Browsing by Author "Rabel, Hayden Daniel"

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    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
    (Massey University, 2023) Rabel, Hayden Daniel
    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; https://hdrab127.github.io/modskurt/) 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.