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Where mathematics and biology meet

Picture of a brain made out of gears
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Oct 22 2020

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Faculty, Students

Theoretical population biology is a field that informs research in demography, ecology, evolution, epidemiology and genetics. Mathematical models from scholars in this field can have broad applications – sometimes decades after they are first developed. Combining biology and mathematics, it’s been used to address the passing of genes down through generations and of culture through communities, the relationships between predators and prey, the flow of diseases between populations and – most recently – our response to a globe-spanning pandemic.

“When I read the news about epidemiological models describing the spread of the novel coronavirus and the projections about its potential trajectories, I see in the background the years of abstract mathematical models that have made it possible to produce the immediate, policy-relevant work that is happening now,” said Noah Rosenberg, the Stanford Professor of Population Genetics and Society and a professor of biology in Stanford’s School of Humanities and Sciences, who specializes in mathematical evolutionary biology and genetics.

At the same time that these scholars are seeing the power of their field highlighted by the coronavirus pandemic response, they are also recognizing the 50th anniversary of the journal Theoretical Population Biology, which Rosenberg currently helms as editor-in-chief. The journal was established in 1970 by Stanford mathematician Samuel Karlin and Marcus Feldman – who had been Karlin’s student and who was the journal’s managing editor for 41 years. In the intervening years, theoretical population biology has grown in reputation and influence alongside advances in genetics, computing and data science.

“In most biological systems, we have lots of information, and processing and organizing all that data may depend on very deep mathematical results. That’s why this field exists,” said Shripad Tuljapurkar, the Dean and Virginia Morrison Professor of Population Studies and professor of biology at Stanford.

One theory about cooperation, for example, could describe processes happening in both people and cancer cells. Mathematical models that underlie inferences about the relationships between populations of humans (or other organisms from which samples of DNA or RNA have been taken) allow investigators to develop hypotheses about how these relationships came about. Kaleda Denton, a graduate student advised by Feldman, studies conformity – a bias in how individuals adopt cultural traits – which is a phenomenon that affects humans but also exists in fruit flies, fish and birds.