Abstracts of the talksKassie Archer: Fractal Dimension of Strange Attractors Associated with One-Island Migration Model
Meghan Fitzgerald, Jenny Celin, Jenny Yang: Modeling Stealing Behavior in a North Carolina Dung Beetle
Rachel Fovargue: Integration of Source and Sink Dynamics into Habitat Equivalence Models
Sarah Fox: Interactions between Staphylococcus aureus and Psuedomonas aeruginosa in the Presence of Aminoglycosides
Yair Goldberg: On Methods of Calculating Zeros of the Derivatives of the Riemann Zeta Function
Robert Gove: The resource allocation game: modeling strategies in Arabidopsis lyrata with trait networks
Jana Hartman: Calcium sparks and calcium homeostasis in a minimal whole cell model
Roumen Iordanov: Mathematical Analysis of Voting Systems
Nathan Ross, Miranda Hayworth: Social Apoptosis in Honeybee Colonies
Matthew Wilhelm: The Mating Game: A Game Theoretic Analysis of the Mating Sign Behavior in the Honeybee
Niha Zubair: Reproduction Rate Strategies in White-Footed Mice
Abstract: Fractal dimension is a value associated with an attractor of a map or model that provides us one way of measuring the chaotic behavior of the system. In biological systems, the dimension can give some indication of “demographic and genetic variability”. The one-island migration model is a 2-dimensional discrete map that was developed by Jim Selgrade of NCSU and James Roberds of the USDA Forest Service to measure allelic variability in a population with migration and in some instances, density dependence. The methods for computing box-counting dimension can be applied to measure the dimension of strange attractors associated with the one-island migration model. I will also talk about some limitations of fractal dimension, some of the difficulties that can arise in computation for certain parameter values, and how we can try to overcome these.
Modeling Stealing Behavior in a North Carolina Dung Beetle
Meghan Fitzgerald, UNCG, Greensboro, NC
coauthored by Jenny Celin, UNCG, Greensboro, NC, and Jenny Yang, UNC, Chapel Hill, NC
mentored by Dr. Mary Crowe and Dr. Jan Rychtář
special thanks to Dr. Mark Broom, University of Sussex, Brighton, UK
Abstract: Forming a brood ball is a necessary but energetically costly reproductive endeavor for the dung beetle Onthophagus taurus. As a way of increasing individual fitness and decreasing time and energy spent on reproduction, certain females have been shown to steal the brood balls built by others and place their own egg inside, a behavior known as brood parasitism. Under certain conditions, this can increase the amount of brood they are able to produce throughout their lifetime. Using previous models of kleptoparasitic behavior and empirical data collected on our model organism, we have developed a deterministic model of this behavior. Our model incorporates stealing and guarding, as well as typical behaviors such as resting, searching for dung or a brood ball, preparing, and laying. We will present the model and behavior strategies, namely Hawk and Marauder, as Evolutionary Stable Strategies.
Abstract: We have been working to develop a model of metapopulation interactions of non-mirgratory birds. We’ve incorporated the idea of an invisible contaminant in one population, creating a sink, with surrounding healthy environments representing source populations. We are currently examining the application of this model into Habitat Equivalency Analysis models so as to include this aspect of surrounding habitat losses through metapopulation interaction, instead of the typically utilized single site evaluation.
Interactions between Staphylococcus aureus and Psuedomonas aeruginosa in the Presence of Aminoglycosides
Sarah Fox, The College of William and Mary, Williamsburg, VA
mentored by Dr. Meagan McNulty, Dr. Mark Forsyth
Abstract: This project investigates the interactions between opportunistic pathogens Staphylococcus aureus and Pseudomonas aeruginosa in the presence of the antibiotic tobramycin. Bacterial infections are common in the human respiratory system, and especially persistent in Cystic Fibrosis (CF) patients. Staphylococcus aureus and Pseudomonas aeruginosa are frequent colonizers of the CF respiratory system. Tobramycin is one of the main antibiotics used to treat pseudomonal bacterial infections. However, when these species are cultured together, P. aeruginosa produces an anti-staphylococcal toxin, 4-hydroxy-2-heptylquinolone-N-oxide (HQNO). In order to survive this toxin, S. aureus develops into a form referred to as the small colony variant (SCV). SCVs are unable to take up tobramycin and hence become resistant. In addition, P. aeruginosa forms biofilms in the presence of tobramycin. The goal of this project is to create a model of these interactions and produce experi mental data to incorporate into the model in hopes of identifying the biological conditions under which it would be effective to use tobramycin.
Abstract:Considering how much is known about the zeros of the Riemann Zeta Function, it is surprising how little we know about the zeros of its derivatives. We will discuss some methods that can be used to approximate the zeros of these functions.
Abstract: We are conducting studies using the rock cress plant, Arabidopsis lyrata, as a model organism to understand resource allocation between growth and maintenance vs. current reproductive output. We choose A. lyrata because it is a sister of the well-studied model plant A. thaliana, and its genome is being sequenced. Moreover, unlike A. thaliana, A. lyrata is a perennial with extensive variation in resource allocation strategies. We have constructed a hypothetical trait network model to generate simulated data sets, and our goal is to determine how different genetic mechanisms affect trade-offs between growth and reproductive traits and how genetic variation in these mechanisms would result in different resource allocation strategies through their effects on the trait network. Using SAS we are able to compare correlations among traits in our model to correlations among traits from field data to verify the validity of our model. We are conducting further growth chamber studies to collect more data for comparison to the network model. The eventual goal is to predict the functions of genes that underlie variation in the trait networks.
Abstract: Calcium concentration is an important cellular signal, particularly in muscle cells such as cardiac myocytes. In calcium-overloaded cardiac myocytes, clusters of calcium-regulated intracellular calcium channels on the membrane of the endoplasmic reticulum (ER) spontaneously open in a cooperative fashion and release calcium from the ER (a phenomenon known as calcium puﬀs or sparks), and on a slower time scale this calcium is resequestered by SERCA-type pumps. I will show how calcium release sites can be modeled as a collection of interacting continuous-time Markov chains. By constructing a whole cell model of calcium homeostasis under the assumption of a large number of release sites, we are addressing how spontaneous puﬀs/sparks contribute to the ER-to-cytosol ”leakage” ﬂux.
Abstract: Given the growing importance of presidential elections, statistical analysis is becoming more and more prominent in the mainstream. Much of the electoral data and concepts can be, and have been, modeled mathematically. This project's goal was to make mathematical models for the election processes of two European countries, Austria and Bulgaria. The Banzhof Power Index was calculated, and the mathematical "fairness" of the two systems was compared, based on Arrow's conditions for a fair election. Ultimately, the European electoral systems were compared to the system of the United States, from a mathematical perspective.
Abstract: Cellular apoptosis, a type of programmed cell death, is one of the most important processes for multicellular organisms to regulate development and maintain homeostasis. It allows an organism to safely dispose of malfunctioning or surplus cells, preventing harm to the surrounding tissue. Social insect colonies are highly integrated units that can be compared to a super-organism. Individual workers can be regarded analogous to individual cells. It is known that workers kill themselves for the benefit of the colony if they can fulfill an essential function (e.g. colony defense). However, it is unknown whether workers would undergo apoptosis if their presence is harmful to the colony. Thus, the purpose of our project was to analyze the mathematical conditions in which apoptosis should occur and to biologically test whether apoptosis does occur, as predicted by the models. So far, our modeling and experimental approach have focused on sick workers that could harm their colony by spreading disease. In our experiment, foragers of the same age were removed from a colony and divided into one control and two treatment groups. The first treatment group was fed with Hydroxyurea, while the second one was anaesthetized with carbon dioxide for two hours. Both treatments resulted in significant mortality and may simulate serious illness. Afterwards, the workers were introduced back into the colony and differences in behavior between the control and treatment groups were observed. Mathematically, this context was explored with cost-benefit analysis utilizing an epidemiological model to explore the circumstances in which it is beneficial from the perspective of the colony for an infected individual to commit suicide (“social apoptosis”).
Abstract: The honeybee, Apis mellifera , exhibits extreme polyandry. After insemination, the male (drone) plugs the queen's genital opening with his endophallus, known as the mating sign. This leads to his immediate death and has been shown to promote additional mating of the queen, casting doubt on the adaptiveness of this behavior: the drone forgoes the chance of future mating and effectively dilutes his genetic contribution to the next generation. On the other hand, the mating sign may be beneficial because it increases the genetic variability of the queen's offspring and greater genetic variability increases colony fitness. With the analysis of this phenomena in mind, we constructed a game theoretic model in order to describe this situation. Using this model, the evolutionary stability of the drone's choice "to plug" or "not to plug" was investigated. Finally, we conclude that the drone's behavior is not adaptive based on data obtained from recent studies.
Abstract: A photoperiod is the measure of the length of daylight each day. This value can potentially determine the behavior and/or biological processes of many species of animals and plants. Peromyscus leucopus (white-footed mouse) responds to changes in photoperiods by altering its reproductive strategies. P. leucopus adjusts reproduction rates due to the high cost of reproduction in the winter and in short photoperiods. In our research we have looked at two groups of mice: Responsive mice (R) which reproduce in warmer months and Non-responsive mice (NR) which reproduce all year around. Interestingly, in Williamsburg, VA there exists a mixture of R and NR mice. The coexistence of these two types of mice suggests some kind of genetic variation. We have created a nonlinear discrete population model to better understand the requirements for the co-existence of the two varying phenotypes. By implementing computer based numerical analysis techniques, we can observe invarian t behavior in our model, such as equilibrium points and periodic orbits. Data such as this can help determine the eventual behavior of the mouse population.