analysis of tiger salamander (Ambystoma tigrinum nebulosum)
survival based on body size and other co-variates.
Brown and Adam Kiser
Murray State University
Abstract: Polyphenisms occur when populations exhibit alternative, discrete phenotypes in response to environmental variation, and are examples of phenotypic plasticity. This phenomenon is thought to be adaptive because it allows quicker response to environmental shifts than those that are genetically fixed. However, few studies have quantified the fitness consequences of polyphenisms. Ambystoma tigrinum nebulosum (Arizona Tiger salamander) inhabits montane ecosystems throughout Colorado, Utah, Arizona, and New Mexico. This species is polyphenic, in that genotypic variation coupled with environmental stimuli trigger two distinguishable adult forms (metamorphic and paedomorphic), which is termed facultative paedomorphosis. Using a capture-recapture database started in 1988, we analyzed survivorship of the Mexican Cut population to test hypotheses about how survival, one component of fitness, varies within this population. MARK was used to estimate survivorship of the salamanders based on parameters such as sex, morph, and size. To incorporate size, we used the ratio of mass to snout-vent length defined as body condition, which was categorized into four size classes. We found that the medium size class had lower survival than other size classes, irrespective of morph, and that neither morph nor sex appears to have a major impact on survival.
modeling tropical termite nest growth rate in relation
to external temperature variations.
Darling and Kayla Stringfield
Murray State University
Design of Incentive Payment Programs for Biodiversity
The classic Lotka-Volterra model for two species in competition is the
basis of a range of results about networks of competing species of
arbitrary size. A review of theoretical and numerical results
gives the impression that coexistence is difficult to achieve.
We give a criterion for stable coexistence of N competing species, and
discuss its implications for the underlying network structure.
Design of Incentive Payment Programs for Biodiversity
University of Tennessee, Knoxville
Governments and conservation organizations invest billions of dollars
each year in habitat conservation. I examine a commonly used
investment strategy in which private landowners are paid to enhance
conditions for biodiversity. I evaluate whether existing payment
programs provide conservation benefits cost effectively and how they
could be improved. I also assess whether alternative designs for
payment programs being promoted in conservation writings are likely to
work for biodiversity.
in a Biological Context: Optimization across the Biological
Professor Louis J. Gross
Directior of the National Institute for Mathematical and Biological Synthesis, University of Tennessee, Knoxville
central concepts in biology involve notions of what is "better" or
"best" in the context of evolution, physiology, and behavior.
Similarly, in many applied areas of the life sciences, we are
concerned with developing a "best" method to carry out drug therapies,
resource harvesting, pest management, and epidemic control. I will
discuss, with audience participation, what it might mean to be "best"
for several problems at different levels of the biological hierarchy.
This includes being clear about differences between maximization and
optimization, and taking account of constraints, historical and
others, on biological systems. Finally, I will discuss notions of
optimal control in biology.
Ordinary Differential Equation Model of Wound Healing.
Virginia Commonwealth University
healing is a concern across many branches of medicine. During many
medical procedures, from a planned surgery to an emergency treatment,
the wound healing process is triggered. When the native biological
processes are incapable of healing the wound, treatment options are
limited. In order to improve patients’ outcomes, there is a need to
develop better methods of identity wounds that are at risk of becoming
chronic and to identify more effective treatment options for these
wounds. It has been shown that altering the levels of systemic
hormones such as estrogen and cortisol impact healing outcomes. This
model is used to identify and test new treatment methodologies for
healing dermal wounds in the presence of these systemic mediators.
Models and Wildlife Management: Modeling Black Bear and Feral
Hog Control Strategies in the Southern Appalachians.
Appalachian State University
explicit, individual‐based models (IBMs) simulate the life history of
individuals on a GIS landscape. The spatial and demographic
capabilities of IBMs can provide unique insight into the management of
wildlife populations. This talk will focus on black bears and feral
hogs in the southern Appalachians, focusing on Great Smoky Mountains
National Park (GSMNP). In this region, both species’ population
dynamics are driven by fall hard mast variation. I will use an IBM
that incorporates fall hard mast to evaluate harvesting strategies for
minimizing potential bear‐human interactions in the southern
Appalachians and controlling the spread of pseudorabies in feral hogs
production in freshwater invertebrates: Species identification
using signal processing.
Murray State University
plays an important role in the communication of many terrestrial
insects such as cicadas, grasshoppers, and katydids. But, little is
known about auditory communication in aquatic invertebrates, though
several studies have documented it. Nevertheless, documentation of
communication between freshwater macroinvertebrates in underwater
environments is extremely rare.
We are currently using a hydrophone and field recorder to listen to aquatic invertebrates under both laboratory and field conditions. Several specimens have yielded extensive vocalizations across a wide range of frequencies. Many beetles and true-bugs all produce vocalizations that can be differentiated by ear. Video recordings and observations suggest that these vocalizations are primarily used as intraspecies communication and alarm signaling.
This is the first time aquatic invertebrates have been documented calling under the water’s surface and we hope to describe these sounds, behaviors, and the mechanisms by which they are produced. We have developed a library of sounds and use the Fast Fourier Transformation to convert recorded calls from the time domain to the frequency domain. We have developed simple coding using Matlab to process each call and subjectively select species specific characters. These methods have been tested in the laboratory, mesocosms, and in situ to differentiate species of macroinvertebrates with up to 95% accuracy. We are interested in exploring new ways these vocalizations could be used in identifying closely related species and in the application of the biomonitoring of our freshwater ecosystems.
the Impact Antibiotic Resitance in Gram-Negative Bacteria.
Mary Ann Horn
National Science Foundation & Vanderbilt University
Abstract: Drug resistance has been an emerging problem since the discovery of penicillin. Resistance is now seen not only in clinical settings, but also increasingly in the community. Bacteria such as methicillin-resistant Staphylococcus aureus (MRSA) impacts healthy adults as well as patients in settings such as hospitals and nursing homes. MRSA is an example of a Gram-positive bacteria. More recently, antibiotic resistance in Gram-negative bacteria such as Escherichia coli and Salmonella aureus is an increasing problem. A primary difference between Gram-positive and Gram-negative bacteria is the composition of the cell walls. Gram-negative bacteria can become resistant to antibiotics through a genetic mechanism, granting them immunity to a wide range of treatments. This talk will give an overview of some of our recent work on modeling of the development and spread of antibiotic resistance. Mathematical modeling and simulation are used to gain insight into the numerous issues that arise, both in terms of the development of resistance and the spread of the bacteria. (Joint work with Erika D'Agata, Joanna Pressley, Shigui Ruan, and Glenn Webb.)
of Animal Groups: The Importance of Communication.
Gerda de Vries
University of Alberta
Abstract: We investigate the formation and movement of self-organizing collectives of individuals in homogeneous environments. We review a hyperbolic system of conservation laws based on the assumption that the interactions governing movement depend not only on distance between individuals, but also on whether neighbours move towards or away from the reference individual. The inclusion of direction-dependent communication mechanisms significantly enriches the model behavior; the model exhibits classical patterns such as stationary pulses and traveling trains, but also novel patterns such as zigzag pulses, breathers, and feathers. The same enrichment of model behavior is observed when we include direction-dependent communication mechanisms in individual-based models.
of amphibian locomotion: from hatching through metamorphosis.
Murray State University
Abstract: Metamorphosis is an awkward period of rapid development. In frogs, this transition includes a switch from swimming like a tadpole with the tail to swimming and jumping and climbing with the limbs. During metamorphosis the tail is resorbed while the limbs are still growing and developing. During this process, the organism is vulnerable to predators because neither the larval nor the adult forms of locomotion are fully functional. This talk explores the development of swimming in salamanders to see how metamorphosis affects an amphibian that retains the tail throughout life. This talk will also explore how the larval density environment affects size at metamorphosis and the development of jumping and climbing performance in red-eyed tree frogs. The development of locomotion is a critical feature of a complex life cycle. Studying the developmental patterns of locomotion gives us insight into both organism-level constraints and adaptations to the predation environment
approaches to estimating population-biology parameters in
College of Charleston and Grice Marine Lab
interesting characteristics of ecological populations are impossible
to observe directly, either because they are rare or because they are
just difficult to measure under field conditions. A large part
of the field of molecular ecology is devoted to using patterns of
genetic diversity to indirectly estimate these parameters in the
context of a population-genetic model. Unfortunately, the
restrictive and unrealistic assumptions of models that relate genetic
diversity to ecology have the potential to seriously bias ecological
estimates. In this presentation, I will 1) describe the general
problem outlined above, 2) describe two types of general genetic
simulation modeling approaches to mitigate the problem, and 3) apply
these approaches to two case studies.
In the first case study, I will show how agent-based simulations of spatial population dynamics and associated population genetics in invasive back cherry (Prunus serotina) populations can be used to estimate the mode and tempo of relatively rare long-distance dispersal events. In the second, I will show how both agent-based and coalescent simulations can be used to test whether individual loci are under selection in natural populations of the estuarine fish,Fundulus heteroclitus.
The Dynamics of Sleep
Ohio State University
Abstract: To sleep "like a baby" means to sleep peacefully and soundly. Yet parents often observe that their infant's sleep has frequent interruptions and perhaps a short sleep-wake cycle; statistical analysis confirms that infant sleep and adult sleep have different dynamical structures. Perhaps it is the prevalence of chronic sleep disorders that has adults looking back wistfully at sleeping babies. Compounding the difficulty of managing a sleep disorder is the news that disruptions in normal sleep-wake activity have been associated with many long-term health consequences. I will discuss what is known about the biological basis of sleep including controversies in the field. I will then show how mathematical models, both deterministic and stochastic, help us to understand sleep-wake rhythms from newborns to adults while also yielding insights into some sleep disorders.
Is There Evidence of
Trade-offs in Cognitive Ability and Parasitism in Adult
White-footed Mice (Peromyscus
Murray State University
A mathematical approach
to polyphenisms in Ambystoma
Morgan Geile and Jeffrey Young
Murray State University
multiple populations, and confounded data: An adventure in
modeling as a tool for untangling complex data, success and
Mississippi State University
will discuss the time line for this project, false starts and
successes in using data of CO2 concentration in a vessel to determine
the action of
1. a small leak in the vessel
2. the out gassing of CO2 when soil in the vessel has water added.
3. The production of CO2 of one class of microorganism .
4. The sequestration of another class of microorganism.
This talk assumes a knowledge of ordinary differential equations, the trapezoid rule for numerical quadrature, and the idea of minimizing least square error for parameter identification.
BioMaPS Faculty, Present and Past Fellows
Murray State University
populations of a tropical forest herb using vital rate-based
stochastic matrix modeling
Murray State University
Abstract: To what extent do populations of organisms naturally vary across the landscape? What if humans have fragmented that landscape? Stochastic sensitivity analysis is a powerful way to answer these demographic questions. Despite its usefulness for both basic and applied ecology, this technique remains uncommon because it is analytically intensive and requires robust, long-term datasets. I will present findings from my recent 11-year study from a fragmented Amazonian landscape using 10 populations of an understory herb (Heliconia acuminata). I found substantial variation among populations in continuous forest habitat, but no clear distinction between those and populations growing in forest fragments.
MSU Libraries and
Murray State University
Murray State University
Terry L. Derting
Murray State University
Mathematical Models of
Leukemia, Cancer Stem Cells, and Drug Resistance
University of Maryland
Abstract: Leukemia is a cancer of the blood that is characterized by an abnormal production of white blood cells. Traditional approaches for treating leukemia combine chemotherapy, radiotherapy, and bone marrow (or stem cell) transplants. The treatment of Chronic Myelogenous Leukemia (CML) was revolutionized over the past decade with the introduction of new molecular-targeted drugs. Unfortunately, these drugs keep many patients in remission but do not cure the disease. In this talk we will present our proposal for improving the treatment of CML. Our main idea is to boost the anti-leukemia immune response by providing timed cancer vaccines in intervals and doses that are adjusted to the individual immune response of each patient. We will also discuss our recent work on mathematical models of cancer stem cells and their role in developing drug resistance. When combined with clinical and experimental data, our mathematical analysis of drug resistance provides new insights on how to approach treating CML. This is a joint work with Peter Kim, Cristian Tomasetti, and Peter Lee.
into Cancer Therapy
Trachette L. Jackson
University of Michigan
Abstract: As a group of genetic diseases, cancer presents some of the most challenging problems for basic scientists, clinical investigators, and practitioners. In order to design treatments that are capable of abating invasive tumor growth, it is necessary to make use of cross-disciplinary, systems science approaches, in which innovative theoretical and computational cancer models play a central role. The goal of this talk is to demonstrate how combining mathematical modeling, numerical simulation, and carefully designed experiments can provide a predictive framework for better understanding tumor development and for improving cancer treatment. In particular, a mathematical model designed to predict the effect of a novel anti-cancer therapy aimed at destroying tumor blood vessels will be presented and experimentally validated.
Testing the Correlation
between Species Diversity and Productivity among Global
Ecoregions, Realms, and Biomes
Kate S. He
Murray State University
Abstract: Considerable amount of research on the relationships between species diversity and productivity at different spatial, ecological, and taxonomic scales has been conducted. However, the overall trend of the correlation at the global scale still remains sketchy and the causal relationship between species diversity and productivity needs further exploration. This is especially true with beta diversity since most studies carried out use alpha diversity as the general term for species diversity. In this study we use the MODIS NDVI as the surrogate of productivity, and the WWF ecoregion systems and its species distribution information to test correlations between beta diversity and differences in productivity at various taxonomic ranks on a global scale. Matrix correlation is performed between species composition measured as beta diversities using Sřrensen similarity index and MODIS NDVI/productivity measured as Bhattacharyya distances through Mantel permutation tests. The correlation coefficients and Mantel test significance levels are reported at the global ecoregion, biogeographical realm, and biome levels respectively. Significant correlations are found at all three taxonomic ranks. Results from realm and biome tests suggest that the highest correlations are reached at the temperate regions when species rank is used. Our findings suggest that species' natural spatial boundaries, such as the biogeographical realms or biogeographic kinship play a critical role in shaping the correlation patterns between beta diversity and productivity differences at the global scale.
Energetic Cost of Innate
and Adaptive Immune Response in Old-field Mice (Peromyscuspolionotus)
Callie Wilson and Erin Keeney
Murray State University
Abstract: Reproductive success is essential to the survival of any species of organisms, and to ensure that those organisms live through successive reproductive cycles, they need a properly functioning immune system. It is believed that during an immune response trade-offs in energy use can occur between different branches of the immune system and between the immune system and other physiological processes. The assumed high cost of the immune system is the proposed cause of these trade-offs. Our goal was to quantify the cost of the immune system to test this assumption. We tested the following null hypotheses: 1) an ongoing humoral immune response has no effect on the development of a cell-mediated immune response and 2) presence of an adaptive immune response has no effect on the innate immune system. We used thirty adult male old-field mice, Peromyscuspolionotus, and randomly assigned ten mice to three groups: control (Ct), cell-mediated (Cm), and cell-mediated/humoral (CH). The CH group was challenged with dinitrofluorobenzene (DNFB) to elicit a cell-mediated response and sheep red blood cells (SRBC) to induce a humoral response. The Cm group was only administered DNFB and the Ct group was not exposed to either DNFB or SRBC. We measured the energetic cost and strength of the immune responses through analysis of daily metabolic rate (DMR), resting metabolic rate (RMR), red and white blood cell counts, pinnae measurements, hemagglutination assays, and bacterial killing assays. The research will contribute to our understanding of how and to what extent immune function may affect other physiological systems.
From Field to Lab: An
Overview of Salamander Population Studies and Genetic Analysis
Morgan Geile and Jessica Whitaker
Murray State University
Abstract: Phenotypic plasticity is a phenomenon that affects many organisms. To explore the costs and benefits of such plasticity, we examined facultative paedomorphosis in salamanders, in which individuals can exhibit one of two distinct adult morphs as a result of environmental and genetic cues. Facultative paedomorphosis is exemplified by the species used in this study, Ambystoma tigrinum nebulosum (tiger salamanders) and Ambystoma talpoideum (mole salamander). Both metamorphic (terrestrial) and paedomorphic (gilled/aquatic) adult forms occur within the populations found around our study areas Land Between the Lakes and the Mexican Cut, CO. To study the interactions of salamanders adapting to their environment, ecological data has been collected in the field and genetic analysis has occurred in the laboratory. Morphological and life history measurements of salamanders were recorded, and a separate study was conducted to examine the effects of body size on behavioral thermoregulation in one species. Our laboratory work was designed to determine the fitness consequences of facultative paedomorphosis. Microsatellite markers are being developed to assign parentage in order to better understand the costs and benefits of paedomorphosis. In optimizing 8 different primers, we found that microsatellite loci were polymorphic, producing 2-9 alleles. We are continuing to evaluate the variability of different primers for parentage assignment, in order to determine the number and types of progeny the different morphs produce. The results of this study will be used to better understand both the ecology of these two species, and the evolutionary costs and benefits of phenotypic plasticity.
Using matrix analysis to
model the spread of an invasive plant, Alternanthera
Samantha Erwin and Aron Huckaba
Murray State University
Abstract: Alternanthera philoxeroides, more commonly known as alligator weed is an invasive specie indigenous to South America. With its alarming invasion of south east United States water ways, understanding its invasiveness of this plant species is both important and imperative. Utilizing experimental growth data obtained over the summer of 2010 matrix analysis is used to precisely model the growth of alligator weed. These matrices are population projection models which represent the growth rate of alligator weed in its different stages of the life cycle. A high growth rate is a key feature of successful invaders. Currently, Monte Carlo simulations are used to predict the patterns of future growth based on derived population projection matrices. The results of the matrix analysis can reveal the respective contributions of demographic components at different stages to its overall success as an invader.
An Introduction to
Zero-Inflated Probability Distributions
Murray State University
Abstract: It is common in many applications, included but not limited to ecology, to model count data. A natural choice is to use standard probability distributions such as the Poisson or negative binomial. Unfortunately, real data are often not well fit by these distributions since zero counts can be more common in practice than would be predicted. To address this issue, zero-inflated distributions are becoming more prevalent in statistical analysis. I will define what these distributions are and give a few examples of their use with data from ecology and environmental chemistry.
Dysfunctional families in
the insect world
Joan M. Herbers
The Ohio State University
Abstract: Many ant colonies have complex family structure, which can set up conflicts of interest among the colony members. A prime example is that the ant queen and the workers have different genetic relatedness to their nestmates. I have been studying the ultimate dysfunctional families, in which one species of ants takes over the social machinery of another species. These “pirate ants” have tightly co-evolved with their host species, and in my talk I will show how we can study the relationship by genetic analysis and simple mathematical modeling.
in sturgeon and respiration in salamanders
James Andrew DeWoody
Abstract: Modern pyrosequencing has the potential to uncover many interesting aspects of genome evolution, even in lineages where genomic resources are scarce. In particular, 454 pyrosequencing of nonmodel species has been used to characterize expressed sequence tags, xenobiotics, gene ontologies, and relative levels of gene expression. In this talk, I illustrate the use of pyrosequencing to study the evolution of genes expressed in the gonads of polyploid lake sturgeon (Acipenser fulvescens) and in the respiratory organs of tiger salamanders (Ambystoma tigrinum).
Around in Circles to Climb Trees: Some Algebraic and Geometric
Aspects of Phylogenetic Reconstruction Using BME
Terrell L. Hodge
Abstract: A central problem in molecular systems biology is the reconstruction of the evolutionary relationships between organisms or genes, starting from observed or experimental data, such as an alignment of DNA sequences. Pictorially and mathematically, these evolutionary relationships are often captured by certain graphs, the phylogenetic trees, whose set of leaves X corresponds to the given taxa or DNA sequences, and whose branch lengths represent some form of evolutionary distance. Mathematically, phylogenetic tree reconstruction becomes the problem of recovering an entire tree given only the pairwise distances d(x,y) between any two leaves x,y in X. Minimum evolution methods for phylogenetic tree reconstruction consider tree shapes corresponding to a fixed set of leaves X, and then minimize total tree distance over these possible tree shapes, using some estimate of branch lengths. In this talk, we will consider some of the theory of one of these minimum evolution methods, the balanced minimum evolution method (BME). In BME, the total tree distance can be elegantly expressed via sums in the pairwise leaf distances d(x,y), by making use of the combinatorics of so-called circular orderings for a tree. These orderings can be neatly visualized in terms of polygons, and, moreover, the BME approach yields a geometric reformulation of aspects of tree reconstruction in terms of certain higher dimensional analogues to polygons, the BME polytopes.
November 9, 2009
A mathematical model for cholera
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.
October 26, 2009
Redwoods of the Reef: Modeling individuals and populations of the giant barrel sponge Xestospongia muta
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.
October 16, 2009
Biostatistics at UAB
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.
September 28, 2009
Evaluation of Microsatellites in Ambystoma tigrinum nebulosum
Phenotypic plasticity is the ability of a trait to change in response to an environmental cue.Â 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.Â Previous research has revealed the mechanisms that produce this polymorphism; however, little is known about the evolutionary mechanisms that maintain it.Â By studying the fitness consequences of facultative paedomorphosis, we can better understand the evolution of this polymorphism.Â 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.Â As a first step, we evaluated polymorphism using previously designed Ambystoma microsatellite markers in spotted salamanders ( Ambystoma maculatum ).Â Tissue samples of 55 salamanders were collected from a local population and DNA was amplified using PCR to assess microsatellite variability.Â 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.Â Because of their dependence on water, amphibians are extremely susceptable to chemicals used in agriculture.Â 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.Â However, an equal amount of studies have concluded that agricultural chemicals and livestock disturbance have a negative impact on amphibian diversity.Â 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 branchesâ€™ responses and overall energy allocation.
September 14, 2009
Judy Day , Mathematical Biosciences Institute, Ohio State University
inflammatory response and the mathematical approaches used to
understand & control it
The inflammatory response and the mathematical approaches used to understand & control it
day our bodies are bombarded by foreign microbes that we inhale or
ingest; and every day our immune system works to eliminate them,
orchestrating an amazing response consisting of numerous cell types
and molecules. This is known as the acute inflammatory response.
Sometimes this response is not even noticeable to the host and other
times not only are the effects (e.g. fever, headaches, elevated heart
rate) clearly felt, it is possible that the immune response is not
capable of effectively resolving the conflict. Consequently, in order
for therapies and vaccines to be effectual, it is necessary to have a
good understanding of the way in which disease causing agents
(pathogens) interact with a host's defense system. In addition,
modulating the inflammatory response is also an important goal and has
become a key focal point in the treatment of critically ill patients.
Mathematical modeling and the application of control methodologies are
tools that can be used to try to understand and modify this complex
process. This talk will discuss some of the work in this area,
highlighting the mathematical approaches used and some interesting
mathematical questions that have come up along the way.
Every day our bodies are bombarded by foreign microbes that we inhale or ingest; and every day our immune system works to eliminate them, orchestrating an amazing response consisting of numerous cell types and molecules. This is known as the acute inflammatory response. Sometimes this response is not even noticeable to the host and other times not only are the effects (e.g. fever, headaches, elevated heart rate) clearly felt, it is possible that the immune response is not capable of effectively resolving the conflict. Consequently, in order for therapies and vaccines to be effectual, it is necessary to have a good understanding of the way in which disease causing agents (pathogens) interact with a host's defense system. In addition, modulating the inflammatory response is also an important goal and has become a key focal point in the treatment of critically ill patients. Mathematical modeling and the application of control methodologies are tools that can be used to try to understand and modify this complex process. This talk will discuss some of the work in this area, highlighting the mathematical approaches used and some interesting mathematical questions that have come up along the way.
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.
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
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
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.
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.
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.
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.
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.
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
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.
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
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
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.
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.
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.
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.
Dr. Sebastian Schreiber
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
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
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
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.
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
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
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
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.
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
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.
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
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 (