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 mice in the wild
We are interested in measuring behaviors of wild. A major difficulty in studying behaviors of mice is that they are nocturnal and cannot be directly observed. We have developed remote sensing techniques to record the behaviors of free living mice without disturbing their behavior.

One particular behavior we are studying is the animals decisions about how to allocate their time. For example, a parent needs to decide whether to provide help at the nest or patrol a territory; these two behaviors cannot be done simultaneously. How do animals make these decisions at a proximate level ? We are currently testing a hypothesis in the field that a rapid release of testosterone results in rewarding effects that illicit a conditioned place preference and therefore their decisions about how to allocate time.

To observe the behavior of mice Dr. Matina Kalcounis-Rüppell in her field work has collected hundreds of nights of infrared video of mice, recordings of ultrasonic vocalizations, and also has outfitted some individuals with radio transmitters to allow identification of individuals. and 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 needed 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 has enabled us, for example, to analyze the activity of free-living individuals under different biolotic and abiotic contexts, where we used the average speed and total distance traveled by individuals in the area observed by the camera in night as measures of activity.

In the upcoming year will work on determining the traveling speed of individual bush mice (Peromyscus boylii) and the California mice (Peromyscus californicus) by combining data obtained from the video analyzes, human observations, and telemetry.

We furthermore will use newly obtained video data to obtain data about the decisions of California mice of how to allocate time.

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.

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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.