Abstract

SAHAGUN-CASTELLANOS, J.. Inbreeding coefficient of a self sterile population with sampling of families. Rev. Chapingo Ser.Hortic [online]. 2008, vol.14, n.3, pp.257-262. ISSN 2007-4034.

To measure the inbreeding intensity produced in finite populations of alogamous species that undergo random mating without selfing [as in the case of some ornamental species of the Primula genus and husk tomato (Physalis ixocarpa Brot.)], a formula for the inbreeding coefficient (IC) has been derived in probabilistic terms under the assumption that in the studied population each cycle was formed by n families of m half sibs each. Each family is formed by the seed of a set of n random individuals from the previous generation, as occurs in mass selection. Since for m = 1 this formula is not reduced to any known formula for this case, theoretical research in probabilistic terms was undertaken to explain the cause of this discrepancy and to identify or derive an exact IC for the case under study. It was found that when cycle zero is formed by mn noninbred and unrelated individuals, for cycles 0, 1, and 2 the exact ICs were F₀ = 0, F₁ = 0, and F₂ = 1/(2mn), respectively, and for t = 3,4,5, ... the exact IC was F_t = (1+F_t-2) /(2mn) + (m-1)(1+F_t-3 + 6F_t-2) /(8mn) + (n-1)F_t-2 /n. For the case where cycle zero is formed by n families of m noninbred half sibs each, the IC formula, as of cycle one produces higher IC values than those produced by the previous case.

Keywords : coancestry coefficient; ideal population; identity by descent; half-sib family; response to selection.