Abstract
Molecular phenotypes link genomic information with organismic functions, fitness, and evolution. Quantitative traits are complex phenotypes that depend on multiple genomic loci. In this paper, we study the adaptive evolution of a quantitative trait under time-dependent selection, which arises from environmental changes or through fitness interactions with other co-evolving phenotypes. We analyze a model of trait evolution under mutations and genetic drift in a single-peak fitness seascape. The fitness peak performs a constrained random walk in the trait amplitude, which determines the time-dependent trait optimum in a given population. We derive analytical expressions for the distribution of the time-dependent trait divergence between populations and of the trait diversity within populations. Based on this solution, we develop a method to infer adaptive evolution of quantitative traits. Specifically, we show that the ratio of the average trait divergence and the diversity is a universal function of evolutionary time, which predicts the stabilizing strength and the driving rate of the fitness seascape. From an information-theoretic point of view, this function measures the macro-evolutionary entropy in a population ensemble, which determines the predictability of the evolutionary process. Our solution also quantifies two key characteristics of adapting populations: the cumulative fitness flux, which measures the total amount of adaptation, and the adaptive load, which is the fitness cost due to a population's lag behind the fitness peak.
Highlights
This is the second in a series of papers on the evolution of quantitative traits in biological systems [1]
Predictability can be defined in a straightforward way [1]: How much of the trait repertoire in an ensemble of parallel-evolving populations is already contained in the trait diversity of a single population? We have shown that fitness seascapes have antagonistic effects: stabilizing selection enhances, lineage-specific directional selection decreases predictability
We have developed a statistical theory for the evolution of a quantitative trait in a stochastic fitness seascape
Summary
This is the second in a series of papers on the evolution of quantitative traits in biological systems [1]. We focus on molecular traits such as protein binding affinities or gene expression levels, which are mesoscopic phenotypes that bridge between genomic information and higher-level organismic traits. Such phenotypes are complex: they depend on tens to hundreds of constitutive genomic sites and are generically polymorphic in a population. Their evolution is often a strongly correlated process that involves linkage disequilibrium, i.e. allele associations due to incomplete recombination, and epistasis, i.e. fitness interactions, between constitutive sites. Our aim is to derive universal phenotypic features of these processes, which decouple from details of a trait’s genomic encoding and of the molecular evolutionary dynamics
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