University of Rochester

Ancient Math Refines Theories of Evolution

June 29, 2000

Evolutionary biologists are used to digging into the past-but rarely in a quest to unearth equations. One group of scientists, however, has dusted off a 200-year-old formula to help reconcile discrepancies that crop up among DNA studies designed to sort out how species are related to one another. In the June 30 issue of Science, John Huelsenbeck, assistant professor of biology at the University of Rochester and his colleagues show how 18th century math can help biologists grapple with the flood of DNA sequences coming from genome sequencing projects. His colleagues are Bruce Rannala, assistant professor of medical genetics at the University of Alberta, and graduate student John Masly of the University of Rochester.

"This method is a revolutionary approach to addressing questions concerning the evolution of important traits," says Paul Lewis, professor of ecology and evolutionary biology at the University of Connecticut and an expert at inferring evolutionary trees from DNA sequences. "This means that determining an evolutionary tree will be less biased by one particular estimate. The investigators of this study continue to be pioneers in this field."

The mathematician to whom Huelsenbeck, Rannala, and Masly have turned is Thomas Bayes, a British Presbyterian minister who devised a formula to account for uncertainties in data-uncertainties such as when one method suggests chimps are more like humans than orangutans, while another says the exact opposite. Bayes' formula allows informed guesses to be combined with new data. As the scientist collects more data, the initial guess carries less weight, and so the most accurate answer, such as which evolutionary family tree correctly depicts how birds split from reptiles, gradually takes shape. Currently, scientists are forced to treat evolutionary trees as ironclad truth, even though the results from different studies often disagree with one another. Bayesian mathematics accommodates uncertainty about the evolutionary history of life, allowing other questions, such as the evolution of the genes of an organism, to be more accurately studied.

"The Bayesian approach reduces the chance that every new discovery completely reverses the one before, because it considers all the possible evolutionary trees and weighs them according to the likelihood that each is correct," says Huelsenbeck. "It's more robust because it compares each new bit of information against the overall understanding we have about evolution."

For centuries the scientific community largely ignored Bayes and his equation, in part because the calculations needed would take years, but the last decade has seen a resurgence of Bayes' popularity as computers have taken over the task of calculating Bayes' formula. Bayes would probably have been stunned to learn that doctors testing new drugs, chemists deducing the structure of unknown molecules, environmentalists tracking dwindling species, and researchers teasing out the last of the human genome, have all become reliant on his statistics as they sort through data.

Ultimately, the team's use of Bayes' formula will allow biologists to be surer of their conclusions, creating a more consistent picture of evolution's history.

Though Bayes may have given scientists a new and powerful tool, his critics point out that a researcher's initial biases can affect calculations, allowing different answers to be generated from the same evidence. Huelsenbeck points out that in drawing the evolutionary tree, certain assumptions must be made because the relationships between species-the starting evidence-is not absolutely known. Huelsenbeck says, "Bayes gave us a way to climb a little higher, even if we aren't so sure of our footing."