Predictive Model and Software for Inbreeding-Purging Analysis of Pedigreed Populations

Abstract

The inbreeding depression of fitness traits can be a major threat to the survival of populations experiencing inbreeding. However, its accurate prediction requires taking into account the genetic purging induced by inbreeding, which can be achieved using a “purged inbreeding coefficient”. We have developed a method to compute purged inbreeding at the individual level in pedigreed populations with overlapping generations. Furthermore, we derive the inbreeding depression slope for individual logarithmic fitness, which is larger than that for the logarithm of the population fitness average. In addition, we provide a new software, PURGd, based on these theoretical results that allows analyzing pedigree data to detect purging, and to estimate the purging coefficient, which is the parameter necessary to predict the joint consequences of inbreeding and purging. The software also calculates the purged inbreeding coefficient for each individual, as well as standard and ancestral inbreeding. Analysis of simulation data show that this software produces reasonably accurate estimates for the inbreeding depression rate and for the purging coefficient that are useful for predictive purposes.

Inbreeding depression for kit survival at birth in a rabbit population under long-term selection

“…This method is called "expressed opportunity of purging" and can be applied only to purging that occurs within a few generations, more details are in Gulisija and Crow [20]. Conversely, a fourth approach, called the "inbreeding-purging method", can be applied to purging that occurs over a long time [21]. According to López-Cortegano et al [22], the "inbreeding-purging method is based on a purged inbreeding coefficient that predicts how mean fitness and inbreeding load are expected to evolve in a population undergoing inbreeding".…”

Detection of genetic purging and predictive value of purging parameters estimated in pedigreed populations

“…A simple recurrence equation calculates g each generation as a function of d, the effective population size N, and the F and g values in the previous generation, or from pedigree data. García-Dorado et al (2016) generalized the pedigree recurrence equations to allow for overlapping generations. These equations parallel those classically used to predict the evolution of F using Malecot's coancestry coefficients, introducing an additional term that depends on d. Thus, the model can predict either the average fitness expected at generation t (W t ), or the expected fitness for an individual i with pedigree records (W i ).…”

“…1 by numerically searching for estimates that minimize the residual sums of squares . The expected fitness value in the non-inbred population, E(W 0 ), is obtained in a previous step as the mean fitness of noninbred individuals with non-inbred ancestors (F = F a = 0), as explained in García-Dorado et al (2016). Therefore, the program produces estimates of δ and d that are conditional to this estimate of the non-inbred expected fitness.…”

“…An updated version of the PURGd software (PURGd 2.0) published by García-Dorado et al (2016) is available from https://www.ucm.es/genetica1/mecanismos.…”

“…Furthermore, equations have been derived to obtain IP predictions for pedigreed individuals and have been implemented in the free software package PURGd. This software analyzes pedigreed fitness data to obtain estimates of the IP parameters, namely the rate of inbreeding depression δ and the purging coefficient d (García-Dorado 2012; García-Dorado et al 2016). Preliminary analysis of simulated data showed that this software accurately discriminates between situations with and without purging, and that the genealogical IP approach consistently provided a good fit to the data.…”