Natural selection has been a cornerstone of evolutionary theory ever since Darwin. Yet mathematical models of natural selection have often been dogged by an awkward problem that seemed to make evolution harder than biologists understood it to be. In a new paper appearing in Communications Biology, a multidisciplinary team of scientists in Austria and the United States identify a possible way out of the conundrum. Their answer still needs to be checked against what happens in nature, but in any case, it could be useful for biotechnology researchers and others who need to promote natural selection under artificial circumstances.

A central premise of the theory of evolution through natural selection is that when beneficial mutations appear, they should spread throughout a population. But this outcome isn’t guaranteed. Random accidents, illnesses and other misfortunes can easily erase mutations when they are new and rare—and it’s statistically likely that they often will.

Mutations should theoretically face better odds of survival in some situations than others, however. Picture a huge population of organisms all living together on one island, for example. A mutation might get permanently lost in the crowd unless its advantage is great. Yet if a few individuals regularly migrate to their own islands to breed, then a modestly helpful mutation might have a better chance of establishing a foothold and spreading back to the main population. (Then again, it might not—the outcome would depend entirely on the precise details of the scenario.) Biologists study these population structures to understand how genes flow.

Martin Nowak, the director of the Program for Evolutionary Dynamics at Harvard University, became interested in the effects of population structures on natural selection while studying cancer. Sharona Jacobs

Martin Nowak, who is today the director of Harvard University’s Program for Evolutionary Dynamics, began thinking about how population structures could potentially affect evolutionary outcomes in 2003 while studying the behavior of cancer. “It was clear to me then that cancer is an evolutionary process that the organism does not want,” he said: After malignant cells arise through mutation, competition among those cells selects for the ones best able to run rampant through the body. “I asked myself, how would you get rid of evolution?” Attacking mutations was one solution, Nowak realized, but attacking selection was another.

The problem was that biologists had only loose ideas about how specific population structures might affect natural selection. To find more generalizable strategies, Nowak turned to graph theory.

Mathematical graphs are structures that represent the dynamic relations among sets of items: Individual items sit at the vertices of the structure; the lines, or edges, between every pair of items describe their connection. In evolutionary graph theory, individual organisms occupy every vertex. Over time, an individual has some probability of spawning an identical offspring, which can replace an individual on a neighboring vertex, but it also faces its own risks of being replaced by some individual from the next generation. Those probabilities are wired into the structure as “weights” and directions in the lines between the vertices. The right patterns of weighted connections can stand in for behaviors in living populations: For example, connections that make it more likely that lineages will become isolated from the rest of a population can represent migrations.

With graphs, Nowak could depict diverse population structures as mathematical abstractions. He could then rigorously explore how mutants with extra fitness would fare in each scenario.