Phenotypic differences between species may be attributable to natural selection. However, it is a difficult task to quantify the strength of evidence for selection acting on a particular trait. Here we develop a population-genetic test for selection acting on a quantitative trait, which is based on multiple-line crosses. We show that using multiple lines increases both the power and the scope of selection inference. First, a test based on three or more lines detects selection on a quantitative trait with strongly increased statistical significance, which is quantified by our analysis. Second, a multiple-line test allows to distinguish selection from neutral evolution as well as lineage-specific selection from selection under uniform selection strength. This is in contrast to tests based on two lines, where only differences in selection coefficients can be inferred. Our analytical results are complemented by extensive numerical simulations. We apply the multiple-line test to QTL data on floral character traits in plant species of the Mimulus genus and on photoperiodic traits in different maize strains. In both cases, we find a signature of lineage-specific selection that is not seen in a two-line test. We also extend the multiple-line test to short divergence times.

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.

The seasonal human influenza A (H3N2) virus undergoes rapid evolution, which produces significant year-to-year sequence turnover in the population of circulating strains. Adaptive mutations respond to human immune challenge and occur primarily in antigenic epitopes, the antibody-binding domains of the viral surface protein haemagglutinin. Here we develop a fitness model for haemagglutinin that predicts the evolution of the viral population from one year to the next. Two factors are shown to determine the fitness of a strain: adaptive epitope changes and deleterious mutations outside the epitopes. We infer both fitness components for the strains circulating in a given year, using population-genetic data of all previous strains. From fitness and frequency of each strain, we predict the frequency of its descendent strains in the following year. This fitness model maps the adaptive history of influenza A and suggests a principled method for vaccine selection. Our results call for a more comprehensive epidemiology of influenza and other fast-evolving pathogens that integrates antigenic phenotypes with other viral functions coupled by genetic linkage.

Molecular traits, such as gene expression levels or protein binding affinities, are increasingly accessible to quantitative measurement by modern high-throughput techniques. Such traits measure molecular functions and, from an evolutionary point of view, are important as targets of natural selection. We review recent developments in evolutionary theory and experiments that are expected to become building blocks of a quantitative genetics of molecular traits. We focus on universal evolutionary characteristics: these are largely independent of a trait's genetic basis, which is often at least partially unknown. We show that universal measurements can be used to infer selection on a quantitative trait, which determines its evolutionary mode of conservation or adaptation. Furthermore, universality is closely linked to predictability of trait evolution across lineages. We argue that universal trait statistics extends over a range of cellular scales and opens new avenues of quantitative evolutionary systems biology.

Histone–DNA complexes, so-called nucleosomes, are the building blocks of DNA packaging in eukaryotic cells. The histone-binding affinity of a local DNA segment depends on its elastic properties and determines its accessibility within the nucleus, which plays an important role in the regulation of gene expression. Here, we derive a fitness landscape for intergenic DNA segments in yeast as a function of two molecular phenotypes: their elasticity-dependent histone affinity and their coverage with transcription factor binding sites. This landscape reveals substantial selection against nucleosome formation over a wide range of both phenotypes. We use it as the core component of a quantitative evolutionary model for intergenic DNA segments. This model consistently predicts the observed diversity of histone affinities within wild Saccharomyces paradoxus populations, as well as the affinity divergence between neighboring Saccharomyces species. Our analysis establishes histone binding and transcription factor binding as two separable modes of sequence evolution, each of which is a direct target of natural selection.