Biomathematics Seminar – Abstracts
October 9, 2006
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.
September 25, 2006
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.
September 11, 2006
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.
April 17, 2006
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
March 6, 2006
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.
February 6, 2006
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.
October 31, 2005
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.
September 12, 2005
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.
March 30, 2005
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,
March 14, 2005
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
February 28, 2005
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.
January 24, 2005
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.
November 8, 2004
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.
October 4, 2004
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.
April 29, 2004
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).
April 8, 2004
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.
March 25, 2004
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.
March 4, 2004
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.
February 23, 2004
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.
February 19, 2004
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.
January 29, 2004
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 (