Résumé
When are mutations beneficial in one environment and deleterious in
another? More generally, what is the relationship between mutation effects
across environments? These questions are crucial to predict adaptation in
heterogeneous conditions in a broad sense. Empirical evidence documents
various patterns of fitness effects across environments but we still lack
a framework to analyse these multivariate data. In this paper, we extend
Fisher’s geometrical model to multiple environments determining distinct
peaks. We derive the fitness distribution, in one environment, among
mutants with a given fitness in another and the bivariate distribution of
random mutants’ fitnesses across two or more environments. The geometry of
the phenotype-fitness landscape is naturally interpreted in terms of
fitness trade-offs between environments. These results may be used to
fit/predict empirical distributions or to predict the pattern of
adaptation across heterogeneous conditions. As an example, we derive the
genomic rate of substitution and of adaptation in a metapopulation divided
into two distinct habitats in a high migration regime and show that they
depend critically on the geometry of the phenotype-fitness landscape. --