon leads to important economic, ecological and natural-resource management implications. Yet despite the recent advances in technology and scientific methods, questions remain in terms of understating the complexities of movement patterns and robust quantification. Key factors impeding the investigation have been the lack of accurate data and incisive mathematical and quantification models. Animal movement in general, and foraging in particular, are vital characteristics of species which constantly adapt to changes in physical, biological, and social dynamics. Measuring animal movement patterns poses critical questions surrounding specification of appropriate representations of data generation. Accurate methods that identify underlying patterns from incomplete or imprecise raw data are therefore much desired in movement analysis. A better and deeper understanding of the actual heterogeneous patterns of movement can enable more effective management, conservation and development activities. Since the initial identification of a specific pattern termed Lévy flights in foraging animals by Viswanathan et al. (1996, 1999), many later studies have explored this phenomenon. Lévy flight is a special type of random walk derived from the so-called power-law distribution. A vast and diverse variety of foraging animals have been found to exhibit this movement pattern. However, Edwards (2011) overturned previous conclusions surrounding the existence of Lévy flights within a diverse sample of ecological settings, including five species: reindeer in Sweden (Mårell et al. 2002); side-striped jackals in Zimbabwe (Atkinson et al. 2002); microzooplankton (Bartumeus et al. 2003); grey seals (Austin et al. 2004); and humans in the form of fishers (Bertrand et al. 2007; Marchal et al. 2007) and hunter gatherers (Brown et al. 2007). Re-analysing the above data sets using a modern likelihood approach, Edwards found that Lévy flights pattern is not as common a phenomenon as once thought. The overarching aim of this thesis is to contribute to a better understanding of animal foraging movement patterns, and thus inform the improved management of the landscapes in which iii foragers are found. Central to achieving this aim is the testing of the hypothesis that Lévy flight is not a common phenomenon in nature, through the adaptation and application of two robust Bayesian statistical approaches to a number of distinct data sets. The results obtained through Bayesian approaches are compared with previous findings. Methodologically, this thesis employs the Standard Bayesian estimation approach (SBEA) (likelihood-based Bayesian method) and the Approximate Bayesian Computation (ABC) (likelihood-free Bayesian method), to re-analyse three of the original data sets re-analysed by Edwards (2011). These data sets include; (a) Dobe Ju/’hoansi human hunter-gatherers in Botswana and Namibia (Brown et al. 2007) (b) reindeer in Sweden (Mårell et al. 2002) and (c) Dutch beam-trawler fishing boats (Marchal et al. 2007). Standard Bayesian analysis is dependent on the specification of a likelihood function. For more complex models such as those for identifying movement patterns, specifying a likelihood function is computationally difficult. Therefore, the application of a simulation-based likelihood-free ABC method provides additional precision and robustness. Results reveal that irrespective of the species or foraging objective, humans in the form of hunter gathers and fishers, as well as reindeer, exhibit a bounded Lévy flight foraging pattern. This finding disproves and simultaneously improves the previous findings by Edwards (2011) and other original authors. The thesis also finds that foraging patterns evolve with the availability of prey across time, which is in par with earlier studies. In terms of the methodology, comparing the two Bayesian techniques, the thesis concludes that the likelihood-free Bayesian framework is better able to capture the underlying patterns of animal movement compared to the conventional approaches. This is a crucial finding specifically in terms of animal movement exploration where there is a lack of precise and complete data. Rather than simply assume that a Bayesian approach is “better”, in this thesis the robustness and relevance of using Bayesian approaches is then further explored through a number of simulations and applications. First, movement patterns are simulated to ensure that the two Bayesian methods do indeed recover the true movement pattern. Second, one of the datasets used is progressively truncated to determine how sensitive these methods are to the number of data observations. Third, a number of applications of these methods of relevance to resource management are discussed in the thesis, for which improvement and further modifications to Bayesian simulation-based methods allow more efficient and accurate investigations: wildlife iv corridors developed to minimise the negative impacts of fragmented landscapes; and optimal containment of invasive species. In each case, policy makers require improved understanding of how species move and the rate of spread of species, respectively, often when there is little available data.