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Mate a number of males (sires) with a number of females (dams). Each
sire is mated to more than one dam, but each dam mates only with one
sire. Do an analysis of variance on the phenotype in the progeny,
treating sire and dam as main effects. The result is shown in
Table 5.
Table 5:
Analysis of variance table for a full-sib analysis of
quantitative genetic variation.
| |
|
|
Composition of |
| Source |
d.f. |
Mean square |
mean square |
| Among sires |
 |
 |
 |
| Among dams |
 |
 |
 |
| (within sires) |
|
|
|
| Within progenies |
 |
 |
 |
 |
 |
 |
|
Now we need some way to relate the variance components (
,
, and
) to
,
, and
.5 How do we
do that? Well,
estimates the variance among the means of the half-sib
familes fathered by each of the different sires or, equivalently, the
covariance among half-sibs.6
Now consider the within progeny component of the variance,
. In general, it can be shown that any among
group variance component is equal to the covariance among the members
within the groups.7 Thus, a within group
component of the variance is equal to the total variance minus the
covariance within groups. In this case,
There remains only
. Now
,
, and
. Thus,
So if we rearrange these equations, we can express the genetic
components of the phenotypic variance, the causal components
of variance, as simple functions of the observational components
of variance:
Next: An example: body weight
Up: Estimating heritability
Previous: Regression analysis
Kent Holsinger
2010-12-13