Bayesian distributions of species abundance along environmental gradients : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Statistics at Massey University, Albany, New Zealand

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Massey University
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Understanding the relationship between species abundance and environmental conditions is crucial for conservation and management efforts. This thesis presents a novel approach for predicting distributions of species abundance along environmental gradients (DAEG) by refining the parameter space of a nonlinear zero-inflated negative binomial with modskurt mean (NZM) model and utilising Bayesian prior probability. Chapter 2 elucidates the NZM model, highlighting the challenges posed by the intricate nature of parameter estimation due to the model’s complexity. A refined parameter subspace is proposed to address the issue of multimodality in the likelihood surface, enhancing the reliability of predicting DAEGs. Chapter 3 employs Bayesian inference and proposes a prior distribution for the NZM model that increases the ecological structure used in the parameter estimation process and improves the reliability of making realistic predictions. A step-by-step workflow for using the Bayesian implementation is presented and demonstrated with a case study. The thesis includes as a supplement an R package and interactive resources (Appendix A; that enable straightforward fitting of DAEGs using Bayesian NZM models. This work contributes to more accurate predictions of DAEGs, provides a practical tool for ecological research, and promotes effective conservation and management efforts.