Numerical analysis of the Fokas method in two and three dimensions

This thesis considers the numerical solution to elliptic boundary value problems (BVPs) in convex domains. Specifically we look at the two-dimensional problem in a polygon, and the three dimensional problem in a polyhedron. The nature of elliptic equations means that, knowing the values of a solution on the boundary, one can reconstruct this function inside the domain. This amounts to finding a Dirichlet-to-Neumann (D2N) map, which reconstructs the unknown (Neumann) boundary data from the known (Dirichlet) boundary data. Much is known about the solution to elliptic equations, both theoretically and numerically, but we shall pursue a newer development called the unified approach of [Fok08], or “Fokas method”. It is hoped that the positive results we present here will motivate further inclusion of the Fokas method in numerical packages

Free-ranging domestic cats reduce the effective protected area of a Polish national park

Poland's Animal Protection Act, as of 2002, made it legal to shoot free-ranging cats and dogs. The act triggered substantial social debate with opponents arguing that this legislation was weakly supported by scientific evidence of the ecological impacts of free-ranging pets. Our main research goal was to examine the activity of free-ranging domestic cats within a Polish protected area by applying radio-telemetry methods to determine space use and degree of encroachment into the national park. We trapped and radio-tracked 19 animals from three sites (focal households) located in Ojcow National Park (ONP) in southern Poland from June 2003 to March 2006. Annual 100% MCP home range size varied from 0.02 km2 to 1.46 km2, and was significantly larger for males (mean ± SE = 0.79 ± 0.34 km2; median = 0.53 km2) than for females (mean ± SE = 0.13 ± 0.05 km2; median = 0.13 km2). The distance travelled by individual cats from focal sites did not significantly differ between males (mean ± SE = 232.00 ± 21.05 m; median = 191 m) and females (mean ± SE = 232.50 ± 12.47 m; median = 228 m), with maximum distances of 1.5 km for males and 1.1 km for females. All monitored cats were in close proximity to nature reserves and ranged into protected areas without any human control. Cats living in the households in the park and its surrounding buffer zone, roaming at 200 m and 1000 m radius distances from their households, occupied from 6% to 100% of the park area, respectively. Our results reveal that free-ranging domestic cats roam through and potentially impact the entire national park, thus reducing its effective protected area

Economic Consequences of the Wolf Comeback in the Western United States

Gray wolves were eradicated from most of the United States in the 1940’s but have made a comeback in parts of their historic range over the last two decades. First reintroduced into the Greater Yellowstone Ecosystem and central Idaho in the mid-1990’s, wolves have subsequently dispersed into at least 7 western states. Coloradoans became the latest state to take interest in bolstering wolf populations, as residents passed a ballot initiative in November 2020 to reintroduce a self-sustaining population of gray wolves by the end of 2023. Conflicts between people in rural areas that might incur costs (such as livestock loss) and people in urban areas geographically removed from direct contact with wolves suggest that the distribution of benefits may not align uniformly with the distribution of costs. Given that Colorado will imminently make many policy decisions that have an impact on costs and benefits, we review available literature to better understand the magnitude of gainers and losers from wolf reintroduction in western states. Although no single study has included all possible economic values, the magnitude of impacts can be inferred by assembling a broad range of estimates for different types of values into a single space. Our review of existing valuation literature from western states indicates that the magnitude of economic benefits of wolves is many times higher than what it costs to manage wolves and to reduce or compensate for losses to livestock producers and others

A systematic map of human-carnivore coexistence

Carnivore populations globally have largely declined, and coexistence, where humans and carnivores share landscapes, plays a crucial role in carnivore conservation. However, the term “coexistence” is often used in scientific and popular literature without being clearly defined. Herein, we provide a global perspective on what coexistence is and how it is studied. We conducted a systematic map of 366 articles published between 1987 and 2020 to characterize human-carnivore coexistence literature according to coexistence definitions, temporal trends, geographic and taxonomic focus, and four thematic aspects of coexistence: carnivore ecology, human endeavors, social conflict and human-carnivore conflict. We used chi-squared tests and generalized linear models to describe the thematic, taxonomic and geographic focus of the literature. The human-carnivore coexistence literature increased exponentially in the past 30 years, but few articles defined the term “coexistence” and those that did used inconsistent definitions. Thematically, coexistence research showed less emphasis on social conflict, even though it is a major driver of conflict regarding carnivores. The literature also focused primarily on larger carnivores, rather than endangered carnivores, and was primarily led by European and North American authors. We offer a simplified, formal definition of “coexistence” that incorporates the four thematic aspects of coexistence encountered in the literature: Co-occurrence of sustainable carnivore populations and human endeavors with minimal human-carnivore and human-human conflict. We encourage researchers to focus on the social dimensions of coexistence, such as human attitudes towards carnivores or the underlying causes of social conflict, and to broaden the taxonomic and cultural breadth of their projects

An agent-based movement model to assess the impact of landscape fragmentation on disease transmission

Landscape changes can result in habitat fragmentation and reduced landscape connectivity, limiting the ability of animals to move across space and altering infectious disease dynamics in wildlife. In this study, we develop and implement an agent-based model to assess the impacts of animal movement behavior and landscape structure on disease dynamics. We model a susceptible/infective disease state system applicable to the transmission of feline immunodeficiency virus in bobcats in the urbanized landscape of coastal southern California. Our agent-based model incorporates animal movement behavior, pathogen prevalence, transmission probability, and habitat fragmentation to evaluate how these variables influence disease spread in urbanizing landscapes. We performed a sensitivity analysis by simulating the system under 4200 different combinations of model parameters and evaluating disease transmission outcomes. Our model reveals that host movement behavior and response to landscape features play a pivotal role in determining how habitat fragmentation influences disease dynamics. Importantly, interactions among habitat fragmentation and movement had non-linear and counter-intuitive effects on disease transmission. For example, the model predicts that an intermediate level of non-habitat permeability and directionality will result in the highest rates of between-patch disease transmission. Agent-based models serve as computational laboratories that provide a powerful approach for quantitatively and visually exploring the role of animal behavior and anthropogenic landscape change on contacts among agents and the spread of disease. Such questions are challenging to study empirically given that it is difficult or impossible to experimentally manipulate actual landscapes and the animals and pathogens that move through them. Modeling the relationship between habitat fragmentation, animal movement behavior, and disease spread will improve understanding of the spread of potentially destructive pathogens through wildlife populations, as well as domestic animals and humans

Willingness to pay for reintroducing wolves in a divided voting base

Wolves will soon be reintroduced in Colorado based on a statewide ballot initiative that narrowly passed in November 2020. Using an economic choice experiment, we estimate the benefits that wolf introduction might bring to Colorado. We calculated willingness to pay (WTP) for a sustainable wolf population by considering six program attributes: 1) state wolf population, 2) compensation for livestock-related losses, 3) cost-sharing for conflict reduction, 4) number of livestock killed statewide, 5) lethal government control of wolves, and 6) wolf hunting. Respondents who reported they voted yes on the ballot initiative had a positive WTP for a population of 200 wolves, referred to as the minimum sustainable population in the survey, but WTP diminished for larger populations. Preferences for a population of 200 wolves amounts to an annual WTP of approximately $31.1 million when extrapolating to all yes-voting households statewide. In contrast, respondents who reported they voted no would have to be paid to accept wolf populations. We also found statistically significant preferences for other attributes of the management program, such as cost sharing for conflict reduction measures to livestock producers or compensating livestock losses. When these attributes were included, the willingness to pay increased to$115 million statewide among yes-voting households. We estimated a $57.5 to$1 benefit-cost ratio for a sustainable wolf population. However, benefits and costs are not evenly distributed across urban and rural residents, which suggests that mechanisms to transfer resources from those willing to pay to those that incur costs would be needed to balance that distribution

Assessing the umbrella value of a range-wide conservation network for Jaguars (Panthera onca)

Umbrella species are employed as conservation short-cuts for the design of reserves or reserve networks. However, empirical data on the effectiveness of umbrellas is equivocal, which has prevented more widespread application of this conservation strategy. We perform a novel, large-scale evaluation of umbrella species by assessing the potential umbrella value of a jaguar (Panthera onca) conservation network (consisting of viable populations and corridors) that extends from Mexico to Argentina. Using species richness, habitat quality, and fragmentation indices of similar to 1500 co-occurring mammal species, we show that jaguar populations and corridors overlap a substantial amount and percentage of high-quality habitat for co-occurring mammals and that the jaguar network performs better than random networks in protecting high-quality, interior habitat. Significantly, the effectiveness of the jaguar network as an umbrella would not have been noticeable had we focused on species richness as our sole metric of umbrella utility. Substantial inter-order variability existed, indicating the need for complementary conservation strategies for certain groups of mammals. We offer several reasons for the positive result we document, including the large spatial scale of our analysis and our focus on multiple metrics of umbrella effectiveness. Taken together, our results demonstrate that a regional, single-species conservation strategy can serve as an effective umbrella for the larger community and should help conserve viable populations and connectivity for a suite of co-occurring mammals. Current and future range-wide planning exercises for other large predators may therefore have important umbrella benefits