Digital Commons Network^™

Utilizing Markov Chains To Estimate Allele Progression Through Generations, Ronit Gandhi

Honors Theses

All populations display patterns in allele frequencies over time. Some alleles cease to exist, while some grow to become the norm. These frequencies can shift or stay constant based on the conditions the population lives in. If in Hardy-Weinberg equilibrium, the allele frequencies stay constant. Most populations, however, have bias from environmental factors, sexual preferences, other organisms, etc. We propose a stochastic Markov chain model to study allele progression across generations. In such a model, the allele frequencies in the next generation depend only on the frequencies in the current one.

We use this model to track a recessive allele …

Adult Atlantic Sturgeon Population Dynamics In The York River, Virginia, Jason E. Kahn

Graduate Theses, Dissertations, and Problem Reports

Sturgeon first appear in the fossil record in the Triassic Period just over 200 million years ago and are among the most primitive of the bony fishes. Despite their large size and historic presence along the East Coast, Atlantic sturgeon were not targeted for their meat and caviar as a commercial fishery until 1880. By 1905 they had declined to less than one percent of their pre-fishing abundance but the fishery continued. Prior to 1980, there had been very little research on Atlantic sturgeon, primarily limited to documenting landing location and poundage, maximum longevity, or weight of eggs per fish. …

Mathematical Modeling And Simulation Of Multialleic Migration-Selection Models, Chad N. Vidden

Journal of Undergraduate Research at Minnesota State University, Mankato

Population ecology is concerned with the growth and decay of specific populations. This field has a variety of applications ranging from evolution and survival at the environmental level to the spread of infectious disease at the cellular and molecular levels. Many ecological circumstances require the use of mathematical methods and reasoning in order to acquire better knowledge of the issue at hand. This study considered and analyzed multiple different mathematical models of population dynamics along with their purposes. This foundation was then applied in order to explore the migration of populations from one isolated region to another along with the …

Coexistence Of Multi-Allelic Polymorphism With Migration And Selection, Andrew Flick

Journal of Undergraduate Research at Minnesota State University, Mankato

Population ecology is concerned with the growth patterns of populations. This field has many applications, ranging from survival at the environmental level, to the spread of infectious diseases at the cellular level. Mathematical modeling and computer simulation can be powerful tools in researching this area. I will be investigating the spatial patterns in populations (or gene frequencies) due to migration and selection. My research conditions are for the maintenance of polymorphism under a variety of migration schemes in discrete-space and continuous-time mathematical models. The results will be applicable from the ecological level to the molecular level. Some species are better …

Grts And Graphs: Monitoring Natural Resources In Urban Landscapes, Todd R. Lookingbill, John Paul Schmit, Shawn L. Carter

Geography and the Environment Faculty Publications

Environmental monitoring programs are an important tool for providing land managers with a scientific basis for management decisions. However, many ecological processes operate on spatial scales that transcend management boundaries (Schonewald-Cox 1988). For example, adjacent lands may influence protected-area resources via edge effects, source-sink dynamics, or invasion processes (Jones et al. 2009). Hydrologic alterations outside management units also may have profound effects on the integrity of resources being managed (Pringle 2000). The impacts of climate change are presenting challenges to resource management at local-to-global scales (Karl et al. 2009). This potential disparity between ecological and political boundaries presents an interesting …