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Evolutionary biology

The geometry of adaptation

Nature volume 395, pages 751–752 (1998)Cite this article

Darwin1 explained the evolution of complex adaptations, such as the vertebrate eye, through the gradual “accumulation of innumerable slight varia- tions, each good for the individual possessor”. In contrast, the early geneticists emphasized the role of major mutations, and disregarded natural selection2. The mathematical theory of Fisher, Haldane and Wright reconciled Mendelian genetics with Darwinian gradualism by showing that genetic variants that slightly enhanced reproductive success would quickly replace their competitors. Nevertheless, the conflict over the magnitude of the genetic changes responsible for adaptation continues to this day3. Although classical population genetics can find the consequences of a given pattern of selection, it says nothing about the causes of such selection. Indeed, theoretical support for gradualism rests mainly on a geometrical analogy, proposed by Fisher4 in 1930, which suggests that large changes to a complex system are unlikely to be favourable. Now, reporting in Evolution, H. Allen Orr5 shows that adaptation may be based on larger factors than previously supposed.

But a fundamental flaw in Fisher's argument was found, half a century later. Kimura6 pointed out that although small changes are most likely to increase fitness, they are also most likely to be lost by chance. Even in a large population, a single mutation that increases relative fitness by s has a chance of only around 2s of being established4. Kimura showed that if the selective advantage of a mutation is proportional to its effective size, x, then the chance that the mutant is favourable and becomes common is 2x(1-φ(x)). The expected effective size of successful mutations is . Thus, mutations of intermediate effect are most likely to contribute. For example, with n=50 dimensions, the first adaptive step will average 30% of the distance to the optimum, d/2. However, because its direction is random, it will take the population only about 4% further towards the optimum.

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Figure 1: Approach of a population towards an optimum through selection of a series of random mutations, through a space of ten dimensions.

References

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  1. the Institute of Cell, Animal and Population Biology, Kings Buildings, University of Edinburgh, EH9 3JT, Edinburgh, UK

    Nick Barton

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Barton, N. The geometry of adaptation. Nature 395, 751–752 (1998). https://doi.org/10.1038/27338

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