Genetic implications of a bivariate threshold model for litter size components.

Abstract

A bivariate threshold model for ovulation rate and embryonic survival was developed and the genetic relationships in the observed scale among ovulation rate, embryonic survival, and litter size were derived. This model was applied to data of nulliparous Lacaune sheep. Heritabilities assumed were .30, .05, and .12 for ovulation rate, embryonic survival, and litter size, respectively. Three values for genetic correlation between ovulation rate and embryonic survival were considered: -.78, -.30, and 0. Three criteria to increase litter size were studied: a linear index combining ovulation rate and embryonic survival, ovulation rate, and litter size. The linear index used gave an increasing weight to embryonic survival with higher ovulation rates. A selection scheme was simulated to test predications of response for the different criteria. A nucleus of 10 sires and 300 dams was simulated. Females were selected according to their own performance (mean of three records) and males according to their dam's performance. Selection was continued for six discrete generations. Response with an index was better than direct selection only in the short term, whereas this superiority was not maintained in the last generations of selection. Indirect selection on ovulation rate was clearly inferior to both index and direct selection. In the situation analyzed here, litter size seems to be close to the optimum 'natural index' combining ovulation rate and embryonic survival.