The concept of a fitness landscape is a powerful metaphor that offers 10 insight into various aspects of evolutionary processes and guidance for the study of 11 evolution. Until recently, empirical evidence on the ruggedness of these landscapes 12 was lacking, but since it became feasible to construct all possible genotypes containing 13 combinations of a limited set of mutations, the number of studies has grown to a 14 point where a classification of landscapes becomes possible. The aim of this review 15 is to identify measures of epistasis that allow a meaningful comparison of fitness 16 landscapes and then apply them to the empirical landscapes to discern factors that 17 affect ruggedness. The various measures of epistasis that have been proposed in the 18 literature appear to be equivalent. Our comparison shows that the ruggedness of 19 the empirical landscape is affected by whether the included mutations are beneficial 20 or deleterious and by whether intra-or intergenic epistasis is involved. Finally, the 21 empirical landscapes are compared to landscapes generated with the Rough Mt. Fuji 22 model. Despite the simplicity of this model, it captures the features of the experimental 23 landscapes remarkably well.

Background: Bread wheat (Triticum aestivum) is an important staple food. However, wheat gluten proteins cause celiac disease (CD) in 0.5 to 1% of the general population. Among these proteins, the α-gliadins contain several peptides that are associated to the disease.

Understanding epistasis is central to biology. For instance, epistatic interactions determine the topography of the fitness landscape and affect the dynamics and determinism of adaptation. However, few empirical data are available, and comparing results is complicated by confounding variation in the system and the type of mutations used. Here, we take a systematic approach by quantifying epistasis in two sets of four beneficial mutations in the antibiotic resistance enzyme TEM-1 β-lactamase. Mutations in these sets have either large or small effects on cefotaxime resistance when present as single mutations. By quantifying the epistasis and ruggedness in both landscapes, we find two general patterns. First, resistance is maximal for combinations of two mutations in both fitness landscapes and declines when more mutations are added due to abundant sign epistasis and a pattern of diminishing returns with genotype resistance. Second, large-effect mutations interact more strongly than small-effect mutations, suggesting that the effect size of mutations may be an organizing principle in understanding patterns of epistasis. By fitting the data to simple phenotype resistance models, we show that this pattern may be explained by the nonlinear dependence of resistance on enzyme stability and an unknown phenotype when mutations have antagonistically pleiotropic effects. The comparison to a previously published set of mutations in the same gene with a joint benefit further shows that the enzyme's fitness landscape is locally rugged but does contain adaptive pathways that lead to high resistance.

For a quantitative understanding of the process of adaptation, we need to understand its “raw material,” that is, the frequency and fitness effects of beneficial mutations. At present, most empirical evidence suggests an exponential distribution of fitness effects of beneficial mutations, as predicted for Gumbel-domain distributions by extreme value theory. Here, we study the distribution of mutation effects on cefotaxime (Ctx) resistance and fitness of 48 unique beneficial mutations in the bacterial enzyme TEM-1 β-lactamase, which were obtained by screening the products of random mutagenesis for increased Ctx resistance. Our contributions are threefold. First, based on the frequency of unique mutations among more than 300 sequenced isolates and correcting for mutation bias, we conservatively estimate that the total number of first-step mutations that increase Ctx resistance in this enzyme is 87 [95% CI 75–189], or 3.4% of all 2,583 possible base-pair substitutions. Of the 48 mutations, 10 are synonymous and the majority of the 38 non-synonymous mutations occur in the pocket surrounding the catalytic site. Second, we estimate the effects of the mutations on Ctx resistance by determining survival at various Ctx concentrations, and we derive their fitness effects by modeling reproduction and survival as a branching process. Third, we find that the distribution of both measures follows a Fréchet-type distribution characterized by a broad tail of a few exceptionally fit mutants. Such distributions have fundamental evolutionary implications, including an increased predictability of evolution, and may provide a partial explanation for recent observations of striking parallel evolution of antibiotic resistance.