Applications of Mathematical and Statistical Modeling to Wildlife Management, Animal Husbandry, and Circadian Physiology

Human history, health, and culture are profoundly linked to our relationships and management of animals. Balancing the advancement of societies while maintaining sustainable relationships with other species faces several challenges, such as climate change, diseases, pollution, and exploitation. We present three mathematical models to address ecological, agricultural, and animal husbandry crises, while also weighing their relative causal factors, testing hypothesized management scenarios, and uncovering new strategies to advance sustainability efforts. Our first model explores the parasitic relationship between winter ticks and moose. This seasonal parasite's impact on moose conservation has the potential to compound as the affect of climate on season lengths could increase the success of the parasite to find moose. We develop a mathematical model that projects the sustainability of this relationship and measures the effectiveness of an increased hunting strategy posed by resource managers. Our second model synthesizes nearly a dozen previous mathematical models that attempted to explain the impacts that stressors have on social bees. Bees are an agricultural linchpin in many systems, and their conservation against a plurality of stressors has been highlighted by a number of studies since the turn of the century. Unfortunately, the compatibility of these previous models is not known, nor have they fully explored the characteristics of what a stressor entails, therefore, our model serves to fill these foundational primary gaps in the literature. Our third model explores an emergency medical dataset for unexpected deaths in Wake County, North Carolina. We leverage a Bayesian hierarchical model to test the hypothesis that circadian-based physiological factors give rise to disproportionate deaths during parts of the 24-hour cycle. We found evidence both for and against this theory when stratifying across demographic and clinical conditions. In our final mathematical model, we examine the factors that mitigate, foster, and prevent scabby mouth outbreaks on ruminant farms. Economically, several developing countries rely on a steady sheep export, while culturally, certain religious holidays are observed with the slaughter of numerous sheep. Our model generates insights for managers to prevent outbreaks from occurring and how to use vaccination and/or quarantining to limit the scope of developing outbreaks.