Math-Biology REU at UNCG

Research Projects

The specifics of the research projects will depend on the mutual interest of the involved faculty and students.

Potential 2018 projects

Honey bee health - Analyzing virus transmission and social immunity in complex societies
Lead mentor: Dr. Olav Rueppell
Honey bees (Apis mellifera L) are of significant ecological and economic importance and present excellent experimental study systems. Usually, one reproductive queen lives with thousands of female workers in a cohesive colony, coordinated by a complex communication and division of labor system. The bee colony represents in many regards a functional unit that can be compared to a superorganism. Thus, the colony is a dense, integrated network of individuals, which makes it susceptible to diseases. Recently, honey bee health has declining dramatically, threatening the pollination services that the apicultural industry provides. Multiple disease agents have been identified and we will study an important virus, Israeli Acute Paralysis Virus from a practical and theoretical perspective. We will investigate IAPV transmission in small experimental groups of honey bees with varying transmission routes to understand the dynamic of a IAPV outbreak and individual infection risk. This work should contribute to understanding of honey bee – virus interactions and help improving honey bee health.

Vaccination Game Theory
Lead mentor: Dr. Igor Erovenko
As witnessed by the recent outbreak of measles, there is a gap between interest of the individuals and the interest of the population as a whole. From the individuals' perspective, the benefits of vaccination (i.e. not getting the disease) may not be high enough to outweigh the cost of the vaccination (i.e. potential vaccine side effects) especially when majority of the population is vaccinated that the disease outbreak seems highly unlikely. Such scenarios are successfully modeled by game theory. During the Summer 2018, our team will work on developing game theoretical models for diseases of students' interest as well as try to extend the results for the spatially structured populations.

Evolution of life history traits
Lead mentor: Dr. David Remington
We will study the genetic basis for adaptive evolution of life history traits in plants, which has important implications for how plants will respond to climate change. We use the perennial rock cress (Arabidopis lyrata) as a model system to study the evolution of perenniality in response to variation in climate. Our empirical research has found that trade-offs in reproduction vs. vegetative growth in populations from the warm vs. cool extremes of the A. lyrata range (North Carolina vs. Norway) result from quantitative trait loci (QTLs) that affect aspects of perenniality. North Carolina alleles lead to greater reproductive output at the expense of vegetative growth, but reduce survival without increasing reproduction under Norway conditions. Previous research by UNCG undergraduates found that genetic differences between the extreme populations affect the allocation of time to vegetative vs. reproductive growth on individual shoots. We proposed a conceptual model to explain reproductive output and survival differences between populations in different environments, and thus a potential mechanism for local adaptation. We will explore the behavior of a deterministic model incorporating relationships between trait values, fitness components, and environmental variables using differential equations. Students will develop mathematical representations of the model, find parameter values that optimize fitness under different climate conditions, and predict the trajectory of natural selection under changing climates.

2017 projects

Honey bee health - Analyzing virus transmission and social immunity in complex societies
Lead mentor: Dr. Olav Rueppell
Honey bees (Apis mellifera L) are of significant ecological and economic importance and present excellent experimental study systems. Usually, one reproductive queen lives with thousands of female workers in a cohesive colony, coordinated by a complex communication and division of labor system. The bee colony represents in many regards a functional unit that can be compared to a superorganism. Thus, the colony is a dense, integrated network of individuals, which makes it susceptible to diseases. Recently, honey bee health has declining dramatically, threatening the pollination services that the apicultural industry provides. Multiple disease agents have been identified and we will study an important virus, Israeli Acute Paralysis Virus from a practical and theoretical perspective. We will investigate IAPV transmission in small experimental groups of honey bees with varying transmission routes to understand the dynamic of a IAPV outbreak and individual infection risk. This work should contribute to understanding of honey bee – virus interactions and help improving honey bee health.

Vaccination Game Theory
Lead mentor: Dr. Igor Erovenko
As witnessed by the recent outbreak of measles, there is a gap between interest of the individuals and the interest of the population as a whole. From the individuals' perspective, the benefits of vaccination (i.e. not getting the disease) may not be high enough to outweigh the cost of the vaccination (i.e. potential vaccine side effects) especially when majority of the population is vaccinated that the disease outbreak seems highly unlikely. Such scenarios are successfully modeled by game theory. The 2017 projects focused on voluntary vaccination policies to eradicate Ebola, optimal vaccination strategies to reduce endemic levels of meningitis in Africa, optimal vaccination strategies to combat S. Typhi transmission in South Asia.

2016 projects

Disease Transmission in Honey Bee Colonies
Honey bee populations are declining and diseases play a central part in the sustained honey bee health declines. Importantly, viruses are vectored by parasitic mites. Natural defenses of honey bee against their diseases include an adaptive colony demography and specific behaviors. Using experimental and modeling approaches, this project will address the impact of these features on disease transmission and dynamics in honey bee hives, as a more general model for understanding infectious diseases in complex societies.

Vaccination Game Theory
As witnessed by the recent outbreak of measles, there is a gap between interest of the individuals and the interest of the population as a whole. From the individuals' perspective, the benefits of vaccination (i.e. not getting the disease) may not be high enough to outweigh the cost of the vaccination (i.e. potential vaccine side effects) especially when majority of the population is vaccinated that the disease outbreak seems highly unlikely. Such scenarios are successfully modeled by game theory. During the Summer 2016, our team will work on developing game theoretical models for spatially structured populations.

Territorial Raider Games
Many animals are territorial and a lot of animal interactions revolve around the territories, the protection of its own territory against an aggression of a neighbor, or an aggressive invasion into neighbor’s territory. Especially for highly heterogeneous population structure, finding optimal behavior (to protect or to raid) is analytically impossible and we will adopt several machine learning techniques to help us to gain an insight into how the population structure influences the optimal behavior.

Evolution of Cooperation
In a biological context, the evolution of cooperation can be conceived as a contest between populations who exhibit alternate organizing principles that control the fitness performance of their respective individuals. These differences influence not only the local dynamics of interact groups but also their spatial distribution within a regional community. During the 2016 summer, we will continue to develop a population dynamics model formulated in the previous years of our program and consider alternate mechanisms by which cooperation could be introduced and reinforced, including mutation, step-wise transition states, and behavioral switching.

Weighted Hard Threshold Signal Approximation for Robust Change Point Detection with Application to Copy Number Variation Detection
Copy number variation (CNV) detection becomes an important issue in cancer research since CNVs can confer risk to complex disease. However, most CNVs data are noisy and outliers and human errors are often involved during or after the normalization process. In this project, we propose a Weighted Hard Threshold Signal Approximation (WHATSA) method for robust detection of copy number variation change points. There are two important contributions from this project: 1) improve the robustness and efficiency of the true DNA copy number signals recovery from existing methods and 2) develop a unique approach for simultaneous outlier detection with the signal approximation. The project will involve: a) CNV microarray data collection b) formularization of WHATSA method for signal approximation b) large amount of simulations by comparing WHATSA method with selective existing methods d) preparation of an efficient algorithm for WHATSA and public available R program.

2015 projects

Territorial Raider Games
Many animals are territorial and a lot of animal interactions revolve around the territories, the protection of its own territory against an aggression of a neighbor, or an aggressive invasion into neighbor’s territory. Especially for highly heterogeneous population structure, finding optimal behavior (to protect or to raid) is analytically impossible and we have thus adopted several machine learning techniques to help us to gain an insight into how the population structure influences the optimal behavior.

Vaccination Game Theory
As witnessed by the recent outbreak of measles, there is a gap between interest of the individuals and the interest of the population as a whole. From the individuals' perspective, the benefits of vaccination (i.e. not getting the disease) may not be high enough to outweigh the cost of the vaccination (i.e. potential vaccine side effects) especially when majority of the population is vaccinated that the disease outbreak seems highly unlikely. Such scenarios are successfully modeled by game theory. During the Summer 2015, our team worked on developing game theoretical models for spatially structured populations.

Comparative Analysis of Transcriptomic Data
The life sciences are revolutionized by massive genomic data generation. Most of these data are in the form of genome-wide gene expression analysis (transcriptomics). In this project, we evaluate the current statistical methods to relate different data sets to each other, specifically determining significant overlap in differentially regulated gene sets. We will relax the underlying assumption of gene equality and model gene expression profiles assuming genomes that harbor different classes of genes. These simulations will assess how current methods may have to be adjusted to biological reality.

Evolutionary Graph Theory
A population structure is often modeled using graphs. Individuals are assumed to live on the vertices of the graph and can interact only with their neighbors. The classical evolutionary graph theory (EGT) has been very successful in capturing the basic principles and reasons behind the evolution of cooperation in the structured population. However, some underlying assumptions behind the EGT are highly unrealistic and especially for heterogeneous populations can lead to anomalies where some individuals are forced to interact with too many of their neighbors. During our summer 2015 project, we provided alternative underlying model and studied the classical results in this new setting.

Evolution of Cooperation
In a biological context, the evolution of cooperation can be conceived as a contest between populations who exhibit alternate organizing principles that control the fitness performance of their respective individuals. These differences influence not only the local dynamics of interact groups but also their spatial distribution within a regional community. During the 2015 summer, we continue to develop a population dynamics model formulated in the first year of our program and consider alternate mechanisms by which cooperation could be introduced and reinforced, including mutation, step-wise transition states, and behavioral switching.

2014 projects

Evolution of Cooperation in Mobile population
This project concerned a system of discrete agents operating within a sparsely populated network of patches. The project focused on how these agents moved about the network and formed aggregations. As with many agent-based simulation studies the project model involves stochastically driven events (e.g. movement, competition) in the lifespan of an individual agent. The distinguishing feature of the research conducted here was the mobility of the agents. Each agent move aimed at maximizing agent's long term fitness. We have investigated how various parameters of the simulation influenced the evolution of cooperation. We found that both greater mobility and larger neighborhood size inhibit the evolution of cooperation because it allows the defectors to find the cooperators faster and exploit them more.

Age-Structured Populations
This project studied the fixation rate of cooperation within an age-structured agent-based network. Many animals have distinct life phases (pre-reproductive, reproductive, and post-reproductive) in which interactions vary with respect to the age of individuals, and that the duration of these phases was subject to selection pressures. The model of this project shared many features with the previous project (e.g. agents that could be either Cooperators or Defectors), but the system transpired on a two-dimensional lattice network of sites and each agent was fixed at a particular location. Individuals were subject to aging and mortality events as well as reproduction and competition for resources with individuals in neighboring cells. The propensity of these events were influenced by an individual's fitness score, itself a function of the present and historic compositions of its neighborhood. We focused on the effects of memory of past interactions and neighborhood size on the evolution of cooperation. We showed that larger neighborhood sizes are detrimental to cooperation. Further, we showed that larger memories actually hurt the spread of cooperation in small neighborhood sizes. For larger neighborhood sizes, however, longer memories are more favorable to the spread of cooperation than shorter memories.

Social Dynamics
This project regarded the contest between cooperation and defection as a question of behavioral responses amid shifting social compositions. Prior research into the trustworthiness of public signals had shown that one could obtain results that diverged from classic game theory outcomes when there was a mixed-constituent audience or multiple players involved. This project adapted that idea to describe the behavioral changes within a society composed of three inter-dependent classes (taxpayer elites, government and law enforcement, general citizens). Members of each class had a binary choice of actions for dealing with society at large (e.g. being charitable or stingy with resources) that could be equated with either cooperation or defection according to an external assessment of what constituted a just or ideal society. Our goal was to determine the underlying structural dynamics of these models and, secondarily, the conditions necessary to maintain a utopian social archetype where all classes adopted their respective equivalent of cooperate. Charitability was lost under most parametric combinations without a utopian preference among the elite taxpayers, and society either defaulted to a dystopian outcome or cycled through periods of oppression, relaxation, rioting and restoration of order. Although social ideals could stabilize the utopian archetype, that alone did not eliminate the possibility of other attractors within the system, and the system remained initial condition dependent.

Cooperation and Kleptoparasitism
This project placed cooperation and defection in the context of theoretical ecology and per capita fitness functions. A number of papers have recently established a framework for studying the dynamics and spatial distributions of populations capable of adaptive movement. For this project, we considered three variations of a fitness function that describes the local performance in recovering resources from the environment. The three variations are stereotypical expressions of selfishness, cooperation, and exploitation. Respectively, these variations consist of a fitness function that strictly declines with density, another which features an Allee effect at smaller densities, and an exploitative interaction wherein gathered resources are transferred from host individuals to kleptoparasites. We found that host fitness functions mediated the community dynamics under invasion from parasites, with destabilizing cycles affecting cooperative hosts in high resources. Moreover, selfish and cooperative populations were mutually exclusive to one another.