Genetic evaluation of traits distributed as Poisson-binomial with reference to reproductive characters

Summary A procedure of genetic evaluation of reproductive traits such as litter size and survival in a polytocous species under the assumption of polygenic inheritance is described. Conditional distributions of these traits are assumed to be Poisson and Bernoulli, respectively. Using the concept of generalized linear models, logarithmic (litter size) and probit (survival) functions are described as linear combinations of nuisance environmental effects and of transmitting abilities of sires or individual breeding values. The liability of survival is expressed conditionally to the logarithm of litter size. Inferences on location parameters are based on the mode of their joint posterior density assuming a prior multivariate normal distribution. A method of estimation of the dispersion parameters is also presented. The use of a truncated Poisson distribution is suggested to account for missing records on litter size.On leave from INRA, Station de Génétique Quantitative et Appliquée Centre de Recherches Zootechniques, F-78350 Jouy-en-Josas, FranceOn leave from INRA, Laboratoire de Biometrie, Centre de Recherches de Toulouse, B.P.27, F-31326 Castanet-Tolosan Cedex, France