Bayesian Modeling for Annual Abundance in Ecological Communities Incorporating Zero-Inflation

Abstract

In this dissertation, we present models that are developed to accommodate challenges and advance insights from modeling ecological abundance data. All the models presented in this work are fit within a Bayesian hierarchical framework. Species distribution models (SDMs) relate observed species abundance or occurrence data to geographically referenced environmental variables. In this dissertation, we focus mainly on multi-species or joint SDMs to incorporate the dependence between multiple species. We provide a dynamic mechanistic modeling framework that combines several biological and physiological processes that are known to operate within a species community. More specifically, we include the processes of local species growth as well as species movement within a geographic region. The mechanisms are represented as parameters to be estimated in our model. As an illustrative example, we first apply our model to the citizen science dataset eBird. We then provide an application to fisheries data from the Northeast Fisheries Science Center that develops a richer model for species redistribution that incorporates time-varying environmental covariates.As ecological data often exhibit a high incidence of zeros, we also develop models that address the issue of zero-inflation. While there is a wealth of literature on zero-inflated models for count data, we focus on data with continuous support. The familiar Tobit model accommodates positive continuous data with an excess of zeros, but does not allow for multiple interpretations of a zero as the also-familiar zero-inflated Poisson model does. We address this gap in the literature by first providing spatial and non-spatial zero-inflated Beta (ZIB) regression models for data that lie on the unit interval. We also provide a multivariate zero-inflated Tobit (MVT ZI-Tobit) regression model that can capture dependence between elements at a given observation index at multiple stages of the model. For both the ZIB and MVT ZI-Tobit, we present model comparison metrics for predictive performance that specifically target a model’s ability to capture zeros or dependence between observation elements. We apply our ZIB and MV ZI-Tobit models to percent cover of plant species in the Cape Floristic Region and total basal area of trees using Forest Inventory Analysis data, respectively.