Four Colleges Biomathematics Consortium

The NSF-Funded Four Colleges Biomathematics Consortium, 4CBC, provides opportunities for students and faculty from Amherst, Hampshire, Mount Holyoke, and Smith Colleges to collaborate on projects that explore the mathematical aspects of biology.

What is Biomathematics?

The explosion of data being produced in all fields of biological investigation is one of the leading phenomena of 21st-century science. Extracting meaning from these complex data sets requires an interaction between biologists capable of asking sophisticated mathematical questions and mathematicians willing to delve into biology to develop tools relevant to living systems.

Biomathematics Faculty / Projects

Janice Gifford

Janice A. Gifford, Professor of Statistics

Projects

  • Invasion, Disturbance and Community Dynamics — Collaborating with Martha Hoopes, Ji Young Kim, and Amy Wagaman
  • Propagule Pressure, Disturbance, and Invasion Dynamics — Collaborating with Martha Hoopes, Ji Young Kim, and Amy Wagaman
  • Spatial Parasitoid Community Dynamics — Collaborating with Martha Hoopes and Ji Young Kim
Martha Hoopes

Martha Hoopes, Professor of Biological Sciences

Projects

  • Invasion, Disturbance, and Community Dynamics — Collaborating with Janice Gifford, Ji Young Kim, and Amy Wagaman
  • Propagule Pressure, Disturbance and Invasion Dynamics — Collaborating with Janice Gifford, Ji Young Kim, and Amy Wagaman
  • Spatial Parasitoid Community Dynamics — Collaborating with Janice Gifford and Ji Young Kim
Craig Woodard, Professor of Biological Sciences

Craig T. Woodard, Christianna Smith Professor of Biological Sciences

Projects

  • Micro-Array Statistical Analysis — Collaborating with Ji Young Kim

Projects

Invasion, Disturbance and Community Dynamics

  • Biology: Martha Hoopes (Mount Holyoke College)
  • Math and Statistics: Janice Gifford (Mount Holyoke College)
  • Math and Statistics: Ji Young Kim (Mount Holyoke College)
  • Mathematics: Amy Wagaman (Amherst College)

Description:

Invasive species alter community dynamics by changing access to resources and potentially altering abiotic environments. We can assess these changes with the experimental removal of invaders from natural communities or with common garden or greenhouse experiments that create communities. The field removals start with random replicates containing very different initial communities and then remove different relative proportions of the community. Analyzing subsequent community responses offers possibilities for basic factorial statistical analysis, as well as matrix geometric approaches of community characterization. Students will collect data in the field and greenhouse and explore statistical analysis and community characterization.

Propagule Pressure, Disturbance, Invasion Dynamics

  • Biological Sciences: Martha Hoopes (Mount Holyoke College)
  • Math and Statistics: Janice Gifford (Mount Holyoke College)
  • Math and Statistics: Ji Young Kim (Mount Holyoke College)
  • Mathematics: Amy Wagaman (Amherst College)

Description:

Species composition in a local habitat reflects the regional species pool and any transport and disturbance mechanisms that disperse species between local patches to colonize new sites. This project examines plant community composition in wet and dry meadows in areas open to recreational use and closed to the public. The data offer insight into the effect of disturbance, propagule pressure, and regional species richness on invasion and community dynamics. Students will collect plant community data and analyze it. There is also the possibility of testing metacommunity theories in a terrestrial system, a gap in the current ecological literature. Mathematical approaches include basic factorial statistical analysis, robust methods for variable selection and clustering for multivariate responses, and examination of several measures of similarity and dissimilarity, model optimization, matrix geometric approaches.

Spatial Parasitoid Community Dynamics

  • Biological Sciences: Martha Hoopes (Mount Holyoke College)
  • Math and Statistics: Janice Gifford (Mount Holyoke College)
  • Math and Statistics: Ji Young Kim (Mount Holyoke College)
Description:

There is a long history of examining host-parasitoid dynamics in ecology and particularly of looking for factors that help to stabilize the dynamics of these interactions. The consideration of spatial dynamics and additional species interactions has suggested several ways in which dispersal, aggregation, and competition or hyperparasitism can contribute to stabilization. Theory has significantly outstripped empirical studies in this area, but confronting the theory with data leads to very complicated analyses. We have a 28 generation data set exploring the dynamics of a specialist galling midge and a community of parasitoids and hyperparasitoids in a factorial experimental design. We crossed two plant community sizes with caged and uncaged treatments (as well as a cage control) in five blocks across two sites. Even the simplest parametrical statistical analysis of this dataset is somewhat complex because it forces confrontation with response variables that indicate stability (outbreak number and type, cycling) but also because the data are field data and are unavoidably messy and nested. These difficulties in analysis present rich opportunities for student challenges. More complex analyses offer insight into ways to combine statistics with dynamic population and community models. Students work on dissecting galls and identifying larvae, data management, statistical analysis, and modeling. Differential equations in dynamical systems, time-series analysis, and multivariate non-parametric statistical analyses that are robust against contamination are some of the mathematical techniques necessary for this project.

Control of Animal Development by Steroid Hormones

Control of Animal Development by Steroid Hormones and Evaluation of Microarray Data

  • Biological Sciences: Craig Woodard (Mount Holyoke College)
  • Math and Statistics: Ji Young Kim 

Description:

We study metamorphosis in the fruitfly, Drosophila melanogaster as a model system in which to examine the control of animal development by steroid hormones. Steroid hormones act in conjunction with receptor proteins to regulate the expression of target genes, ensuring that these genes are activated in the right tissues (tissue-specific gene induction) and at the right times (stage-specific gene induction). The goal of our research is to answer one of the central questions of developmental biology – how can a single hormonal signal elicit different responses at different times and in different tissues during development? We are investigating the tissue- and temporal-specific regulation of gene expression during Drosophila metamorphosis using DNA microarrays to identify differential gene expression. We are now developing the mathematical tools required to link gene expression information to developmental events. Furthermore, for clusters of relevant genes, we intend to investigate the transcriptional regulatory network by studying the relationship between gene expression and transcription factors through shrinkage methods.

Genetic and Cellular Determinants

Genetic and Cellular Determinants of Susceptibility to Immune Deficiency

  • Biological Sciences: Sharon Stranford 

Description:

Using a mouse model of AIDS (called MAIDS) to study genetic and cellular determinants of susceptibility to immune deficiency, we can create infection resulting in a chronic and life-threatening AIDS-like disease in one strain (C57BL/6) and a mild, resolvable illness in the other strain (BALB/c).  We study differential responses within the lymphoid tissues (spleen and lymph node) between the two strains in the first 2 weeks post infection for clues to productive immune response pathways. These studies have involved using DNA microarrays to identify differential gene expression, followed by some limited real time PCR assays and protein-based assays on individual genes/proteins in an attempt to confirm these differences. We published our first joint math and biology collaboration on this work in Immunogenetics (Tepsuporn et al. 2008). We would now like to evaluate the methods used for computational analysis and how these relate to biological outcome. For each of methods, we would convert the statistic to an estimated false discovery rate and use this value to identify differentially expressed genes. Using a systematically varying collection of artificial data, each method can then be compared for accuracy of FDR estimation and success at identifying differentially expressed genes. These alternative methods can also be used to reanalyze our actual data sets and compare the outcomes. We used the permutation methods in our statistical analysis of differential expression and would like to compare this with a principle component analysis, an empirical Bayes procedure, and a hierarchical Bayesian analysis. Students would be involved in all laboratory work and analysis.