Theor Appl Genet (1993) 87:446-454 9 9Springer-Verlag 1993 Long-term effects of selection based on the animal model BLUP in a finite population E. Verrier 1, J. J. Colleau 2, J. L. Foulley 2 1 Institut National Agronomique Paris-Grignon, D6partement des Sciencesanimales, 16 rue Claude Bernard, 75231 Paris Cedex 05, France 2 INRA, Station de G6n~tique Quantitative et Appliqu~e, 78352 Jouy-en-Josas Cedex, France Received: 4 January 1993 / Accepted: 20 April 1993 Abstract. Monte Carlo simulation was used to assess the long-term effects of truncation selection within small populations using indices (I = of + m) combin- ing mid-parent If = (as + ae)/2] and Mendelian-samp- ling (m = a-f) evaluations provided by an animal model BLUP (a =f + m). Phenotypic values of pan- mictic populations were generated for 30 discrete gen- erations. 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 co = 1 (animal model BLUP), co = 1/2, or co = 0 (selection on within-family deviations). Mass selection was also considered. Selection based on the animal model BLUP (co = 1) maximized the cumulative gen- etic gain in L populations. In S populations, selection using co = 1/2 and mass selection were more efficient than selection under an animal model ( + 3 to + 7% and + 1 to + 4% respectively, depending on h2). Selec- tion 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 vari- ance and the average coefficient of inbreeding (F) were highly affected by selection with co = 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 Communicated by L. D. VanVleck Correspondence to: E. Verrier 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. Key words: Animal model BLUP - Genetic response - Genetic variability - Inbreeding Introduction Mid- and long-term responses to selection depend on changes in additive genetic variance. Under a purely additive polygenic model, and even for an infinite population, directional selection modifies the genetic variance by inducing linkage disequilibrium (Lush 1945; Bulmer 1971). If populations are of finite size, selection affects the family structure, increasing the loss of genetic variability by inbreeding (Lush 1946; Rober- tson 1961). In this case, the choice of a selection cri- terion should be made on the basis of the expected cumulative genetic gain in the long term rather than the response to one generation of selection. Some simulation results (Dempfle 1975; Toro and Perez- Enciso 1990) or deterministic prediction results (Verrier et al. 1989a) suggest that using the conven- tional weights (according to selection index theory) for individual and family information does not lead to maximum response in the long term. Furthermore, a too-high rate of inbreeding might have direct econ- omic consequences as a result of inbreeding depres- sion which mainly affects reproduction and viability traits.