Mathematical and Computational Applications in Disease and Landscape Ecology

The Individualized Interdisciplinary Program (IIP) at the University of Montana allows students to work with faculty in the design of a graduate curriculum tailored to their unique academic, creative, and professional needs. The principal goal of the National Science Foundation\u27s IGERT: Montana - Ecology of Infectious Diseases (MEID) program is to produce graduates with expertise to lead the collaborative, cross-, and inter-disciplinary efforts in education and research needed to address complex problems as exemplified by the ecology of endemic, epidemic, and emergent infectious diseases. Under the envelope of these two programs, I have developed a Ph.D. program in which I received an interdisciplinary education in applied mathematics and computational ecology. I strongly feel that spatial modeling is one of the most promising approaches to advance the sciences of disease ecology and landscape ecology. Mathematical and computational modeling provide powerful tools for evaluating relationships between mechanisms and responses in a spatially complex environment. Past progress in these fields has been limited by the lack of computational power and flexible mathematical models to simulate the actions of ecosystem and population processes in complex environments. My specific research focus is in the development of mathematical and computational models to synthesize environmental data for describing and predicting the characteristics of population and disease dynamics on the landscape. The results from this research are documented in the following chapters: 1) Mathematical Disease Ecology. This uses numerical and qualitative analysis to study a model for Tick Borne Relapsing Fever in an island ecosystem. 2) Computational Landscape Ecology. The development and applications of a spatially-explicit computer model to predict population connectivity and geneflow on complex landscapes are described

Why Did the Bear Cross the Road? Comparing the Performance of Multiple Resistance Surfaces and Connectivity Modeling Methods

There have been few assessments of the performance of alternative resistance surfaces, and little is known about how connectivity modeling approaches differ in their ability to predict organism movements. In this paper, we evaluate the performance of four connectivity modeling approaches applied to two resistance surfaces in predicting the locations of highway crossings by American black bears in the northern Rocky Mountains, USA. We found that a resistance surface derived directly from movement data greatly outperformed a resistance surface produced from analysis of genetic differentiation, despite their heuristic similarities. Our analysis also suggested differences in the performance of different connectivity modeling approaches. Factorial least cost paths appeared to slightly outperform other methods on the movement-derived resistance surface, but had very poor performance on the resistance surface obtained from multi-model landscape genetic analysis. Cumulative resistant kernels appeared to offer the best combination of high predictive performance and sensitivity to differences in resistance surface parameterization. Our analysis highlights that even when two resistance surfaces include the same variables and have a high spatial correlation of resistance values, they may perform very differently in predicting animal movement and population connectivity

Inter-Individual Isolation by Distance: Implications for Landscape Genetics

Many approaches to understanding the influence of landscape on gene flow account for isolation by distance, a phenomena where individuals that are closer together are more likely to be more closely related. Most theoretical research has focused on isolation by distance between populations. We simulated the expected isolation by distance patterns between individuals within a finite population and found an asymptotic pattern. New null models are needed in landscape genetic approaches to correctly account for isolation by distance patterns. We will briefly review isolation by distance and discuss the factors (time, variance in dispersal, and mutation rates) influencing isolation by distance patterns. Our results have implications for estimating how difficult it is for animals to move through the landscape

Unicor: A Species Connectivity And Corridor Network Simulator

Maintenance of species and landscape connectivity has emerged as an urgent need in the field of conservation biology. Current gaps include quantitative and spatially-explicit predictions of current and potential future patterns of fragmentation under a range of climate change scenarios. To address this need, we introduce UNIversal CORridor network simulator (UNICOR), a species connectivity and corridor identification tool. UNICOR applies Dijkstra’s shortest path algorithm to individual-based simulations and outputs can be used to designate movement corridors, identify isolated populations, and characterize zones for species persistence. The program's key features include a driver-module framework, connectivity maps with thresholding and buffering, and graph theory metrics. Through parallel-processing computational efficiency is greatly improved, allowing for larger ranges (grid dimensions of thousands) and larger populations (individuals in the thousands), whereas previous approaches are limited by prolonged computational times and poor algorithmic efficiency; restricting problem-size (range and populations), and requiring artificially subsampling of target populations

Re-evaluating causal modeling with mantel tests in landscape genetics

The predominant analytical approach to associate landscape patterns with gene flow processes is based on the association of cost distances with genetic distances between individuals. Mantel and partial Mantel tests have been the dominant statistical tools used to correlate cost distances and genetic distances in landscape genetics. However, the inherent high correlation among alternative resistance models results in a high risk of spurious correlations using simple Mantel tests. Several refinements, including causal modeling, have been developed to reduce the risk of affirming spurious correlations and to assist model selection. However, the evaluation of these approaches has been incomplete in several respects. To demonstrate the general reliability of the causal modeling approach with Mantel tests, it must be shown to be able to correctly identify a wide range of landscape resistance models as the correct drivers relative to alternative hypotheses. The objectives of this study were to (1) evaluate the effectiveness of the originally published causal modeling framework to support the correct model and reject alternative hypotheses of isolation by distance and isolation by barriers and to (2) evaluate the effectiveness of causal modeling involving direct competition of all hypotheses to support the correct model and reject all alternative landscape resistance models. We found that partial Mantel tests have very low Type II error rates, but elevated Type I error rates. This leads to frequent identification of support for spurious correlations between alternative resistance hypotheses and genetic distance, independent of the true resistance model. The frequency in which this occurs is directly related to the degree of correlation between true and alternative resistance models. We propose an improvement based on the relative support of the causal modeling diagnostic tests

Female-biased introductions produce higher predicted population size and genetic diversity in simulations of a small, isolated tiger (Panthera tigris) population

Isolation of wildlife populations represents a key conservation challenge in the twenty-first century. This may necessitate consideration of translocations to ensure population viability. We investigated the potential population and genetic trajectory of a small, isolated tiger (Panthera tigris) population in Thailand’s Dong Phayayen-Khao Yai forest complex across a range of scenarios. Using an individual-based, spatially-explicit population modelling approach, we simulate population and genetic trajectories and evaluate the relative impact of translocations from a related population. Population and genetic trajectories in our study were most sensitive to sex and number of individuals translocated and translocation frequency. Translocation of females produced consistently higher population, allelic richness, and heterozygosity compared to equal numbers of males. Despite population increases, declines in allelic richness and heterozygosity across simulations were stark, with simulations predicting a mean decline of allelic richness and heterozygosity of 46.5% and 53.5% without intervention, respectively. Translocations of four females every generation or every other generation were required to prevent substantial heterozygosity declines. While translocations could increase population size, they may fail to prevent long-term loss of genetic diversity in small populations unless applied frequently. This reinforces the importance of incorporating realistic processes of genetic inheritance and gene flow in modelling small populations