Selecting Chromosomes for Polygenic Traits

Abstract

AbstractWe define and study the problem ofchromosomal selectionfor multiple complex traits. In this problem, it is assumed that one can construct a genome by selecting different genomic parts (e.g. chromosomes) from different cells. The constructed genome is associated with a vector of polygenic scores, obtained by summing the polygenic scores of the different genomic parts, and the goal is to minimize a loss function of this vector. While out of reach today, the problem may become relevant in the future with emerging future technologies, and may yield far greater gains in the loss compared to the present day technology of as embryo selection, provided that technological and ethical barriers are overcome. We suggest and study several natural loss functions relevant for both quantitative traits and disease. We propose two algorithms, a Branch-and-Bound technique, to solve the problem for multiple traits and any monotone loss function, and a convex relaxation algorithm applicable for any differentiable loss. Finally, we use the infinitesimal model for genetic architecture to approximate the potential gain achieved by chromosomal selection for multiple traits.