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

Abstract

Abstract. We present an efficient computational approach for detecting genetic interactions from fitness comparison data together with a geometric interpretation using polyhedral cones associated to partial orderings. Genetic interactions are defined by linear forms with integer coefficients in the fitness variables assigned to genotypes. These forms generalize several popular approaches to study interactions, including Fourier-Walsh coefficients, interaction coordinates, and circuits. We assume that fitness measurements come with high uncertainty or are even unavailable, as is the case for many empirical studies, and derive interactions only from comparisons of genotypes with respect to their fitness, i.e. from partial fitness orders. We present a characterization of the class of partial fitness orders that imply interactions, using a graph-theoretic approach. Our characterization then yields an efficient algorithm for testing the condition when certain genetic interactions, such as sign epistasis, are implied. This provides an exponential improvement of the best previously known method. We also present a geometric interpretation of our characterization, which provides the basis for statistical analysis of partial fitness orders and genetic interactions.

Inferring genetic interactions from comparative fitness data

“…Consequently, the partial order does not reveal whether or not the system has epistasis, and further comparisons are needed for a conclusion. A more detailed treatment of partial fitness orders can be found in Lienkaemper et al (2017) .…”

“…This feature may prove useful in guiding fitness experiments that aim for testing specific interactions and allow for iteration. We have developed this idea further in Lienkaemper et al (2017) , where we consider partial fitness orders of genotypes and develop efficient algorithms to detect genetic interactions, as well as study the geometry of such partial orders. Evolutionary aspects of partial orders and gene interactions are studied in Crona and Luo, 2017 .…”

SNVformer: An Attention-based Deep Neural Network for GWAS Data

“…Additionally, typical GWAS are done using a simple additive model, that fails to account for potential dominance effects of different genotypes (Zhu et al, 2015; Hivert et al, 2021). They also often simplify complex multi-dimensional phenotypes to a one-dimensional response variable (Lienkaemper et al, 2018). If epistasis contributes to the genetic architecture of a trait, then identifying epistatic variants is important for improving the predictive power of a GWAS (Crona et al, 2017).…”

A Fast Lasso-Based Method for Inferring Higher-Order Interactions

“…Epistatic gene interactions have practical implications for personalised medicine, and synthetic lethal interactions in particular can be used in cancer treatment [4]. Discovering these interactions is currently challenging at a practical scale [35, 25, 14, 16], however. In particular, there are no methods able to infer three-way effects.…”