New statistical models for multiple species distributions

<p>With global declines in biodiversity, tools to manage and conserve species are needed.  Single species distribution models (SDMs) are statistical models that can determine key environmental relationships, but they do not allow for species-interactions that may determine which species can co-exist.   Joint Species Distribution Models (JSDMs) extend SDMs using correlation to model interspecies dependencies and interactions.  The aim of my thesis is to improve JSDM models by extending existing models and proposing new approaches that can address issues such as imperfect detection and reporting bias and allow for both spatial and interspecies correlations.</p> <p>Chapter 1 provides a short introduction to this work which outlines the  aims, research questions and contributions of this thesis.  This chapter provides background information to these aims and introduces the  species and species data used in case studies throughout the thesis.  A detailed literature review of current approaches to SDMs and JSDMs can be found in chapter 2 which highlights issues requiring further research for JSDMs. Chapter 2 also overviews the modelling methods used in this thesis.</p> <p>Correlation between species results from  a combination of intrinsic interspecies relationships, common relationships to environmental factors, or spatial correlations.  Chapter 3 investigates an existing multivariate probit model to better understand how the environmental and intrinsic correlations determine the overall correlation between species. It then determines how the latent correlations used in the probit model relate to binary data. Finally, it uses simulations to explore how imperfect detection alters the perception of correlations between species when detection issues are ignored by researchers: it finds the apparent magnitude of correlations between species is reduced.</p>   <p>Chapter 4 proposes an extension to the previous model  to explicitly allow for imperfect detection using a  hierarchical Bayesian model.  Simulation scenarios were used to determine the number of survey replications required to accurately estimate correlation for different probabilities of detection and occupancy. While the model can accurately estimate correlation, estimates can be biased for low probabilities of detection and insufficient survey replications. A model not explicitly accounting for detection but fitted to collapsed data (where species data is summarised over multiple survey replications) made similar parameter estimates. However, it had limited ability to disentangle detection from occupancy and estimate the actual species distribution.</p> <p>Spatial correlation is commonly found in species observation data. Chapter 5 proposes a model that allows for both spatial and interspecies correlations using a multivariate Gaussian process and Bayesian analysis.  The impact of data resolution and number of sites on parameter estimation was determined using simulations which found the model can be adversely affected by course resolution data and low numbers of sites. A case study  using Victorian forest species data compared this model to models allowing for interspecies correlations only and spatial correlations only.  This comparison showed that the multivariate Gaussian model performed the best at predicting species distributions.</p> <p>Species survey data is often only available in limited quantities while presence-only data derived from  museum records  or citizen science initiatives such as eBird is abundant.  However, presence-only data suffers from reporting bias, where human behaviour  influences species observations.  To address this bias, Chapter 6 proposes a data-integration approach based on the multivariate Gaussian process model from  Chapter 5 that combines survey and presence-only data.  The data-integration model demonstrated superior performance compared to presence-only and survey data only models for simulated data and case studies.  Further, a new correlated approach to modelling reporting bias was tested which performed better in the case study than a conventional reporting bias model.</p> <p>In conclusion, the novel JSDMs proposed in this thesis lead to an enhanced understanding of interspecies correlations and better models for joint species distributions.  These innovations and further extensions of them will allow JSDMs to take advantage of presence-only data enabling wider use of these models.  Further, the multivariate Gaussian process approach suggested here are widely supported by software packages and are more accessible to researchers than  alternative approaches.</p>