Department of Mathematics and Statistics

NSF Math-Bio Undergraduate Fellowship

Research Projects

The primary goals of our project are to generate new knowledge at the interface of mathematics and biology and to provide an integrated bio-mathematical research opportunity for undergraduate students at the University of North Carolina at Greensboro (UNCG). Each year, eight students, in two teams of four will work in close collaboration with faculty members on specific research projects. The choice of the project will be determined by the interest of the majority of participants. Please click on a faculty member's name to read more about their research project.

Dr. Sat Gupta, Dr. Mary Crowe

Randomized Response Models for Medical Sciences

There are many situations in the medical field where the information to be collected is of sensitive nature. In these situations, there is a greater danger of respondent bias which must be eliminated in order for the policy makers to implement effective disease control programs based on accurate estimates of prevalence and extent of undesirable behavior in a population. An important data acquisition technique that is found to be very effective in such situations is the Randomized Response Technique (RRT). Randomized response models were introduced by Warner (Journal of the American Statistical Association, 1965) to circumvent response bias among survey respondents when faced with confidential or incriminating questions in face-to-face interviews. These models allow a respondent to provide a scrambled response using a researcher provided scrambling device where by the researcher can unscramble the response at the aggregate level but not at the individual level.

RRT models have been used quite extensively in health sciences. Cross et al. (Preventive Veterinary Medicine, 2010) have used these models to obtain sensitive information on animal disease prevalence. Lara et al. (Sociological Methods Research, 2004) have used these models to estimate the prevalence of induced abortions in Mexico. Volicer and Volicer (Journal of Studies on Alcohol and Drugs, 1982) have used these models to estimate the link between daily use of alcohol and higher noncompliance in taking prescribed medicines for hypertension. This is one of the major areas of interest for Gupta. He has introduced several new models in the RRT family through a series of papers such as Gupta, Gupta and Singh (Journal of Statistical Planning and Inference, 2002), Gupta and Shabbir (Statistica, 2004) and Gupta, Shabbir and Sehra (Journal of Statistical Planning and Inference, 2010). The usual approach to work in this area is to a) identify a potential problem, b) come up with an appropriate RRT model for the problem, and c) study properties of the chosen model and validate these properties through computer simulations. Time permitting, the model can even be field tested. There are many types of sensitive behaviors college students engage in and some of these could be targeted as the potential research problem.

Dr. Matina Kalcounis-Rüppell, Dr. Sebastian Pauli

Computer aided observation of behaviors of nocturnal animals in the wild

We are interested in measuring behaviors of wild bats and mice. Bats and mice are interesting because they use ultrasound as part of their behavioral repertoire. Bats use ultrasound for echolocation and communication. Mice use ultrasound for communication. A major difficulty in studying behaviors of bats and mice is that they are nocturnal and cannot be directly observed. We have developed remote sensing techniques to record the behaviors of free living wild bats and mice without disturbing their behavior.

Dr. Matina Kalcounis-Rueppell in her field work has collected hundreds of nights of infrared video of bats and mice. Animals are outfitted with radio transmitters to allow identification of individuals. Microphones, are placed in the observation area to record animal vocalizations. The video, audio, and identity data together contains a wealth of information, but these data need to be processed and compiled to make conclusive observations of behavior patterns. Because of the amount of data, specialized processing computer processing methods need to be developed.

We are using computer vision techniques, such as blob tracking, to process video data. This allows us to automatically track the movement of free living animals. Automated tracking enables us, for example, to measure the speed of free-living individuals for the first time under different biolotic and abiotic contexts. For example, we can test hypotheses about the speed of animals in the context of varying predation predation pressure, interspecific interactions, intraspecific interactions and ambient conditions. The two species of mice we are currently examining differ markedly in their mating system. The brush mouse (Peromyscus boylii) is promiscuous and the California mouse (Peromyscus californicus) is monogamous. Our computer vision techniques are allowing us to test hypotheses about how running speed varies with parental behaviors associated with monogamous and promiscuous mating systems.

In the coming year we will extend our investigation to examine interactions among tracks of animals as opposed to examining single tracks. For this extension, we are looking for a biology student with a keen interest and foundation in classical animal behavior and a mathematics or computer science student keen on using computer vision techniques. Programming experience is required of the second student.

Dr. David Remington and Dr. Roland Deutsch

Modeling Genetics of Complex Trait Variation

Resource allocation refers to the processes by which living organisms invest nutrient reserves, cell lineages or other resources into different aspects of their life history, such as reproduction vs. growth and survival. Understanding how and why different resource allocation strategies evolve in plants is a key question in evolutionary biology, with major implications for understanding crop productivity and plant responses to environmental change, but little is known about the underlying genetic mechanisms. New tools in genomics and molecular genetics, combined with new approaches for modeling and statistical analysis, provide promising resources for understanding these processes. We are currently using a wide-ranging and highly variable rock cress plant, Arabidopsis lyrata, to study variation in resource allocation strategies.

Previous Math-Bio students have developed a developmental trait network model to explain how genetic variation at quantitative trait loci (QTLs) might affect resource allocation processes in A. lyrata. Simulations under their model give realistic predictions of actual correlations between resource allocation traits, but do not predict how effects of QTLs change in different growing environments to explain local adaptation. We anticipate having Math-Bio students extend the current model to include more detailed genetic mechanisms and the effects of climatic variables such as annual temperature cycles, and test the models using greenhouse and growth chamber studies in A. lyrata.

Dr. Olav Rueppell and Dr. Jan Rychtář

Analyses of mechanisms that lead to high genetic diversity in social insects

Social insect colonies are functional superorganisms with many individuals cooperating. This coopersation is largely responsible for the ecological success of social insects and has evolved by kin selection because colony members in most social insects are closely related. This genetic similarity among nestmates poses at the same time a problem because diseases can spread quickly through a group of genetically similar individuals that live in close quarters. Also, genetic homogeneity hinders an efficient division of labor among the colony members because most behaviors have a genetic predisposition. Thus, intra-colonial genetic diversity is favored for several reasons and some social insects have evolved adaptations to increase intra-colonial genetic diversity. One mechanism is to mate multiply because different fathers contribute different sets of alleles. Another way to increase genetic diversity is to increase the genetic recombination rate during meiosis to generate novel maternal gene combinations. In fact, some social insects, e.g. honey bees, have very high mating frequencies and the highest recombination rates known from animals. In this project we will study theoretically and mechanistically these phenomena that make social insects such dominant life forms today.

For more information visit: http://www.uncg.edu/%7Eo_ruppel/

Dr. Jan Rychtář and Dr. Mary Crowe

Modeling kleptoparasitic systems in dung beetles

Kleptoparasitism, the stealing of food items, is a common biological phenomenon that as been observed in many contexts. It is especially common amongst seabirds, but is observed in mammals, birds, fish, spiders, and insects. The main goal of the project is to model stealing/defending behavior in order to understand the evolution of kleptoparasitism. Biological part will be to study real kleptoparasitic systems, provide examples, and help with creation and testing of the model. Mathematical part will be to create and analyze new models of kleptoparasitism. Biological part will be to to test the outcomes on real populations. Computer simulations will be an important part of the project.

In particular, we will study a perfect model organism, dung beetle Onthophagus Taurus. Those cute little beetles play an important roles in an agriculture (as they bury the cow dung underneath the surface in a form of dung balls). For our purposes, they are important as they also play a lot of games, such as steal balls made by other beetles.

Dr. Jan Rychtář and Dr. Olav Rueppell

Evolution of cooperation in dynamically structured population

A cooperator is an individual who pays a cost C, so that another individual could receive a benefit B. A defector accepts any offered benefit, but does not deal out any (and thus pays no cost). When modeled as a simple game of Prisoner's dilemma (Axelrod 1984), it becomes obvious that defectors do better. However, cooperation and altruistic behavior between animals, including humans, is widespread in many taxa (Dugatkin 1997). One important aspect of social behavior is spatial organization of the interactants, which can be modeled as networks. Network reciprocity, a reciprocity based on spatial clustering, is one of the major five mechanisms for the evolution of cooperation including that have recently been proposed (Nowak 2006). An explicit demonstration that cooperation can spread to the whole population from a small initial cluster of cooperators if a population structure is fixed and if only the individuals that are close to each other can interact was provided (Nowak et al. 2006).

In this project, we will consider spatially structured populations of individuals that can move (and thus change the spatial structure) based on their interactions with other individuals (Zimmermann et al. 2004). Under the mentorship of both mentors, participants will devise an agent based simulation model to implement a cooperator-defector interaction network that allows movement and thereby dynamic reorganization of the network structure. We will search for stable solutions and characterize the conditions and network structure (=population structure) of evolutionary stable states. We will start with simple rules dictating to move closer to a cooperator and away from a defector and extend the experiments to more complex scenarios.

The main objective is to relax the assumption of a fixed population structure and identify behavioral rules of movement that allow the evolution of cooperation. Specific dynamical components will be investigated for their inhibitory or stimulatory effect on the evolution of cooperation compared to populations of fixed network structure. The students will be encouraged to compare their results with real-world findings from the social insect literature and other theoretical analyses.

Dr. Malcolm Schug and Dr. Roland Deustch

The Role of Crossing-over and Recombination in Adaptive Evolution

Crossing-over that results in the rearrangement of alleles on chromosomes (recombination) is a major mechanisms generating evolutionary diversity. The explosion of biotechnology during the past two decades has generated large amounts of genome sequence data and genetic maps for many organisms. These data have clearly shown that the frequency with which recombination occurs in genomes varies widely among different species, and the patterns of recombination vary significantly along the length of chromosomes within each species. Our studies are focused on evolutionary models that predict why recombination rates should vary among species and test the prediction that recombination rates themselves are an evolving unit subject to adaptive evolution. We use a variety of methods including data mined from genome sequencing databases, genetic maps, and newly developed computational tools to identify rapidly evolving genes focusing on humans and model organisms. Our empirical studies are focused on Drosophila ananassae, a species that has a wide geographic distribution throughout the subtropical and tropical regions of the world. Evolutionary theory predicts that recombination rates should be highest in subdivided populations. In contrast to D. melanogaster, the most common model Drosophila species, D. ananassae exists in highly subdivided populations throughout the species range. Furthermore, we know a great deal about its genome because it has been the focus of genetic studies since the 1940's, and the whole genome has been sequenced. The genome sequence has recently been annotated, but we are still confirming the position of the scaffolds on the physical chromosome map. Students in my laboratory who focus on the bioinformatics methods will be involved in both the genome assembly, mining the genome sequence for signatures of recombination, and using a combination of available genome analysis scripts and newly developed scripts, primarily written in Perl and Python to organize publicly available genome sequence data and integrate it into mathematical and statistical models to test hypotheses regarding the rate of recombination among genomes of different species and the distribution of recombination rates across chromosomes within Drosophila species.

Dr. Gideon Wasserberg and Dr. Cliff Smyth

Ecology of Infectious Diseases

Ecology of infectious diseases is a new and very dynamic field of research that applies an ecological perspective to address epidemiological problems. Due to the inherent complexity of such systems, this approach necessitates the integration of both empirical and modeling work. One of the two following topics will be chosen for the project:

(1) Vector-host coupling: understanding its theoretical and epidemiological implications. The conventional models currently used for vector-borne diseases such as Malaria or Dengue fever assume that except for obtaining a blood-meal from the host the ecology of the vector (e.g., a Mosquito) and the host (e.g., human) are independent. In this project, we explore the theoretical and epidemiological implications of varying the degree of dependence of the vector on the host and try to fit these models to real systems. Hence, the work incorporates model development and meta-analysis of information from the literature.

(2) Ecology of La-Crosse encephalitis in Western-Carolina. La-Crosse encephalitis virus LACV is a mosquito-borne viral disease transmitted by Aedes mosquitoes. Severe La-Crosse encephalitis (LACE) symptoms often involves encephalitis (an inflammation of the brain) and can result seizures, coma, paralysis, and even death. Severe disease occurs most often in children under the age of 16. In North-Carolina LACE it is endemic to the mountains region often affecting sensitive populations. There is no treatment for LACV infection. Therefore,The best way to reduce risk of infection with LACV is to prevent exposure. This requires a thorough understanding the ecological processes that underlie its dynamics and distribution. LACV ecology is very complex and involvevs three transmission routes (horizontal - between mosquitoes and infected rodents), vertical (between infected female mosquitoes and their progeny), and venereal (from infected male mosquitoes to female mating mates). In this project, we will develop an individual-based model of the system to try to understand the relative importance of these transmission routes and use field and lab work as well as literature review to estimate some of the model's critical parameters.