Inferring fitness landscapes by regression produces biased estimates of epistasis

Jakub Otwinowski, Joshua B. Plotkin
(Submitted on 3 Apr 2014)

The genotype-fitness map plays a fundamental role in shaping the dynamics of evolution. However, it is difficult to directly measure a fitness landscape in practice, because the number of possible genotypes is astronomical. One approach is to sample as many genotypes as possible, measure their fitnesses, and fit a statistical model of the landscape that includes additive and pairwise interactive effects between loci. Here we elucidate the pitfalls of using such regressions, by studying artificial but mathematically convenient fitness landscapes. We identify two sources of bias inherent in these regression procedures that each tends to under-estimate high fitnesses and over-estimate low fitnesses. We characterize these biases for random sampling of genotypes, as well as for samples drawn from a population under selection in the Wright-Fisher model of evolutionary dynamics. We show that common measures of epistasis, such as the number of monotonically increasing paths between ancestral and derived genotypes, the prevalence of sign epistasis, and the number of local fitness maxima, are distorted in the inferred landscape. As a result, the inferred landscape will provide systematically biased predictions for the dynamics of adaptation. We identify the same biases in a computational RNA-folding landscape, as well as in regulatory sequence binding data, treated with the same fitting procedure. Finally, we present a method that may ameliorate these biases in some cases.

Stability and response of polygenic traits to stabilizing selection and mutation

Harold P. de Vladar, Nick Barton
(Submitted on 3 Apr 2014)

When polygenic traits are under stabilizing selection, many different combinations of alleles allow close adaptation to the optimum. If alleles have equal effects, all combinations that result in the same deviation from the optimum are equivalent. Furthermore, the genetic variance that is maintained by mutation-selection balance is 2μ/S per locus, where μ is the mutation rate and S the strength of stabilizing selection. In reality, alleles vary in their effects, making the fitness landscape asymmetric, and complicating analysis of the equilibria. We show that that the resulting genetic variance depends on the fraction of alleles near fixation, which contribute by 2μ/S, and on the total mutational effects of alleles that are at intermediate frequency. The interplay between stabilizing selection and mutation leads to a sharp transition: alleles with effects smaller than a threshold value of 2μ/S‾‾‾‾√ remain polymorphic, whereas those with larger effects are fixed. The genetic load in equilibrium is less than for traits of equal effects, and the fitness equilibria are more similar. We find that if the optimum is displaced, alleles with effects close to the threshold value sweep first, and their rate of increase is bounded by μS‾‾‾√. Long term response leads in general to well-adapted traits, unlike the case of equal effects that often end up at a sub-optimal fitness peak. However, the particular peaks to which the populations converge are extremely sensitive to the initial states, and to the speed of the shift of the optimum trait value.

Protected polymorphisms and evolutionary stability of patch-selection strategies in stochastic environments

Steve Evans, Alexandru Hening, Sebastian Schreiber

We consider consider a population living in a patchy environment that varies stochastically in space and time. The population is composed of two morphs (that is, individuals of the same species with different genotypes). In terms of survival and reproductive success, the associated phenotypes differ only in their habitat selection strategies. We compute invasion rates corresponding to the rates at which the abundance of an initially rare morph increases in the presence of the other morph established at equilibrium. If both morphs have positive invasion rates when rare, then there is an equilibrium distribution such that the two morphs coexist; that is, there is a protected polymorphism for habitat selection. Alternatively, if one morph has a negative invasion rate when rare, then it is asymptotically displaced by the other morph under all initial conditions where both morphs are present. We refine the characterization of an evolutionary stable strategy for habitat selection from [Schreiber, 2012] in a mathematically rigorous manner. We provide a necessary and sufficient condition for the existence of an ESS that uses all patches and determine when using a single patch is an ESS. We also provide an explicit formula for the ESS when there are two habitat types. We show that adding environmental stochasticity results in an ESS that, when compared to the ESS for the corresponding model without stochasticity, spends less time in patches with larger carrying capacities and possibly makes use of sink patches, thereby practicing a spatial form of bet hedging.