Numbers game

A common thread stitches together Nick Patterson’s numerous careers: deep and joyful thinking about mathematics. He has cracked Cold War codes and run numbers on Wall Street. Now a computational biologist in the Broad’s Program in Medical and Population Genetics, he has helped colleagues analyze the migration and mixing of human populations. His work has spanned epochs and analyzed the population history of an entire subcontinent.

Nick recently notched another achievement: He was recognized for a paper of his in theoretical genetics,  which has become one of the most cited in its field. The study in the journal Theoretical Population Biology, written in 2008 with mathematicians Simon Myers and Charles Fefferman, is the most-cited paper in that journal over the last three years.

The paper, “Can one learn history from the allelic spectrum?” can be found here.

Taking time from his work on the 5th floor of the Broad’s main building at 7 Cambridge Center, Nick talks a bit about his work.

He explains that each gene can come in different versions, called “alleles.” Each of those versions occur at different frequencies in the population. Some alleles are only in 1% of people’s genomes, and some in 30%. The allelic spectrum is the frequency of the frequency of each allele, “How many occur at 30%, how many occur at 1%, and so on.”

Nick and his coauthors ask a crucial question: is this information on how often alleles occur in a population enough to allow population geneticists to infer the evolutionary history of a population? Their answer is, basically, no. Although numerous papers have been written that extrapolate the history of a people by looking at allelic spectrum, Nick and his coauthors find that this technique has limitations.
“Here’s a question that would naturally occur to a mathematician. Suppose I were so lucky as to know the spectrum exactly. (Which of course I never could because you’ve got finite data.) Does that determine what the population history was? We showed that’s impossible.”