Abstract
Fisher's geometric model has been widely used to study the effects of pleiotropy and organismic complexity on phenotypic adaptation. Here, we study a version of Fisher's model in which a population adapts to a gradually moving optimum. Key parameters are the rate of environmental change, the dimensionality of phenotype space, and the patterns of mutational and selectional correlations. We focus on the distribution of adaptive substitutions, that is, the multivariate distribution of the phenotypic effects of fixed beneficial mutations. Our main results are based on an “adaptive-walk approximation,” which is checked against individual-based simulations. We find that (1) the distribution of adaptive substitutions is strongly affected by the ecological dynamics and largely depends on a single composite parameter γ, which scales the rate of environmental change by the “adaptive potential” of the population; (2) the distribution of adaptive substitution reflects the shape of the fitness landscape if the environment changes slowly, whereas it mirrors the distribution of new mutations if the environment changes fast; (3) in contrast to classical models of adaptation assuming a constant optimum, with a moving optimum, more complex organisms evolve via larger adaptive steps.
Highlights
Natural populations are constantly faced with environmental changes that force them to either adapt or go extinct
We find that (1) the distribution of adaptive substitutions is strongly affected by the ecological dynamics and largely depends on a single composite parameter γ, which scales the rate of environmental change by the “adaptive potential” of the population; (2) the distribution of adaptive substitution reflects the shape of the fitness landscape if the environment changes slowly, whereas it mirrors the distribution of new mutations if the environment changes fast; (3) in contrast to classical models of adaptation assuming a constant optimum, with a moving optimum, more complex organisms evolve via larger adaptive steps
The statistical description of this process has been at the heart of evolutionary biology (Charlesworth 1996), and is key to addressing seemingly simple questions, such as: From the set of mutations that emerge in a population, which are the ones that will get fixed and what is their effect on phenotype or fitness? Will adaptation proceed by many steps of small effect or just by a few adaptive substitutions of large effect? Do simple organisms evolve faster than complex ones?
Summary
Natural populations are constantly faced with environmental changes that force them to either adapt or go extinct. The brood parasitic common cuckoo (Cuculus canorus) population, for example, declined in size by 6% since 1980, as they failed to synchronize their reproductive and migratory cycles with those of their particular host species, to which they are adapted to in terms of egg size, coloration, and spottiness (Antonov et al 2010; Møller et al 2011). Numerous theoretical studies of the population genetics of adaptation have attempted to provide a formal framework for the observed empirical phenomena (for a review see Orr 2005b). Central to these studies is the description of the fundamental event during adaptation, that is, the substitution of a resident allele (i.e., gene variant) by a beneficial mutation.
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