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Properties of estimators of the inbreeding coefficient and the rate of cross fertilization obtained from gene frequency data in a diploid population

Joel Augusto Muniz^I; Décio Barbin^II; Roland Vencovsky^III

^IDepartamento de Ciências Exatas, Universidade Federal de Lavras, Caixa Postal 37, 37200-000 Lavras, MG, Brasil. Send correspondence to J.A.M.
^IIDepartamento de Matemática e Estatística, Escola Superior de Agricultura "Luiz de Queiroz", Universidade de São Paulo, 13418-900 Piracicaba, SP, Brasil
^IIIDepartamento de Genética, Escola Superior de Agricultura "Luiz de Queiroz", Universidade de São Paulo, 13418-900 Piracicaba, SP, Brasil

ABSTRACT

The properties of the estimators of the inbreeding coefficient and the cross pollination rate were investigated in a diploid population. The estimates, obtained by the moments method, were based on the analysis of variance of the gene frequency of individuals from random samples. Since these estimators were obtained from the ratio of two random variables, approximations were produced by the Taylor series function. The formulas obtained were checked using simulation data. The results indicated that the estimators of the inbreeding and cross pollination rates are positively and negatively biased, respectively. The expression of these tendencies is a function of 1 /n, which becomes smaller as the sample size increases. The simulation confirmed those results and the validity of the expressions to calculate the error of the estimates.

Keywords: inbreeding coefficient; fertilization; gene frequency; diploid population.

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