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

These notes are licensed under the Creative Commons Attribution-ShareAlike License. To view a copy of this license, visit http://creativecommons.org/licenses/by-sa/3.0/us/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA.