Inferring genetic interactions from comparative fitness data

Abstract

Darwinian fitness is a central concept in evolutionary biology. In practice, however, it is hardly possible to measure fitness for all genotypes in a natural population. Here, we present quantitative tools to make inferences about epistatic gene interactions when the fitness landscape is only incompletely determined due to imprecise measurements or missing observations. We demonstrate that genetic interactions can often be inferred from fitness rank orders, where all genotypes are ordered according to fitness, and even from partial fitness orders. We provide a complete characterization of rank orders that imply higher order epistasis. Our theory applies to all common types of gene interactions and facilitates comprehensive investigations of diverse genetic interactions. We analyzed various genetic systems comprising HIV-1, the malaria-causing parasite Plasmodium vivax, the fungus Aspergillus niger, and the TEM-family of β-lactamase associated with antibiotic resistance. For all systems, our approach revealed higher order interactions among mutations.

The Geometry of Partial Fitness Orders and an Efficient Method for Detecting Genetic Interactions

“…The linear order L does not map to a Dyck word (starting in P ) under φ f , since the image of the smallest prefix of L which contains all elements of S contains more N 's than P 's since |S| > |N G (S)|. Therefore, by Theorem 3 from (Crona, Gavryushkin, et al 2017), this partial order does not imply positive f -interaction.…”

“…Moreover, even when a complete fitness ranking of genotypes is available a method to detect interactions from a partial order alone might provide additional insight. Indeed, there are cases where the rank order method fails to reveal interactions even though interactions in the system can be detected from the actual fitness measurements (Crona, Gavryushkin, et al 2017). In this case, partial fitness order methods can be used to conclude diminishing returns or synergistic epistasis and refute sign epistasis.…”

“…We note that the fact that a partial order does not imply positive or negative f -interaction does not necessarily mean that the system does not have finteraction. This situation therefore should be interpreted as the partial order being non-informative with respect to the f -interaction; the issue is discussed in more detail in (Crona, Gavryushkin, et al 2017).…”

“…We now review the results from (Crona, Gavryushkin, et al 2017) about how to detect whether a rank order implies f -interaction. In the terminology used in our paper, this situation corresponds to the case when the partial fitness order is a linear order (also called a total order or a rank order).…”

“…The subwords of ω corresponding to different g i 's appear according to the linear order (from highest to lowest). See (Crona, Gavryushkin, et al 2017) for various examples of this construction.…”