The analysis involves 719 offspring from 74 sires and 192 dams, each with one litter. The offspring were spread over 4 generations, and the analysis is performed as a nested ANOVA with the genetic analysis nested within generations. An additional complication is that the design was unbalanced, i.e., unequal numbers of progeny were measured in each sibship. As a result the degrees of freedom don't work out to be quite as simple as what I showed you.8 The results are summarized in Table 6.
Using the expressions for the composition of the mean square we obtain
Why didn't I give a definite number for after my big spiel above about how we can estimate it from a full-sib crossing design? Two reasons. First, if you plug the estimates for and into the formula above for you get , which is clearly impossible since has to be less than and has to be greater than zero. It's a variance. Second, the experimental design confounds two sources of resemblance among full siblings: (1) genetic covariance and (2) environmental covariance. The full-sib families were all raised by the same mother in the same pen. Hence, we don't know to what extent their resemblance is due to a common natal environment.9If we assume , we can estimate the amount of variance accounted for by exposure to a common natal environment, , and by environmental variation within sibships, .10 Similarly, if we assume , then and . In any case, we can estimate the narrow sense heritability as
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