Stochastic ecological models for predicting species distribution and extinction

Given the unprecedented threats currently facing biodiversity globally, a deeper understanding of how species are distributed and their probability of becoming extinct is of growing importance. This thesis focuses on novel methodological developments in ecological modelling and is divided into two parts. Part I focuses on improving statistical models to make predictions of how species are distributed within a given region, and Part II develops new approaches for combining multiple data sources to get improved estimates of extinction probability. Species distribution models (SDMs) are the focus of Part I and are an approach that takes records of where a species was sited, and uses these along with environmental and biogeographic data to make predictions of where the species is likely to occur in the landscape. Use of SDMs is becoming increasing more prevalent in multiple fields including ecology and conservation biology. Chapter 4 utilises approaches from advanced spatial statistics including spatial point processes, to provide improved predictions of species distributions by combining presence-background (PB) data with site-occupancy (SO) data. An inhomogeneous Poisson point process (IPP) model formed the the basis for constructing an integrated species distribution model that fits both PB and SO data simultaneously. The integrated model is able to account for the imperfect detection of the PB data and counteracts the effects of the small sample size in the SO data. This approach was tested using simulated data and demonstrated by modelling the distribution of the yellow-bellied glider (Petaurus australis) in southeastern Australia using 1136 presence records supplemented by 202 site occupancy records. Incorporating spatial correlation into SDMs is challenging but has the potential to improve predictions when the effects of spatial correlation in the species locations is strong enough. Chapter 5 explores the potential of using a Log- Gaussian Cox Process (LGCP) for modelling spatially correlated data and compares its performance to an SDM based on an IPP, which is commonly used for modelling PB data and ignores correlation. The chapter investigates two sources of spatial correlation in the data (i) the intrinsic correlation caused by the intra- and inter-species interactions, and (ii) by the presence of an environmental covariate that drives the species distribution, but is not included in the model fitting process. The results demonstrate that using LGCP always outperforms IPP on in-sample data, while providing varying results on the out-of-sample datasets. The chapter investigates the limitations of the LGCP model in specific situations and highlights the cases when using it can be most advantageous. Chapter 6 presents the first steps towards extending the integrated model presented in Chapter 4 so that it fits multiple data sources simultaneously, while also accounting for spatial correlation in the species occurrence data. It investigates the possibility of modelling imperfect detection in spatially correlated PB data using a thinned LGCP, and the shortcomings of this approach. It goes on to discuss possible pathways towards creating an integrated model based on the LGCP framework. Finally, it outlines the theoretical and computational difficulties associated with developing and fitting an SDM that integrates multiple data types, while incorporating species detectability and the ability to deal with spatial correlation in species occurrences. Part II explores models to estimate the probability that a taxon has gone extinct using a range of data sources, with the aim developing a new model that helps provide decision support for prioritising conservation interventions and environmental monitoring. The new method developed in Chapter 7 allows researchers to estimate the probability of a species being locally or globally extinct in the area of interest. The chapter's proposed model is a new, accessible framework that combines diverse kinds of evidence collected at different times using various methods. The model takes into account uncertainties in input parameter estimates and provides bounds on estimates of the extinction probability. We illustrate application of the model using the sighting record, for the Alaotra Grebe (Tachybaptus rufolavatus), collected between 1929 and 2017. Taken together, the novel developments of this thesis provide new innovations in modelling where species occur in the landscape, and how likely they are to go extinct. It is hoped that these methods, and further extensions of them, will be of utility to researchers and organisations requiring such predictions for improving how scarce conservation resources are utilised