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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.

Monte Carlo simulation was used to assess the long-term effects of truncation selection within small populations using indices (I=ωf+m) combining mid-parent [f=(a i+a d)/2] and Mendelian-sampling (m=a-f) evaluations provided by an animal model BLUP (a=f+m). Phenotypic values of panmictic populations were generated for 30 discrete generations. Assuming a purely additive polygenic model, heritability (h 2) values were 0.10, 0.25 or 0.50. Two population sizes were considered: five males and 25 females selected out of 50 candidates of each sex (small populations, S) and 50 males and 250 females selected out of 500 candidates in each sex (large populations, L). Selection was carried out on the index defined above with ω = 1 (animal model BLUP), ω=1/2, or ω=0 (selection on within-family deviations). Mass selection was also considered. Selection based on the animal model BLUP (ω=1) maximized the cumulative genetic gain in L populations. In S populations, selection using ω = 1/2 and mass selection were more efficient than selection under an animal model (+ 3 to + 7% and + 1 to + 4% respectively, depending on h (2)). Selection on within-family deviations always led to the lowest gains. In most cases, the variance of response to selection between replicates did not depend on the selection method. The within-replicate genetic variance and the average coefficient of inbreeding (F) were highly affected by selection with ω=1 or 1/2, especially in populations of size S. As expected, selection based on within-family deviations was less detrimental in that respect. The number of copies of founder neutral genes at a separate locus, and the probability vector of origin of the genes in reference to the founder animals, were also observed in addition to F values. The conclusion was that selection procedures placing less emphasis on family information might be interesting alternatives to selection based on animal model BLUP, especially for small populations with long-term selection objectives.