Linkage disequilibrium and the genetic distance in livestock populations: the impact of inbreeding

Genome-wide linkage disequilibrium (LD) is subject to intensive investigation in human and livestock populations since it can potentially reveal aspects of a population history, permit to date them and help in fine-gene mapping. The most commonly used measure of LD between multiallelic loci is the coefficient D'. Data based on D' were recently published in humans, livestock and model animals. However, the properties of this coefficient are not well understood. Its sampling distribution and variance has received recent attention, but its expected behaviour with respect to genetic or physical distance remains unknown. Using stochastic simulations of populations having a finite size, we show that D' fits an exponential function having two parameters of simple biological interpretation: the residual value (rs) towards which D' tends as the genetic distance increases and the distance R at which this value is reached. Properties of this model are evaluated as a function of the inbreeding coefficient (F). It was found that R and rs increase when F increases. The proposed model offers opportunities to better understand the patterns and the origins of LD in different populations and along different chromosomes.