M

Table 10.4 The mean phenotypic value of progeny that result when an individual of the genotype A1A1 mates randomly. All genotypes in the population have Hardy-Weinberg expected frequencies. Therefore, each of the mating pairs has an expected frequency of p2, 2pq, or q2. The mean value of all progeny produced by the A1A1 genotype is the frequency-weighted sum of the progeny phenotypic values. Mprogeny A Ai forms the basis of the breeding value since the breeding value for A1A1 is Mprogeny A Ai - M.

Focal genotype

Mate genotypes

Mating frequency

Progeny genotype and relative frequency from each mating

Progeny values

Progeny mean value

AjAl

2p q

/2 A1A2

/2 A1A1

progeny A1A1 - P2a + 2P9(1/2a + 1/2d) + <?d - aP + dV

q d and then factoring to give

and then noticing that p + q = 1 so that

0 0

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