Stories of mathematics and computational science in genetic mapping

Abstract: Traits of interest often vary within a population, leading biologists to investigate the genetic basis of that observed variation. This can be done directly via an association study, in which one of many methods is used to identify correlational patterns that link genetic variation to trait variation. Alternatively, in experimental systems, individuals can be selectively bred to create a “genetic mapping population” with a more desirable signal-to-noise ratio. In this talk, I will share my experience creating mapping populations as a vehicle to introducing some of the mathematical and computational challenges that have ensued. I will discuss combinational and probabilistic issues that arise in ideal populations, contrasted by some algorithmic concerns that arise in natural populations. My goal is to provide a sampling of accessible problems in mathematics and computational science encountered in a practical biological context. 

Prof. Eric Stone:

I am a quantitative biologist who combines statistical methods and mathematical theory to investigate how genetic variation has shaped biological diversity. Toward that end, I study aspects of the evolutionary process, including the landscape of mutational events that give rise to genetic variation, the genetic basis of fitness-related traits, and the influence of selection and drift on patterns of genetic variation. These pursuits often stimulate the development of new statistical and computational methods, and I seek to make the most useful of these available as user-friendly tools. I value methodology as an essential lens through which biology may be perceived, but I also appreciate its ability to distort the truth. This motivates my use of mathematics to dissect popular methods that we as a community use to make biological inference.

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Topic: Mathematics and Computational Sciences Seminar Series 
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