Abstract

SAHAGUN-CASTELLANOS, Jaime  and  GARCIA-MEZANO, Francisco. The inbreeding coefficient of a population under mass selection. Agrociencia [online]. 2009, vol.43, n.2, pp.119-132. ISSN 2521-9766.

The inbreeding generated in the genetic improvement of finite populations of alogamous species is related to the concepts of ideal population, effective number of the population, and magnitude of the response to selection. Given that for mass selection there are two different equations to determine the inbreeding coefficient, a theoretical study was developed tending to verify the veracity of both. This study was made in probabilistic terms based on the ideal population model, where the advance of generations starts from the cycle 0 (C₀) which was a random sample of mn individuals that were not inbred and not related. In each one of the following cycles the sample was of n families of m half sibs each. It was found that for generation t, the inbreedng coefficient (F_t), derived here, is F_t = (1 + F_t-1) / (2mn) + (m - 1)(1 + F_t-2 + 6 F_t-1) / (8mn)+ (n - 1) F_t-1 / n where t = 2, 3, ...; F₀ = 0 and F₁ = (2mn)^-1. Furthermore, for the case in which C₀ is a sample of n families of m half sibs whose inbreeding coefficient is equal to zero, it was found that for the cycles 0 and 1 the inbreeding coefficients are F_0,F = 0 and F_1,F = 1/(2mn) + (m - 1)/(8mn), and for t = 2, 3,..., the inbreeding coefficient (F_t,F) has the same expression as that of F_t , except that the inbreeding coefficients are F_t-1F and F_t-2t instead of F_t-1 and F_t-2 . To include the effect of the selection pressure in these coefficients, mn, n and m are substituted by Ne(v) (effective number in terms of variance), (nN_e(v)m)^0.5 and (mN_e(v)n)^0.5.

Keywords : Inbreeding coefficient; coefficient of relationship or coancestry; effective number; selection response; mass selection.

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