Effective Family Number Following Selection with Restrictions

Restricted selection and effective population size

“…Both were developed for considering inbreeding effect in offspring (N R by Robertson, 1961; N B by Burrows, 1984) For planning breeding programmes, breeders often need to predict selection differentials (genetic gain) as well as effective population size by using existing information (eg, K value) and designated operation parameters (m, s, P, P i , P 2 in the present case). Here we proceed in analogy with Burrows (1984) and Wei and Lindgren (1996) We assume that U! represents the number of individuals in the jth sampled family with performance exceeding the truncation point relative to P, P 1 and P 2 .…”

“…By using K = 0 as a factor, formulations for predicting effective population sizes have been developed for unrestricted selection and one-step restricted selection (Burrows, 1984;Wei and Lindgren, 1996). Proceeding in a similar way, the relevant hypergeometric sampling moments for the present situation yield and When K = 0, [7] yields the same result as (10!.…”

“…Searching for a truncation point corresponding to P, P 1 , and P 2 becomes complicated. A numerical procedure to calculate N r (K, P, P l , P 2 ) has been documented in previous studies (Wei, 1995;Wei and Lindgren, 1996).…”

“…In the following development the index will be treated in the same way as phenotypic value but with a different value for the ratio (K * ) of the variance of family mean to the total variance given by Wei and Lindgren (1994) Let P 1 = s r/ s and P 2 = m r/ m, the proportions of the restrictions s T and m r to the family size and number respectively. The extreme cases of restricted selection with specified P 1 and P 2 values describe conventional selections and onestep restricted selections as follows (Falconer, 1989;Wei, 1995;Wei and Lindgren, 1996). When both P 1 and P 2 are one, selection is based on either phenotypic or optimal index value but is unrestricted.…”

Combining genetic gain and diversity under an individual selection method in a selected provenance of Eucalyptus cladocalyx

“…In turn, the genetic diversity maintained after selection was estimated by means of the following formula proposed by Wei and Lindgren (1996):…”