Natural Selection as Coarsening
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Analogies between evolutionary dynamics and statistical mechanics, such as Fisher’s second-law-like “fundamental theorem of natural selection” and Wright’s “fitness landscapes”, have had a deep and fruitful influence on the development of evolutionary theory. Here I discuss a new conceptual link between evolution and statistical physics. I argue that natural selection can be viewed as a coarsening phenomenon, similar to the growth of domain size in quenched magnets or to Ostwald ripening in alloys and emulsions. In particular, I show that the most remarkable features of coarsening—scaling and self-similarity—have strict equivalents in evolutionary dynamics. This analogy has three main virtues: it brings a set of well-developed mathematical tools to bear on evolutionary dynamics; it suggests new problems in theoretical evolution; and it provides coarsening physics with a new exactly soluble model.
KeywordsNatural selection Coarsening Scaling limit Self-similarity Regular variation Dissipation
The analogy between selection and Ostwald ripening was pointed out to me by Felix Otto during a visit at the Max Planck Institute for Mathematics in the Sciences. I thank Robert Pego and Baruch Meerson for comments on this manuscript. Research at the Perimeter Institute is supported in part by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation.
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