Bayesian inference in ecological and epidemiological models
Creators: name: KODIKARA, Saritha
Publisher: name: RMIT University
Year: 2024
Subjects: classificationCode: 410102
subject: Ecological impacts of climate change and ecological adaptation
classificationCode: 420299
subject: Epidemiology not elsewhere classified
classificationCode: 490501
subject: Applied statistics

description: Clear signs are emerging that any further loss of critically endangered species might tip the world towards another mass extinction event at the worst, or a global ecological catastrophe at the best. In addition to this, infectious diseases are considered as one of the top five drivers of extinction. On the other hand, scientists find that biodiversity loss can in fact increase rates of infectious disease, which already lands us in a never-ending loop. Of course, infectious diseases, and the problem of eradicating diseases are of interest in their own right. The goal of my thesis is to derive new mathematical and statistical models for studying species extinctions as well as models for studying infectious diseases.<br><br>

Many studies have used historical sighting data to infer the extinction of species. Often, the data is in the form of a time-series specifying in which years the species was sighted over a long time-span, usually a number of decades. My work is largely concerned with datasets of this type and trying to predict whether the species has gone extinct after the last certain sighting, and if so, what date it is likely to have gone extinct. The majority of extinction models developed in the literature have only dealt with certain sightings, where all the sightings were treated as correctly identified and thus valid. However, in reality, for many of the sightings reported it is not one hundred percent certain that the species was correctly identified. In recent years, several new probabilistic models have been developed to incorporate such uncertainties into modelling approaches. In fact, two different modelling methodologies have been developed. In the first phase (Chapter 3) of my research, I examined these two methods in-depth to seek out the true underlying principles, as they give contradictory conclusions on the extinction of the Ivory-billed Woodpecker. This work is significant as it helps to identify which models can be used by ecologists in which situations, and how to untangle the influential factors controlling the signatures of extinction in sighting records.<br><br>

In the second phase (Chapter 4), a new perspective is provided into modelling extinction using a hierarchical Bayesian approach that could be applied to any sighting record consisting of certain and uncertain sightings. This new approach calculates the posterior probability that the species went extinct by the endpoint of the sighting record. The differences in the new proposed method are discussed in contrast to other methods in the literature. The hierarchical Markov Chain Monte Carlo (MCMC) approach I develop for determining extinction date, was applied to the sighting record of the Ivory Billed Woodpecker (IBW) (Campephilus principalis). It was concluded that the IBW went extinct in the 1940s which confirms the validity of recent studies, despite arguable and controversial sightings of the species later.<br><br>

In the third phase of the thesis (Chapters 5-7) I explore several new approaches for inferring species extinction. For instance, in Chapter 5, a model is developed that assumes an independent non-homogeneous Poisson process for the sightings. This work significantly extends models that were developed in phase two (above) which assumed that the certain and uncertain sighting rates are constant (i.e., having constant sighting probabilities). In Chapters 6 and 7, techniques such as the sequential Bayes factor and Survival theory are used as tools for modelling extinction. These new methods are applied to sighting data for different species, such as Ivory-billed Woodpecker (Campephilus principalis), Alaotra Grebe (Tachybaptus rufolavatus), Dodo (Raphus cucullatus), Aldabra Snails (Rhachistia aldabrae), and black-footed ferret (Mustela nigripes). In short, several flexible tools are developed in this thesis for studying species extinction. Most of these allow working with distributions of parameters including extinction time, rather than point estimates in contrast to other methods in the literature.<br><br>

In the final part of the thesis (Chapter 8) I turn my attention to studying disease transmission in infectious disease problems. These relate to the above ecological extinction problems, in that disease extinction is the ultimate goal, and the processes that lead up to disease extinction are of intrinsic interest. The main objective in this final phase of the thesis is to improve and extend current Bayesian algorithms that infer the transmission network of an outbreak and thus help to make effective disease control decisions to eradicate a disease. A transmission network is a graph that links all infected cases with their possible sources of infection from whom they caught the disease. The network thus provides the big picture of \who infected whom". The modern transmission network reconstruction methodologies combine both epidemiological and genetic sequence data. In this chapter, one of the most successful methods (Lau et al., 2015) is extended so that it considers animal movements between farms. This methodology is used to assess the accuracy of the inferred transmission network based on a simulated spatio-temporal epidemic. Through the simulation study I demonstrate that the accuracy of a transmission network is significantly improved through the addition of contact(/movement)-data (in comparison to using sequence data and epidemiological data alone). Having 100% of sequence data along with no contact data resulted in a coverage rate of 44%. However, this coverage rate was doubled by just including 50% of the movement data. Thus, including movement data into the inference gave a big boost in the inferred transmission network coverage rate. The methodology described in this section is intended to be applied to the early stages of the 2019 Mycoplasma bovis outbreak in New Zealand. <br><br>

In conclusion, the models developed in this thesis collectively reveal the importance and contribution of mathematical approaches for studying ecological and epidemiological problems relating to species extinction and the dynamics of disease extinction.