Evolutionary dynamics on any population structure

• Published in: Nature (London) Vol. 544; no. 7649; pp. 227 - 230
• Main Authors: Allen, Benjamin, Lippner, Gabor, Chen, Yu-Ting, Fotouhi, Babak, Momeni, Naghmeh, Yau, Shing-Tung, Nowak, Martin A.
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 13.04.2017; Nature Publishing Group
• Subjects: 631/181/2468; 631/181/2469; 639/705/1041; Algorithms; Animals; Biological Evolution; Biological research; Coalescence; Computer Graphics; Cooperative Behavior; Ecosystem; Evolution (Biology); Game Theory; Genetics, Population - methods; Humanities and Social Sciences; Humans; letter; Models, Biological; multidisciplinary; Population biology; Population structure; Science; Selection, Genetic; Sociology - methods
• ISSN: 0028-0836; 1476-4687
• DOI: 10.1038/nature21723

The authors derive a condition for how natural selection chooses between two competing strategies on any graph for weak selection, elucidating which population structures promote certain behaviours, such as cooperation. Evolution, the great game Evolution is a game that anyone can play. The traits that evolve in a population depend on how the players interact. Students are familiar with toy populations in which every member of the population can interact equally with any other, but as W. S. Gilbert wrote, “When everyone is somebody, then no one's anybody”. In the real world, the numbers and identities of the players can change, and realistic simulations of evolution have proven exceedingly hard to create. Recent models have worked only in special cases in which all individuals have the same number of neighbours. Benjamin Allen and colleagues have now devised a model that works for any number of neighbours, providing that natural selection is weak. They simulate how small changes in population structure can affect evolutionary outcomes, and that cooperation flourishes most in populations with strong ties between pairs of individuals. Evolution occurs in populations of reproducing individuals. The structure of a population can affect which traits evolve 1 , 2 . Understanding evolutionary game dynamics in structured populations remains difficult. Mathematical results are known for special structures in which all individuals have the same number of neighbours 3 , 4 , 5 , 6 , 7 , 8 . The general case, in which the number of neighbours can vary, has remained open. For arbitrary selection intensity, the problem is in a computational complexity class that suggests there is no efficient algorithm 9 . Whether a simple solution for weak selection exists has remained unanswered. Here we provide a solution for weak selection that applies to any graph or network. Our method relies on calculating the coalescence times 10 , 11 of random walks 12 . We evaluate large numbers of diverse population structures for their propensity to favour cooperation. We study how small changes in population structure—graph surgery—affect evolutionary outcomes. We find that cooperation flourishes most in societies that are based on strong pairwise ties.