Mutation choice biases the structure of empirical fitness landscapes

Evolution can be thought of as taking place in a fitness landscape which maps each genotype to a fitness value. This abstraction has motivated significant efforts to quantify the statistical properties of random fitness landscapes with different amounts and types of interactions among loci---broadly referred to as epistasis. New high-throughput experimental techniques measuring the phenotypes of thousands of genotypes promise to bridge this theory with data. Yet, while impressive, thousands is still small relative to the size of genotype space. Moreover, experiments often assay a highly non-random subset of the fitness landscape. For example, a common experimental approach is to generate all possible 2M sequence intermediates between ancestral and evolved sequences differing by M much less than L mutations. Here, we ask to what extent the statistics of an empirical landscape constructed under distinct ascertainment protocols recapitulate the statistics of a random subset of the global landscape in a few well-studied random landscape models. We show that, in most landscapes, selecting mutations which occurred along an adaptive trajectory inflates the variance explained by lower order epistasis, reduces the number of local maxima, and increases the number of accessible paths relative to a random fitness landscape. Selecting the most beneficial or deleterious mutations, on the other hand, results in distortions to these statistics which depend more critically on the amount of epistasis in the global landscape. We then take advantage of several large-scale mutagenesis datasets to simulate the effects of ascertainment in more realistic settings.