NSF Math-Bio Undergraduate Fellowship

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  6. Funded by
    National Science Foundation

    7. Grant 0634182 (2006-2010)
    and 0926288 (2009-2012)

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

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. Roland Deutsch and Dr. Sebastian Pauli

Genomic coding theory simulations

The redundant structure of the genetic suggests that techniques similar to those in algebraic coding theory are used for error detection and error correction. In this project we will simulate the reproduction of simple virtual creatures, that use algebraic codes to detect and correct errors in their genome. We investigate how the choice of codes, the mutation probability, and the kind of reproduction (sexual or non-sexual) influence the survival of the species.

We will use the computer algebra system Sage and the statistics package R to implement the reproduction rules and to simulate the development of a population of these creatures. The student will implement algorithms that simulate the reproduction of the creatures. He will simulate how the population changes under certain parameters, including: probability of mutations, code used for error corrections and/or correction, simple or sexual reproduction.

We will start by setting up rules of reproduction. In the following we give a draft for such rules. Mutations occur at random and can be corrected using an error correcting and or detecting code. The genome of each creatures consists of a certain number of bits, say N, which can be 0 or 1. The genome of the children of the creatures is changed by flipping each bit with probability P.

The creatures use coding theory to correct and detect these errors that occur during reproduction.

  • If there are no errors detected the child develops according to its genome.
  • If an error is detected that cannot be corrected the child dies.
  • If the error can be corrected the child develops according to the corrected genome. Its original (uncorrected) genome is used in reproduction.
In simple reproduction changes in the genome occur through mutation only, while in sexual reproduction for each gene the value from the father or mother is chosen with probability 1/2 and in addition mutations occur.

Dr. Stan Faeth

Ecology and evolution of plant-microbe-herbivore interactions and urban ecology

Dr. Faeth’s research group has two primary foci: 1) the ecology and evolution of species interactions, specifically interactions among plants, their microbial symbionts and plant herbivores, and 2) how urbanization and suburbanization alters biodiversity, trophic interactions, and food web structure. For the first, we study how endophytic fungi alter plant physiology, growth, reproduction, fitness and competitive interactions with other plants. Asexual endophytic fungi inhabit cool season grasses, remain asymptomatic, and are vertically-transmitted by hyphae growing into seeds. Asexual, vertically-transmitted symbionts are predicted to be strong mutualists because fungal reproduction and transmission are closely link to growth and reproduction of the host grasses (Cheplick and Faeth 2009). In introduced, agronomic grasses, this prediction generally holds, with endophyte infection providing an array of benefits ranging from protection from herbivores via production of fungal alkaloids, changes in physiology and morphology that increase resistance to environmental stresses, and increased competitive abilities. The manipulation of endophytes in turf and pasture grasses has become an important industry worldwide. However, in native grasses, endophyte effects are much more variable and range from mutualistic to parasitic depending on host and endophyte genotype and environmental factors. Furthermore, the direction of interaction changes over the lifespan of the perennial host grass. Overall, our recent findings suggest that contrary to conventional evolutionary wisdom, asexual endophytes may be sexual parasites and manipulate host allocation to reproduction to increase their own transmission at the expense of lifetime fitness of their hosts. We currently use controlled and manipulative greenhouse and field experiments and field observational methods to address these questions.

For the second focus, we test how urbanization and suburbanization affects biological communities. With now (as of 2008) more than half of the world’s population living in cities, urban and suburban areas are the most rapidly growing habitat type for biological communities. Whereas is well documented that urbanization affects biodiversity usually, but not always, in negative ways, there is little understanding of the underlying causes for these changes. In cities of the future where much of the world’s biodiversity may reside and be managed, it is imperative to understand the causes for diversity changes. Our group focuses on how urbanization alters relative abundances of species, species interactions, trophic dynamics and food web structure. Control of biodiversity may differ radically from more ‘natural’ ecosystems, with shifts in trophic dynamics and relative importance of species interactions (Faeth et al. 2005). We use controlled experiments in urban settings, long term monitoring, and mining of existing databases.

Both research focal points involve strong statistical and mathematical components. The greenhouse and field experiments require experimental design methods, including power analysis, to ensure adequate design and replication. Data from experiments, observational studies, and existing databases are analyzed using general linear models (ANOVA, ANCOVA) and multivariate (e.g., MANOVA, multiple regression, prinicipal component analyses), and non-parametric statistics. In collaboration with mathematicians, we have developed analytical models for endophyte vertical transmission (Faeth et al. 2007) and are developing analytical models for food webs in urban areas based upon classic food web models in ecology. Undergraduate students afforded the opportunity to research fundamental ecological questions of broad significance to society using quantitative, statistical and mathematical applications and approaches.

Dr. Bruce Kirchoff, Dr. Clifford Smyth

The evolution of plant architecture

The evolution of plant form is one of the most fascinating and least understood aspects of evolutionary biology. Our Math/Bio project is a study of the evolution of plant form in eleven species of the plant genus Banksia. These species have a wide variety of growth forms, from creeping shrubs ( Fig. 1) to small trees ( Fig. 2). Our initial work will focus on converting field measurements of branch lengths and angles to growth rules that will then be used to create models that will accurately simulate the growth and mature forms of the various species ( Fig. 3). We will use these models to investigate how plant form evolved in Banksia. One question we will examine is how difficult is it for one set of growth rules to be converted into another. Knowing this will allow us to measure the ease of evolutionary change from one plant architecture to another. The result of our research will be a better understanding of how plant form evolves.

Dr. Elizabeth Lacey

TBA

TBA

Dr. David Remington

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 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.

Previous and current Math-Bio students have developed a developmental trait network model to explain how genetic variation might affect resource allocation processes in A. lyrata . They used their model to simulate trait variation in genetic crosses, and comparisons of their model predictions to actual field data show that the model gives realistic predictions. Ongoing and future projects for Math-Bio students include additional modeling to predict how variation in resource allocation affects fitness (annual reproduction and year-to-year survival) and growing populations from new crosses in order to evaluate a larger number of the traits that are simulated in the trait network model.

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

Dr. Olav Rueppell

Social Evolution 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 manipulations. My research focuses on select aspects of honey bee biology, ranging from the genetic to the societal level. In this program we will use this scientific model system to advance our understanding of the causes and consequences of social evolution through a combination of mathematical analyses and practical experiments. Particular projects that are amenable to this combined approach will be developed with the students.

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

Dr. Scott Richter

Nonparametic methods applied to linear models

Dr. Richter's research interests have focused mainly on nonparametric methods applied to linear models. The most common inferential procedures in statistics require assumptions regarding the model generating the data, most frequently that errors are normally distributed with common variance. In cases where the assumption of normality is not tenable, it is often the case that nonparametric procedures can provide valid, and often more powerful, inferences. Assumptions regarding normality and equal variance are often violated for data from biological investigations. Count data, for example, often follows an approximate Poisson distribution, for which the variance is related to the mean. It is common in many areas of application to transform the data to lessen the apparent degree of the violation of assumptions, but common transformations (e.g., logarithmic) can produce unexpected interactions between experimental factors (Payton, et al, 2006). The use of aligned ranks can improve the power of tests in multifactor analysis of variance when errors are nonnormal (Richter & Payton, 1999, 2005), but the aligned rank transformation does not have adverse effects on interactions (Payton, et al, 2006). When errors are normal but have nonhomogeneous variances, Richter and Payton (2003) presented method that can provide valid inferences. More recently, Richter and McCann (2007) developed a nonparametric pairwise comparison procedure, based on medians, that is more powerful than analogous procedures on means when errors are nonnormal. Recent research has also been motivated by collaboration with biologist Robert Stavn (UNCG Department of Biology) on a problem in ocean optics. Dr. Richter derived, for the case of multiple predictors, estimators for Model II regression slope coefficients, and used nonparametric bootstrapping to compute standard errors and confidence intervals for the slope coefficients. Current research is ongoing to further develop the theory and application of multiple Model II regression.

Dr. Jan Rychtar, 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 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.

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. Malcolm Schug

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. Shan Suthaharan

Bio-Inspired Computing for Computer Networking

Bio-Inspired Computing is a useful technology to solve many research problems in computer networking. For example immune system characteristics, swam intelligence in ants and biological feedback loops have been used in computer networking to address the problems related to network security, congestion control and routing mechanisms. In this project we will study these bio-inspired computing technologies with the goal of understanding the mathematical relationships between the complex biological systems and large-scale computer networks including wired and wireless networks and wireless sensor networks and developing efficient bio-inspired computing techniques to solve the problems in computer networking. The following are two useful references for this project:
1. Michael Meisel, Vasileios Pappas and Lixia Zhang, "A Taxonomy of Biologically Inspired Research in Computer Networking," Download .
2. F. Dressler and B. Kruger, "Cell biology as a key to computer networking, "german Conference on Bioinformatics 2004 (GCB'04), Bielefeld, Germany, Poster, Oct. 2004 Download.

Dr. Gideon Wasserberg

Ecology of Infectious Diseases

Projects focus on applied and basic science questions using observational, experimental, and modeling studies.

Project 1: Ecology of zoonotic and vector-borne diseases. I study the role of anthropogenic disturbance in the resurgence of Cutaneous Leishmaniasis (CL) in southern Israel. Particularly, I focus on studying the environmental, demographic, and spatial aspects of the system using observational and experimental studies and use simulation models to address potential intervention approaches. I am also using GIS and remote sensing to develop a risk model for that area. I am planning to use a similar approach for the study a range of local diseases such as Rocky Mountain spotted fever, West-Nile virus, la Cross encephalitis, Lyme’s disease and others. Current mathematical modeling in this context involvevs elaboration of a prototype individual-based spatially explicit simulation model of CL.

Project 2: Wildlife diseases. I study the ecology Chronic Wasting Disease (CWD) in White-Tailed Deer using a simulation model. CWD is an emerging fatal neurodegenerative prion disease belonging to a family of diseases known as transmissible spongiform encephalopathies (TSE) and is the only TSE that acts as an infectious disease in free-ranging animals. My model studies the role of transmission mode and demographic contact structure on disease dynamics and their implications for disease control in southern Wisconsin. Further development of this model could accomodate student projects.

Project 3: Disease Ecology - basic research. Using a combination of experimental and modeling approaches, I am addressing basic question such as the effect the degree of vector-host coupling on dynamics of vector-borne diseases as well as disease community ecology. Studying effect the degree of vector-host coupling on dynamics of vector-borne diseases could be a potential student project.

 

Page updated: 23-Oct-2009

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Math-Bio Undegraduate Fellowship
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