Biomathematics Seminar Abstracts
November
9, 2009
A mathematical model for cholera
Elsa Schaefer
Marymount
University
We’ve known what causes cholera for several hundred years, and yet in areas with poor infrastructure and inadequate sanitation thousands of people are dying each year from cholera. We will explore the factors that are most important in describing how and why cholera is still creating such havoc in our world, as well as our arsenal of intervention strategies. We will see how these puzzle pieces can fit into a mathematical model, and see how the mathematical technique of optimal control theory can suggest how we can best apply our intervention strategies to succeed in saving the lives that will otherwise be lost in future cholera outbreaks.
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Redwoods of the Reef: Modeling individuals and populations of the giant barrel sponge Xestospongia muta
Timothy Henkel
Murray State University
The Caribbean barrel sponge, Xestospongia muta , is a large and common member of the coral reef community at depths greater than 10 m, and has been called the “redwood of the reef” for its size and supposed long-life. Despite its prominence and importance to habitat complexity, very little was known about the basic biology of this massive sponge. For over 10 years, populations of X. muta were monitored at different depths on coral reefs off of Key Largo, FL. Twice a year sponges were photographed and examined for predation, mortality, disease and recruitment. Image analysis was used to establish a growth curve for the sponge, generating age estimates of sponges over a meter tall to be > 100 years old. In addition, a stage-based matrix model was constructed to determine future population growth of X. muta under present reef conditions. Elasticity and life table response analysis revealed that survival of individuals in the largest size class has the greatest effect on population growth. Projections indicate that populations of X. muta will continue to increase under present conditions, however population growth may be negatively affected by continued mortality of the largest individuals from a recently described pathogenic syndrome.
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Biostatistics at UAB
Jeffery
M Szychowski
University of Alabama, Birmingham
Biostatistics is a growing field that offers diverse opportunities for application and research. We will introduce the discipline of biostatistics, explore career opportunities, and describe the graduate programs in biostatistics offered at the University of Alabama at Birmingham (UAB). We will specifically outline the admissions procedures, funding and research opportunities, and MS and PhD requirements. Students from all academic backgrounds are encouraged to attend and questions are welcome.
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Evaluation of Microsatellites in Ambystoma tigrinum nebulosum
Sarah Thomason
Phenotypic plasticity is the ability of a trait to change in response to an environmental cue. Salamanders are known to exhibit phenotypic plasticity in the form of facultative paedomorphosis, producing a paedomorphic (aquatic) or a metamorphic (terrestrial) body morphology, which provides a unique vertebrate model for understanding the evolution of phenotypic plasticity. Previous research has revealed the mechanisms that produce this polymorphism; however, little is known about the evolutionary mechanisms that maintain it. By studying the fitness consequences of facultative paedomorphosis, we can better understand the evolution of this polymorphism. We have proposed using nuclear markers to assign parentage and to create a pedigree within a closed population of tiger salamanders as a way of measuring fitness differences among morphs. As a first step, we evaluated polymorphism using previously designed Ambystoma microsatellite markers in spotted salamanders ( Ambystoma maculatum ). Tissue samples of 55 salamanders were collected from a local population and DNA was amplified using PCR to assess microsatellite variability. In this ongoing study, nine loci have been successfully amplified, six of which are polymorphic and will be used to determine relatedness in this population. The results of this study will eventually be applied to a population of facultatively paedomorphic tiger salamanders to better understand the evolution of phenotypic plasticity.
Impact of Agriculture on Amphibian Diversity
Glenna Buford & Mandy Main
Agricultural impact on native environments has been considered to be the top cause for declines in diversity of local fauna throughout the world. Because of their dependence on water, amphibians are extremely susceptable to chemicals used in agriculture. Previous studies have concluded that pond size and temperature might have a greater impact on amphibian species diversity than the proximity of the pond to active agricultural activity. However, an equal amount of studies have concluded that agricultural chemicals and livestock disturbance have a negative impact on amphibian diversity. We sought to compare amphibian diversity in small ponds located within wooded areas in Land Between the Lakes Recreation Area to ponds located within agriculture in Calloway Co. Kentucky.
Investigating Energy Costs and Trade-offs Between Cell-Mediated and Humoral Branches of the Immune System in Old-Field Mice ( Peromyscus polionotus )
Sarah Hargis & Renee Levesque
The BioMaPS program has allowed us to get a firsthand understanding of research in a way that is beyond what the typical student may experience. For our project we studied the immune system which can be quite a variable system with numerous factors affecting different components. There have been noted differences within the immune system itself in the responses to stressors and challenges. These varying responses led us to our research question: Is the response by one branch of the immune system affected by a simultaneous challenge to another branch? In order to test this, over the past summer we challenged the humoral and cell-mediated branches of the adaptive immune system in male Old-Field Mice ( Peromyscus polionotus ). To compare the strength of the responses of the immune system we measured inflammation, hematocrit, and antibody titers and obtained a complete blood count, as well as a white blood cell differential. We also measured the amount of energy used and its allocation by taking both the resting and daily metabolic rate, and the final organ masses. By comparing all these data we plan on gaining a better understanding of energy use and allocation during separate and simultaneous immune challenges. We will be using various statistical tests to compare the two branches’ responses and overall energy allocation.
September 14, 2009
Judy Day , Mathematical Biosciences Institute, Ohio State University
April 27, 2009
Grace M. Kepler, Center for Research in Scientific Computation (CRSC), North Carolina State University
Modeling CMV infection in transplant patients
HCMV infection is a significant health threat to immunosuppressed patients. Patient health outcome could be improved with suitable mathematical modeling that could predict the disease course in individuals and one that could suggest optimized treatment strategies. I illustrate our approach to within-patient modeling and prediction with similar HIV-1 modeling work by our research group. I then present an initial model for HCMV infection in healthy and immunosuppressed patients and show how this model can begin to provide a window into the dynamics of HCMV infection in transplant patients.
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March 30
Emily Croteau, Murray State University
Population History and Phylogeography of Bobcats ( Lynx rufus ) across North America
Bobcats ( Lynx rufus ) are mobile, medium-sized carnivores with a broad distribution in North America . Throughout this expansive range twelve bobcat subspecies have been described based on skeletal and pelage characteristics. To characterize the geographical distribution of genetic diversity in bobcats across their distributional range and assess subspecies designations, 185 individuals representing nineteen locations were analyzed using a 464 base pair fragment of the mitochondrial DNA (mtDNA) control region. Overall, it appears that bobcats have undergone a recent population expansion, with generally little phylogeographic structure present within regions, contrary to prior subspecific designations. However, an analysis of molecular variance (AMOVA), f ST estimates, median joining network and phylogenetic trees elucidated genetic subdivision between eastern/midwestern populations and western populations, thereby distinguishing two phylogeographic groupings. These data confirm that bobcats historically have not experienced large barriers to dispersal but that recent habitat alterations may be disrupting dispersal corridors over large scales.
February 4, 2009
Terry Derting, Murray State University
Research Ethics
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Seth Oppenheimer
Mississippi
State University
A Model for
Gene Activation
The purpose of this talk is to develop a model for the activation
of the gene responsible for the production of the cytokine interleukin 6,
IL-6. This is motivated by experimental
work that indicates that exposure to certain exogenous chemicals results in
changes in cytokine production. In
particular, exposure to the widely used pesticide atrazine
and the legacy pesticide dieldrin, still very much
present in the environment, resulted in the reduction of the production of
IL-6. We develop of model of twelve
ordinary differential equations to model the effect of changes in transcription
factor levels on IL-6 production rates and establish basic qualitative
properties of solutions.
This is joint work with Stephan Pruet and his student Ruping Fan. The project is supported by National Institutes of Health grants DHHS/NIH 5 P20 RR17661 and NIH ES 11278
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Olcay Akman
Illinois
State University
Ask Not What
Mathematics Can Do For Biology - Ask What Biology Can Do For Mathematics
During the last decade or so Genetic Algorithms (GA) have been routinely used in high-dimensional optimization problems. As they get implemented in various problems, GA natural selection and evolution tools, such as methods of mating, rates of mutation keep getting modified by users. Most, if not all of these modifications aim to increase GA efficiency at the expense of available computing resources. We propose a modification that reduces the needed computations without losing efficiency.
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Marcia Edson
Murray
State University
An
Introduction to Algorithms and Combinatorial Structures with Biological
Applications
Currently, extreme amounts of data are being generated daily in molecular biology, and, as such, there is an ever-increasing need to process this information. Efficient algorithms are needed to search for patterns and analyze macromolecular biological sequences, structures, and functions. We will discuss simple algorithms for comparing sequences, including computational runtime, as well as examples of discrete combinatorial structures such as graphs and trees. These structures can be used to find patterns in sequences or even to suggest a likely evolution. This talk is a brief introduction to the computational side of molecular biology.
BioMaPS
Recruitment Symposium
Using Mathematical
Models and Molecular Markers to Study the Patterns of Genotypic Diversity of an
Invasive Plant, Alligator Weed (Alternanthera philoxeroides)
Glenna Buford & Jona Kos
Alligator weed (Alternanthera philoxeroides) is a successful invader native to South America. It has invaded all continents except Africa and Europe. In spite of its serious invasiveness all over the globe, alligator weed has been rarely studied in terms of its spatial spread and invasion mechanisms. It is even more surprising that knowledge on the relationships between its genetic diversity and invasiveness is still very limited. This project attempts to uncover the mechanisms of alligator weed invasion from two aspects: (1) quantifying spatial spread using logistic and diffusion-reaction models; (2) using molecular markers to examine the patterns of genotypic diversity of this successful invader. We have collected plant samples from three states in the southeastern US and used Inter-Simple Sequence Repeat markers (ISSRs) to test the hypothesis that a higher genetic diversity is associated with species’ invasion success. The results of this ongoing study will provide invaluable information on the underlying mechanisms of alligator weed’s invasion success.
Determining Parentage
in the Arizona Tiger Salamander (Ambystoma tigrinum nebulosm)
Sarah Farmer & Sarah Thomason
Tiger salamanders, Ambystoma tigrinum nebulosm, are known to exhibit a polymorphism known as facultative paedomorphosis. Using microsatellite markers to assign parentage to a population would give insight into the life history and the evolutionary effects of paedomorphosis. Spotted salamanders (Ambystoma maculatum) from a local population, that are also known to be polymorphic, were collected and tissue samples were taken. In this ongoing study, nine loci of the spotted salamanders have been successfully amplified in hopes that relatedness can be determined in this population. The goal is to eventually use samples from a specific population of tiger salamanders in Colorado and apply the same methods.
K. Renee Fister
Curing Cancer
with Mathematics
Optimal control techniques are applied to mathematical models describing cancer dynamics. The results include discussion of bang-bang and singular controls. Numerical results are presented.
Robert Donnelly
Murray State University
Applications
of game theory to biology
Game theory is a 20th century mathematical innovation that has been applied in many disciplines (economics, political science, biology) to study conflict and cooperation. Our goals for this talk are to introduce some basic game theoretic ideas and see how these ideas can be used to help understand certain animal behaviors such as reproductive strategies and aggression.
Scott Wissinger
Allegheny College
Causes &
Consequences of Cyclic Fluctuations of Top Predators in Subalpine Ponds
The abundance of tiger salamanders (Ambystoma tigrinum nebulosum), the top predators in subalpine ponds in Colorado, have fluctuated cyclically over the past 20 years at our study site near the Rocky Mountain Biological Laboratory. The purpose of this talk is to summarize what my collaborator and I have learned about the cause(s) of these cycles and present some preliminary information on the effects on the pond community. It appears that the primary cause of these fluctuations is related to intrinsically driven cycles in recruitment. Field data reveal that recruitment correlates strongly with the presence of dominant cohorts of paedomorphic adults and large larvae. Experimental data suggest cannibalism on young-of-the-year larvae by paedomorphs can lead to extended periods in which there is little or no recruitment. This decline phase in the observed cycles ends when dominant cohorts senesce, resulting in a "recruitment boom" and the establishment of the next dominant cohort. We have time series data that suggest these large amplitude fluctuations in salamander abundance are negatively coupled with fluctuations in prey biomass. However, because of trophic omnivory (both within and between salamander year classes), the top-down effect does not lead to a classic trophic cascade. Nonetheless, several key prey species are impacted and we present preliminary data that suggest their fluctuations alter basic ecosystem processes in the ponds. We conclude that nearly all aspects of the population and community ecology of the subalpine ponds at our study sites are influenced directly or indirectly by large amplitude fluctuations in the top predators in this system.
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Christopher Brooks
Mississippi State
Temporal
Variation in Spatial Networks Predict Both Outbreaks and Persistence
There is an increasing recognition that individual-level spatial and temporal heterogeneity may play an important role in metapopulation dynamics and persistence. In particular, the patterns of contact within and between aggregates (e.g., demes) at different spatial and temporal scales may reveal important mechanisms governing metapopulation dynamics. Using seven years of data on the interaction between the anther smut fungus (Microbotryum violaceum) and re pink (Silene virginica) we show how the application of spatially-explicit and -implicit network models can be used to make accurate predictions of infection dynamics in spatially structured populations. Explicit consideration of both spatial and temporal organization reveals the role of each in spreading risk for both the host and the pathogen. The present work suggests that the application of spatially-explicit network models can yield important insights into how heterogeneous structure can promote the persistence of species in natural landscapes.
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Holly Gaff
Old Dominion
Identifying
disease outbreaks using semi-synthetic modeling experiments
Rapid identification of emerging infectious disease outbreaks is vital for there to be any hope of controlling the outbreak and providing proper response coordination. To this end, the field of bio-surveillance has emerged with the premise that disease outbreaks can be identified by signatures within real world data such as hospital records, absenteeism, pharmacy sales, etc. The biggest challenge with creating an algorithm to identify outbreaks is how do we know if we are correct? To this end, we have created a unique experiment environment to test various disease detection algorithms. The Veterans Affairs health care system has an extensive and well-respected electronic patient record system. From that real-world database, we extract various background datasets. We then use a mathematical model to create a theoretical outbreak. We add the outbreak to the background dataset and then test to see how quickly a given algorithm can find the outbreak. Our completed experiments show that the results of time to detection as well as the number of false alerts depend on all components of this semi-synthetic system in some unexpected ways
Alexey Arkov
Murray
Using the
fruit fly as a model organism to study cell formation and specification
Many genes of the fruit fly Drosophila melanogaster are similar to human genes. Therefore, understanding the genetic mechanisms of cellular processes in the fruit fly is likely to contribute to our understanding of human cell biology. Our laboratory focuses on the formation and specification of primordial germ cells. These cells give rise to sperm and eggs and therefore produce next generation. Several genes have been directly implicated in germ cell development and function in a highly hierarchical fashion. We are characterizing two new genes involved in germ cell formation and have shown that they regulate the expression of oskar gene which is a principal player in this process. In addition, we are studying another new gene that acts in germ cell formation by regulating division and migration of the embryonic nuclei. Finally, our data indicate that germ cells have metabolic requirements that are different from other cells and we are testing importance of various energy-producing pathways for germ cell specification.
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BioMaPS
Recruitment Symposium
Microsatellite Analysis of a Polymorphic Population of Tiger Salamanders, Ambystoma tigrinum.
Todd Schoborg & Ashley Hagan
Pedigrees can be extremely useful in understanding particular life history traits in a population of organisms. The Tiger Salamander, Ambystoma tigrinum, which can exhibit two body morphologies, provides an opportunity to examine evolutionary forces acting on both morphologies which can influence life history traits. Here we attempt to reconstruct a parent/prodigy pedigree using molecular markers within a polymorphic population of A. tigrinum.
A growth model for E. coli
Sarah Thomason & Michael Whitby
The goal for this project was to find a more suitable growth model for the bacterium E. coli in a closed system. To do this an introduction to commonly accepted, basic growth models was needed. The model for a closed system is more complicated due to metabolic byproducts, thus causing the model to take the form of a system of differential equations. After experimenting, the system was created using six differential equations that demonstrate the relationship between population size, carrying capacity, pH, salinity, and the availability of resources.
GIS Analysis of Lyme
Risk in Kentucky
Courtney Thomason & Jake Elliott
Peromyscus leucopus is a reservoir species for the spirochete that causes Lyme disease, Borrelia burgdorferi. Previous research has suggested that humoral immunity of the white-footed mouse plays a significant role in the probability of transmission of Lyme disease from host to host. In addition, biodiversity has a dilution effect on vector-borne diseases, such as Lyme disease, especially when coexisting species are not competent as reservoirs (Ostfeld and Keesing 2000, Schmidt and Ostfeld 2001, LoGuidice et. al. 2003). Disturbance and habitat fragmentation also have a negative impact on both humoral immunity in P. leucopus and biodiversity. Our objective is to create a GIS model predicting the risk of Lyme borreliosis throughout Kentucky based on presence of Peromyscus leucopus, their immunocompetence, the dilution effect caused by other mammalian species, and disturbance of the surrounding landscape through habitat fragmentation
BioMaPS
Students
Murray
Mathematics
and Biology Curriculum – what MSU students think!
A report by MSU BioMaPS students on how Math and Biology should be used together.
This summer Biology and Mathematics majors from the BioMaPS program attended a two day short course on
Implementing Biology Across The Mathematics Curriculum
at the Mathfest /Society for Math Biology meeting in
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Tim Johnston
Murray
The Archaeal
Diversity in a Flood Plain at the Mouth of a Third Order Stream of a Major
Reservoir is Affected by Factors other than Water Level Manipulation.
The flood plain created at the mouth of a third order stream that empties into a large reservoir should show significant microbial diversity. The water level is manipulated for flood control and transportation, such that the sediment is submerged in the summer and exposed in the winter. Nutrient input is affected seasonally by farming practices and decaying allochthonous sources. The temperature differences between summer and winter should affect the organisms that dominate the community. Presently, little is known about the Archaeal community within this environment. This study was conducted to characterize the Archaeal community of this environment and to determine if any changes in the community that occur seasonally are affected by water level manipulation. Molecular techniques were applied to study the Archaeal community in sediment samples from five sites within the flood plain of Ledbetter Creek embayment of Kentucky Lake , one site above the flood plain, and one site within the embayment. DNA was extracted, the rDNA amplified using Archaeal specific primers, and the amplified fragments cloned and sequenced. Ninety sequences were identified using the rRNA database. These sequences showed above 91% identity to 10 methanogenic species of Archaea. No other groups were found, but some sequences had very high identity with 5 unknown, uncultured Archaea. To determine if there are changes in the community as the temperature or water-level changes, samples were taken monthly for one year, DNA extracted, amplified, and subjected to RFLP analysis. Site-to-site comparisons found no differences within the flood plain community or when compared to the soil sample and embayment sample. However, when the site data were pooled for each month and then compared to all other months, the data showed significant differences through the year. These data suggest factors other than water level manipulation, such as temperature and/or nutrient availability affect the Archaeal community of this environment. All organisms identified were methanogens. The unidentified species clustered together when subjected to phylogenetic analysis, but did not show a strong relationship to any known group of Archaea. They do appear to be more closely related to methanogens than to any other group of Archaea. A temporal change in the methanogenic community of this environment occurred, but it is likely that a variety of factors, including temperature and nutrient input, affect the methanogenic community diversity rather than water level.
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Andrew Whittle
A modeling approach for the Eurasian Collared Dove
The Eurasian collared dove (Streptopelia decaocto) established breeding populations in Florida in
the mid-1980s and is now spreading across North America. Records from the
spread of the collared dove across Europe, in the mid 20th century, suggest
that the dispersal of the collared dove may be leptokurtic. Mathematical
ecologists use integro-difference equations to model
this type of invasion pattern. However, integro-difference
models typically assume that population-level parameters, such as growth rate,
are spatially homogeneous. We extend the integro-difference
approach by considering the latitudinal effect on the length of agricultural
growing season, which directly affects the collared doves breeding season. We
consider the effect of spatial heterogeneity on the velocity of the invasion
wave front, the density of local populations, and the ultimate boundary of the
species' range. Our model incorporates information on life history (mating
system, breeding period, number of offspring fledged) and the observed
distribution of dispersal distance. Using our model and observations on the
post-invasion population trends of native dove
species; we discuss the potential future distribution of the collared dove and
the consequences for native species.
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Hannah Callender
Vanderbilt University
Modeling Uridine 5' Diphosphate
Signaling Pathways in Macrophages
A mathematical description is
given for the uridine 5'-diphosphate signaling pathway in the RAW 264.7
macrophage, a type of white blood cell that surrounds and kills microorganisms,
removes dead cells, and stimulates the action of other immune system cells. A
comprehensive single-cell mathematical model is developed which includes a
system of nonlinear ordinary differential equations describing the major
pathway components, with an emphasis on the production and degradation of
diacylglycerol, a cellular second messenger molecule which plays an important
role in initiating various changes in cell behavior, including cell activation,
differentiation, proliferation and tumor promotion. Modeling techniques,
challenges, and computational simulations will be presented.
Dr. Jessica Young
Western
State College of Colorado
Love at the Lek: Can
too much sex contribute to extinction?
Dr. Jessica Young of Western State College of Colorado will present her
research and conservation experiences with the Gunnison Sage-Grouse. Dr. Young
studied the behavioral biology and genetics of the Gunnison Sage-grouse in the
late 1980's and 1990's. In 2000, the Gunnison Sage-Grouse were recognized
as a distinct species by the American Ornithological Union from research
conducted by Dr. Young and others. Her presentation will focus on how
behavior may influence speciation, extinction processes, and persistence of
this remarkable bird. In addition, she will discuss current controversies
about its conservation status.
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Jennifer Bartlett
Library Research Techniques for Biomathematics
Join us for an introduction and review of basic
mathematics and biology resources available at MSU Libraries, including
MEDLINE, Biological Abstracts, and more. We'll also discuss effective research
techniques and procedures for requesting hard-to-find materials, as well as
talk about open access journals, a new publishing model for academic research.
Dr. Federica Marcolini
Morphometric
methods to improve fossil rodent biochronology and
continental biostratigraphy
Evolutionary studies with palaeontological data require an accurate sequence of fossil sources. Mammals have long been used for biochronological purposes in Northern Hemisphere terrestrial deposits, and arvicolid rodents in particular have been effectively used to help biochronological ordering of late Neogene and Pleistocene localities. The standard approach to recognise species is sometimes not sufficient and other methods that are able to determine subtle differences in explosively evolving populations are needed. In order to improve the quality of the species identification, new morphometric methods for the analysis of arvicolid first lower molars have been applied (such as decomposition in a Fourier series of teeth patterns as well as Cubic Spline analyses) and a multivariate statistical approach has been used to analyse obtained data.
Todd Schoborg & Ashley Hagan
Microsatellite Analysis of a Polymorphic Population of
Tiger Salamanders, Ambystoma tigrinum
Pedigrees can be extremely useful in understanding particular life history traits in a population of organisms. The Tiger Salamander, Ambystoma tigrinum, which can exhibit two body morphologies, provides an opportunity to examine evolutionary forces acting on both morphologies. Here we attempt to reconstruct a parent/prodigy pedigree using molecular markers within a polymorphic population of A. tigrinum to better understand the long-term fitness consequences for each morph.
Courtney Thomason & Tiffany Hedrick
The Effects of Diet and Social Stress on Humoral and Cell-mediated Immunity in Peromyscus
leucopus
White-footed mice, Peromyscus leucopus, seem to thrive in areas disturbed by humans, such as agricultural fields and residential areas, possibly because left-over seeds and grains in agricultural fields and garbage in residential areas provide ample amounts of high quality food. D iet quality and social stress are two of the main factors that affect the health of animals living in disturbed habitats. We studied the individual and combined effects of poor diet quality and high density situations on stress and immunocompetence in free-born white-footed mice. Our hypothesis was that social stress in the form of high density takes a larger toll on the immune system than a poor quality diet in the form of low protein because P. leucopus regularly experiences stress in the form of low quality diets during the winter. Our goal is to determine which stressor, or which combination of protein and density variables, has a greater effect on the immune system.
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Dr. Sebastian Schreiber
The
Superspreaders
and disease outbreaks
Not all people infected with a disease infect the same number of others. For instance, most people infected with typhoid fever infect no one. However, there are a few individuals like Typhoid Mary who infect scores of others. These highly infectious individuals are called superspreaders. In this talk, I will discuss which diseases are more likely to have superspreaders and how this variation in infectiousness influences disease outbreaks.
Dr. Kate He
Functional Type Diversity Structure in the Naturalized
Flora of
It has been well recognized that community and ecosystem
processes are influenced by the functional types of species, rather than by the
taxonomic identities. In this study, a total of 249 naturalized species from
Dr. Cammey E. Cole
Meredith College
Modeling 4-Methylimidazole: The Effects of Acute and Chronic Exposure
The chemical 4-Methylimidazole (4MI) is used in the manufacture of a variety of pharmaceuticals as well as photographic and agricultural chemicals. The National Toxicology Program is currently investigating the toxicity of 4MI. In support of this study, a physiologically based pharmacokinetic model of the uptake and disposition of 4MI in rats and mice was developed, using a system of nonlinear differential equations, to predict the tissue doses of 4MI resulting from intravenous and oral exposure. The study investigated the effects of both acute and chronic exposure to 4MI. An inverse problem was formulated to determine model parameters that are not available in the literature. The model results are compared to the toxicokinetic data from acute exposure studies and to the data from chronic exposure studies. Numerical results from this work will be presented.
Dr. Steve Cox
Rice University
Inferring Calcium Channel Distribution from Calcium Fluorescence Data
Calcium, the most important of the second messengers, locally modulates the excitability of nerve and muscle. Calcium enters cells through single-protein channels in the cells' outer membrane. We exploit the ability to dynamically monitor cytosolic calcium, throughout intact cells, with sub-millisecond temporal resolution and sub-micron spatial resolution in the construction of a map of channel density. In the process we pose and solve two inverse problems: (1) Infer from the change in cytosolic calcium Fluorescence the associated membrane calcium current in space and time, and (2) Infer from the calcium current the nonuniform distribution of calcium channels. We apply our findings to a nonuniform Morris-Lecar fiber.
Dr. Tim O'Brien
Loyola University
The Mathematical Underpinnings of Applied Statistical Methods
Working with researchers in genetics, medicine, agriculture, and the like, applied statisticians often use statistical and mathematical models to approximate their phenomena in order to help answer important research questions and to help these decision-makers answer their practical queries. This talk underscores and illustrates the mathematical underpinnings of applied statistical methods. A review is first provided of basic statistical methods including one-way ANOVA and simple linear regression, with emphasis placed on the underlying assumptions. A Taylor series expansion next provides a nice method to develop Fisher information and distinguish the popular methods used in estimation and testing. Cochran’s theorem, useful to justify regression and ANOVA methods, is established using the distributions of quadratic forms, and projection matrices illustrate the basic ideas behind simple linear regression. Methods from differential geometry help to understand the differences between linear and nonlinear regression, and to appreciate the differences between the various confidence intervals used in Gaussian nonlinear models. Finally, the measure theory, convexity and abstract algebra (finite geometries and Galois theory) underpinnings of experimental and optimal design theory and methods are also discussed.
Brandon Hale
Biology & Mathematics major
Epidemiology as Related to the Phylogenetic Analysis of the Evolution of the Influenza Virus
The evolution of the influenza virus is characterized by continual changes to its surface structures due to antigenic drift and antigenic shift. The host immune system must alter antibodies in response to the ever-changing virus, allowing for the persistence of influenza in a host population. The spread of related strains through a susceptible population as well as the within-host immune response dynamics are examined, with regard to the strains' phylogenetic distance from an ancestral strain.
Dr. James B. Sickel
Biological Sciences
Analysis of mussel communities in the
The US Army Corps of Engineers is adding a 366 m long
navigation lock at Kentucky Lock and Dam, located at Tennessee River Mile 22.4
in Marshall and Livingston counties,
Dr. Richard L. Boyce
Department of Biological Sciences
Northern
Introducing Fuzzy Set Ordination and How to Combine It
with Spatial Statistics: Why Biologists and Mathematicians Should Care
Dr. Yongzhi Steve Xu
Department of Mathematics
A Mathematical Model of Ductal
Carcinoma in Situ
Ductal carcinoma in situ (DCIS) refers to a specific diagnosis of cancer that is isolated within the breast duct, and has not spread to other parts of the breast. As tumor growth strongly depends upon the availability of nutrients, its diffusion through the growth material is introduced in the description of model. In this talk we discuss a free boundary problem model in a cylinda, a model mimicking the growth of DCIS. The main equation is a diffusion-reaction equation. We study the characteristic stationary solutions of the model, and compare them with the patterns found in DCIS. We also study the evolution solution and the growth of the DCIS. Some inverse problems that relate to diagnose growth tendency of DCIS from biopsy data will also be discussed.
Dr. Christopher Mecklin
Mathematics & Statistics
An Introduction to Bayesian Statistics and an Ecological Application
Most introductory courses in applied statistics emphasize classical statistical methods and pay little to no attention to Bayesian statistics. In my talk, I will give an introduction to the Bayesian paradigm of statistics. In particular, I will discuss recent computational advances and present an ecological application in which Bayesian methods were used to estimate an index of biodiversity.
Dr. Howard Whiteman
Biological Sciences
Evolutionary Ecology of Life History Variation in Tiger Salamanders
Environmentally-cued polymorphisms are found in a wide variety of species and provide ideal systems for testing ecological and evolutionary hypotheses. Facultative paedomorphosis is one such polymorphism in which salamander larvae either metamorphose into terrestrial adults or become sexually mature while still in their larval, branchiate form. Several ecological hypotheses for the production and maintenance of this polymorphism have been modified from the Wilbur-Collins metamorphosis model. A variety of experimental tests of these models have been conducted, yet few field observations are available to evaluate the validity of these results in natural habitats. We tested the predictions of these models by monitoring the fate of larval tiger salamanders, Amybstoma tigrinum nebulosum, over a 13-year period at a series of subalpine ponds in the Colorado Rockies. Larvae that metamorphosed were significantly larger and in better condition than those that became paedomorphic, supporting the “Best of a Bad Lot” hypothesis for the production of the two morphs. Paedomorphs from one pond exhibited earlier reproduction and higher mortality than metamorphs, but across all ponds the two morphs did not differ in survival, age at first reproduction, or growth rates. These and other results suggest that larval growth patterns and the resultant fitness consequences to each morph might be decoupled under some conditions. The ability of ecological models to inform us about evolutionary responses will depend in part on the validity of model assumptions, such as the importance of larval body size to fitness and neutral effects of gender on metamorphosis.
Brandon Hale
Biology & Mathematics major
Numerical Analysis of the Depleting Resources Model
Populations of organisms are traditionally modeled using either the Logistic or the Explosion\Extinction model. While both work fairly well, these models assume that the resources utilized by the population remain constant. However, in reality, resources are almost never kept constant. Previous work by myself, Brian Hale, and Eric Latendresse, led to an analytical model (developed in Maple) which incorporated the decline of a resource by a growing population. Brian and I (along with Lance Harris) have since taken the Depleting Resources Model further, by testing the analytical model against a numerical version written in Matlab. The numerical model utilizes Euler's Method to simulate the growth of an E. coli population and the consumption of glucose by that population. A comparison with the predictions by the analytical model is provided, as well as a comparison to experimental data obtained by Dr. Cann of the University of Leicester, UK.
Dr. Nicole Gerlanc
Biological Sciences
From fieldwork to fitness estimates: an overview of the
statistical processes used to convert mark-recapture
data to a life table
Constructing a life table is a
daunting task. The process begins with extensive field work usually
involving repeated sampling of a population in which individuals are marked at
their first capture and data on subsequent recaptures are used to estimate
everything from individual survival to population size to population
persistence. Our objective for this seminar is to give an overview of the
statistical processes used to convert raw mark-recapture data to a life
table. In addition, an overview of the evolutionary and ecological
questions being addressed with these procedures and some information on the
life history of the organism of interest, the tiger salamander (Ambystoma tigrinum nebulosum), will also be presented. (Joint work with Howard Whiteman).
Brian & Brandon Hale
Biology & Mathematics majors
Model for Depletion of Resources Due to a Growing
Population
The logistic model is a widely used formula that examines the growth and death rates of a species of plants or animals in some environment in which the population can grow until it reaches some stable equilibrium level referred to as the maximum population or carrying capacity. This state of equilibrium is explained by the fact that if the population's birth rate is less than its death rate, then there are not enough resources to support the number of organisms present in the environment. Therefore, the population can never exceed this equilibrium level for an extended period of time. Also, the maximum level acts as a horizontal asymptote, so the population never actually reaches this maximum level.
A major shortcoming with this model is the fact that, for this representation to be true, the resources that the organism relies on must remain at some constant level. For a case in which the resources can be depleted, a more complex model is needed that can account for the decline in resources as the growing population consumes them.
Our group (the two of us along with Eric Latendresse) developed a differential model which examines this case using Maple. The model is parametric in nature, with both Resources and Population dependent upon one another as well as time. A particular solution of the model utilizing data grathered from an experiment using a glucose solution and Escherichia coli bacteria will also be presented.
Dr. K. Renee Fister
Mathematics & Statistics
Optimal Control Applied to Cell-Kill Strategies
The discussion will involve the study of optimal control theory applied to three hypothesis of cell-kill. The object is to determine the optimal drug strategy that minimizes the tumor burden and the drug needed. Mathematical results of existence and uniqueness will be presented. Numerical results will also be discussed.
Brandon Hale
Biology & Mathematics major
Fighting Bacterial Resistance: A Mathematical Model for Antibiotic
Effectiveness
It is known that the effectiveness of an
antibiotic is related to the usage of the drug, as well as the percent
antibiotic resistance in the bacterial population being fought. Bacterial
resistance genes carried on a plasmid can be transferred from parent to
offspring (vertical transfer) as well as from a resistant cell to a
non-resistant cell (horizontal transfer). I shall present a mathematical
model which can be used to minimize the rate of horizontal transfer while also
minimizing the amount of time that the infected person is sick.
Dr. Hem Raj Joshi
Optimal Control Applications in Mathematical Biology
We will talk briefly about the optimal control for ODE's and PDE's. As an application, we will give preliminary report on fish model.
In this model, we find an optimal harvesting strategy in a fish population modeled in a parabolic setting (PDE model) with logistic type growth term and a Dirichlet boundary condition in a multidimensional bounded domain. The harvesting term is the control and our goal is to maximize the profit. We discuss the existence and characterization of an optimal control and derive the optimality system. This problem is linear in control. The talk will conclude with a numerical illustration.
Dr. Terry Derting
Biological Sciences
Can we model impacts of environmental stressors on
health?
A variety of anthropogenic disturbances, including urbanization, agriculture, and habitat fragmentation, are likely to impose stress on animal populations. Increased stress is associated with reduced immunocompetence resulting in increased occurrence and transmission of infections and disease. I will discuss the results of current research on the impacts of two anthropogenic disturbances on the health of a small mammal species, the white-footed mouse, which is a carrier of diseases that impact humans. From these results it may be possible to develop a probability model that predicts the health of white-footed mouse populations in terms of landscape variables. Such a model may, in turn, be used to predict the relative risk that humans incur as a result of proximity to white-footed mouse populations.
Dr. Maeve L. McCarthy
Mathematics & Statistics
Identification of a time dependent parameter in a soil
column study
Soil column studies are used frequently in seeking to understand
the behavior of a particular contaminant in a saturated homogeneous soil of a
given type. The concentration of the contaminant is modelled
by a parabolic partial differential equation. We seek to identify the sorption partitioning coefficient as a function of
time from limited boundary data. We discuss an output least squares formulation
with Tikhonov regularization. We also use a mass
balance law to determine the initial value of the partitioning coefficient.
This is joint work with K. Renee Fister (