Estimating Large Carnivore population using Mixture Distributions
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Context. In order to manage any animal species well, the knowledge and understanding of how abundant they are in their habitats and their spread around the same habitat ought to be as accurate as possible. However, this is not easy given the nature of large carnivores being nocturnal and their poor relationship with human beings. Aims. The main objective of the project is to estimate accurately the current population density and total of Tsavo National Park in terms of Lions and other large carnivores using playback recordings as the main method of luring them to be counted. Methods. Applying mixing distributions to construct a distribution for the number of counts. Justify the use of Bayesian methods to by pass mathematical intractability of many mixtures arising from natural and biological processes. Construct an algorithm for estimating the various parameters of the model(s) by MCMC process in Win- BUGS. Compare lion densities and total counts by habitat.Key results. A model for estimating the number of lions in Tsavo was constructed as an MCMC algorithm in WinBUGS after it was evident that constructing a mathematically tractable equations following the conditions available was not possible. This served to both help estimate the lion density and justify the use of Bayesian methods. The model produced consistent results for parameter estimates making it the best alternative for evaluating the population density under the prevailing conditions. Conclusions. Bayesian methods as implemented with MCMC algorithm provides the best alternative approach to parameter estimation especially in cases where the exact distributions are not known but their general characteristic behaviors are available as was the case here. Implications. Provided the general characteristics of a phenomenon is known, MCMC sampling can be effectively used to estimate the best possible parameters. However, this needs to be checked if it is in agreement with the nearest available mathematically tractable model equations and be used as reference points.. . .
University of Nairobi
A Thesis Submitted to School of Mathematics, University of Nairobi in Partial Fulfillment of the Requirements for the Degree of Masters of Science in Biometry.
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