NSF Math-Bio Undergraduate Fellowship
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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. Maya Chhetri, Mathematics and Statistics
- Dr. David Remington, Biology
- Dr. Olav Rueppell, Biology
- Dr. Jan Rychtar, Mathematics and Statistics
Dr. Maya Chhetri
Population dynamics with harvesting or stocking
Project deals with the mathematical analysis of multi-species population dynamic models (cooperative, competitive and predator-prey) with or without diffusion and harvesting/stocking. First natural question of whether the species will survive for all future time (existence question) will be considered. If the species survive, then analyzing the qualitative properties of steady states (or equilibrium solutions), such as uniqueness/multiplicity (to determine whether there is a unique or more than one steady states to which population will settle down to after a long time) and stability with respect to the initial size of the population, will be the interesting part of the project.
To answer these questions, one is led to the study of positive solutions (representing population densities of species) of systems of differential equations, both ordinary differential equation (without diffusion) and partial differential equation(with diffusion). In systems, effects of the reactions (due to interaction of the species among each other in cooperative, competitive or predator-prey fashion) as well as the interactions of the different source terms (due to multi-species model) of the species present a challenge.
The focus of undergraduate training will be to first understand the mathematics behind one of the three types of multi-species population models described above. Next, students will find real problems, with the help of mathematics/biology mentor. They will analyze the problems mathematically and predict the qualitative outcomes such as coexistence, extinction of one or more species in finite time, stability of the steady states using tools such as eigenvalue method, bifurcation theory etc. accompanied by numerical methods.
For more information visit: http://www.uncg.edu/~m_chhetr/
Dr. David Remington
Genetics of plant resource allocation
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 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 the rock cress plant Arabidopsis lyrata to study variation in resource allocation strategies.
A previous Math-Bio student (Anne Pollok) has already developed a basic model for the resource allocation processes that take place during development in A. lyrata. Students working on this project would extend this work by modeling how genetic variation at different steps in these processes would affect overall resource allocation patterns and/or develop methods for analyzing genetic data for resource allocation traits. The team of students selected to work on this project will have considerable latitude in choosing which aspect of resource allocation to study and developing experimental methods. Our existing A. lyrata study populations and seed stocks will provide resources for experiments to test the models that are developed.
For more information visit: http://www.uncg.edu/%7Edlreming/.
Dr. Olav Rueppell
Life History and Behavior of Honeybees
Honey bees are charismatic insects that live in social groups with decentralized controls that ensure their functioning. Social evolution has created unique selection pressures and adaptations that have made social insects one of the most successful life form on earth. The individual bees and their colony depend on each other in multiple ways. Honeybee colonies represent complex systems but are amenable to experimental manipulation. In this project we will use this scientific model system and try to understand the functioning of the colony through a combination of mathematical analysis and practical experiments. The project focuses on particular aspects of the behavior and the life-history of bees that are amenable to this combined approach and the particular projects will be developed with the students.
For more information visit: http://www.uncg.edu/%7Eo_ruppel/
Dr. Jan Rychtar
Project 1: Modeling kleptoparasitic systems
Kleptoparasitism, the stealing of food items, is a common biological phenomenon that as been observed in many contexts but it is especially common amongst seabirds, but is observed in many context, even among people. 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 and to test the outcomes on real populations. Computer simulations will be an important part of the project.
Project 2: Dynamics on evolving graphs
Graph is a network, i.e. some nodes connected with links. Nodes may represent animals (e.g. social insect), cells (e.g. neurons), small organisms (e.g. bacteria), etc. Links may represent social interactions, physical connectedness, geographical closeness, etc. The goal of this project is to study dynamics on the graphs, which essentially equals to study the question "How much time does certain information (order from the queen, disease, mutated DNA) need to reach every node?". We will also study dynamics whose underlying graph is changing as a result of the spreading information. Biology part will be to study real life networks and help with creation and testing of the model. Mathematical part will be to create and analyze the model to test the outcomes on real populations. Computer simulations will be an important part of the project.
For more information click here.