The initial goals of our initiative were to contribute to raising quantitative proficiency at the undergraduate level through (1) integrating mathematical approaches and statistics into the freshman biology laboratory course; (2) developing a stand-alone statistics course in the context of biological problems; and (3) enabling faculty to integrate quantitative approaches and statistics into their courses through tune-up workshops and walk-in clinics. The need for this initiative came from the tremendous developments in biology, in particular at the molecular level, where massive amounts of data are now available for asking questions we could only dream about 25 years ago. This richness of data has fundamentally changed the way we create new knowledge: data acquisition, data analysis, modeling, and experimentation are increasingly integrated, and computational tools are now routinely used. This was the state of the art in 2006. We are now witnessing a similar revolution in other fields, such as the environmental or agricultural sciences, where sensors are monitoring the environment continually across spatial and temporal scales.
While we have seen tremendous advances in integrating large datasets in research over the last several years, biology education, especially at the undergraduate level, continues to lag behind in training life scientists in the quantitative skills needed to take advantage of these new opportunities across all levels of biological organization. There has been change though. While eight years ago, a one-year calculus course was the standard quantitative education of a biology student, a more diverse set of courses is often now available. I continue to have a textbook “Calculus for Biology and Medicine,” but have developed additional course materials in statistics and modeling that are freely available through my website, which is hosted by BioQUEST. Over the past several years, I have worked closely with colleagues at BioQUEST to run workshops for community and college educators to increase the quantitative skills of those teaching biology.
I have spent my last five years building a graduate program in Biomedical Informatics and Computational Biology. This program attracts students across a broad range of disciplines, from computer science to biology. While my focus eight years ago was on calculus, my experiences of building a graduate program in bioinformatics has shifted my focus and approach to a data-centric view. The rather static approach that is taken in introductory calculus and statistics courses does not prepare students well to deal with high-dimensional data and with processes that are dynamic and stochastic. Data and simulations must become an integral part of the quantitative training of students in the life/health sciences. This lends itself to a more experimental approach to mathematical concepts that appear to mesh well with the way students in the life sciences learn to approach problem solving. We also need to find less abstract ways to introduce mathematical concepts, and only go down the path of abstraction after students have gained some level of comfort through experimentation, data manipulation, simulations, and/or real-life applications. I am experimenting now with hands-on, active learning modules on important concepts that can be presented at different levels of mathematical sophistication. For instance, principal component analysis can be explained to a novice using a football, whereas a more sophisticated approach will require eigenvectors and eigenvalues. With readily available online tools, these sophisticated approaches to high-dimensional data then become available to a much broader audience.
Research in the Neuhauser Lab
As a mathematician, I work at the interface of mathematics and biology. Specifically, my research has ranged from studying the effect of competition on the spatial structure of competitors to the effect of symbionts on the spatial distribution of their hosts or the effect of virotherapy on clusters of cancer cells.
Currently, my research is primarily in the area of bioinformatics and computational biology where I am developing statistical tools ranging from detecting genomic signatures of cancer and other complex diseases in next-generation sequencing data to building dynamic protein-protein networks based on flow cytometry data. Examples of the types of questions that I have pursued with my collaborators are why so many species coexist in ecological communities.
Mathematical models have been used to investigate mechanisms that contribute to coexistence. Many of these models do not take into account the local interactions of organisms that are simply due to spatial proximity. The rigorous analysis of spatially explicit mathematical models has been a particularly vexing problem because of the mathematical difficulties stemming from spatial correlations that are a hallmark of spatially explicit models in which species interact locally. Our work has demonstrated, for instance, that local interactions can impede coexistence, countering a commonly held belief that space could be a mechanism that would facilitate coexistence since it could be viewed as an additional niche.
Other work has shed light on the evolution of specialization in spatially explicit host-symbiont systems. This work has confirmed that specialization is facilitated in coarse-grained habitats and has given new insights into the effects of feedback between hosts and their symbionts that can alter the spatial structure and thus significantly influence the evolutionary trajectory of symbionts.
Current work addresses the development of statistical tools to assess the significance of deviations in the number of expected reads along a genome generated by next generation sequencing technologies to identify copy number variations (CNVs) that may be indicative of certain types of cancer.
Last updated May 2014