Editing Quantitative genetics (section)

==== The mean – generalized fertilization====
A general formula incorporates the inbreeding coefficient '''''f''''', and can then accommodate any situation. The procedure is exactly the same as before, using the weighted genotype frequencies given earlier. After translation into our symbols, and further rearrangement:<ref name="Crow & Kimura"/> {{rp|77–78}}

<math display="block">
\begin{align}
G_{f} & = a (q-p) + [2pqd-f(2pqd)] \\
& = a(p-q) + (1-f) 2pqd \\
& = G_{0} - f\ 2pqd
\end{align} </math>
Here, '''G<sub>0</sub>''' is '''G''', which was given earlier. (Often, when dealing with inbreeding, "G<sub>0</sub>" is preferred to "G".)

Supposing that the maize example [given earlier] had been constrained on a holme (a narrow riparian meadow), and had partial inbreeding to the extent of '''''f '''''= '''0.25''', then, using the third version (above) of '''G<sub>f</sub>''':

'''G<sub>''0.25''</sub>''' = 1.15 − 0.25 (0.48) 0.12 = 1.136&nbsp;cm (rounded), with '''P<sub>0.25</sub>''' = 13.194&nbsp;cm (rounded).

There is hardly any effect from inbreeding in this example, which arises because there was virtually no dominance in this attribute ('''d''' → 0). Examination of all three versions of '''G<sub>''f''</sub>''' reveals that this would lead to trivial change in the Population mean. Where dominance was notable, however, there would be considerable change.