Estimation of effective population size using bivariate discrete distributions for modeling family size in beef cattle

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Pedigree records of 72,808 animals (45,668 females and 27,140 males) from the genetic evaluation program of the Argentine Brangus Association were used to estimate effective number of founders ( N f ), effective number of ancestors ( N a ), and effective population size under random mating ( N e ) or selection ( N eS ), in order to assess genetic variability. The average level of completeness of the pedigree was low (0.17) and the average level of inbreeding ( F) calculated from the pedigree was equal to 0.24%. Animals in the reference population were 21,662 calves born from 2001 to 2005. The estimated measures of variability were N f = 765.7 and N a = 387.5. The numbers of ancestors responsible for 100%, 50%, or 20% of the genes in the reference group, were equal to 12,471, 273, and 22, respectively. Direct estimates of N e and N eS were calculated using the variances and covariances of family sizes, i.e. male and female progeny numbers for bulls and cows. Estimates of the dispersion parameters were from the Bivariate Poisson model for the cows, and from the Generalized Bivariate Negative Binomial (GBIVARNB) distribution for the bulls. The latter probability mass function accounted for overdispersion, a characteristic present in the sampling distribution of family size of bulls. The estimated variances of male and female progeny and the covariance between them for the bulls were 5.70, 271.28, and 30.15, respectively, and 1.15, 2.10, and 1.06 for the cows. Generation intervals (in years) were: sires of bulls = 5.0, sires of cows = 5.7, dams of bulls = 4.4, and dams of cows = 5.2. The estimated N e was 274, which corresponds to a rate of inbreeding ( F) of 0.18%, whereas N eS = 125 and F = 0.40%. As a check of the proposed methodology, all analyses were also performed using the pedigree records of 10,483 Angus animals from a herd with an average level of completeness of 0.68. Using the GBIVARNB model for both bulls and cows the estimated N e = 95.4, thus F = 0.5% in perfect agreement with the calculated average inbreeding from pedigree records. Under selection, N eS = 79.3 and F = 0.6%. The larger difference between estimated N e and N eS in the Brangus was related to the smaller bull to cow ratio in the breed. Therefore, it seems desirable to continue monitoring the effective size of the Argentine Brangus to prevent problems of inbreeding and lack of variability in the future.