Editing Quantitative genetics (section)

==== The sample gamodemes – genetic drift====
Following completion of these five binomial sampling events, the resultant actual gamodemes each contained different allele frequencies—('''p<sub>k</sub>''' and '''q<sub>k</sub>'''). [These are given at ''white label'' "'''5'''" in the diagram.] This outcome is actually the genetic drift itself. Notice that two samples (k = 1 and 5) happen to have the same frequencies as the ''base'' (''potential'') gamodeme. Another (k = 3) happens to have the ''p'' and ''q'' "reversed". Sample (k = 2) happens to be an "extreme" case, with '''p<sub>k</sub> = 0.9''' and '''q<sub>k</sub> = 0.1'''; while the remaining sample (k = 4) is "middle of the range" in its allele frequencies. All of these results have arisen only by "chance", through binomial sampling. Having occurred, however, they set in place all the downstream properties of the progenies.

Because sampling involves chance, the ''probabilities'' ( {{math|<var>∫</var>}}<sub>k</sub> ) of obtaining each of these samples become of interest. These binomial probabilities depend on the starting frequencies ('''p<sub>g</sub>''' and '''q<sub>g</sub>''') and the sample size ('''2N<sub>k</sub>'''). They are tedious to obtain,<ref name="Crow & Kimura"/>{{rp|382–395}}<ref name="Cochran 1977"/>{{rp|55}} but are of considerable interest. [See ''white label'' "'''6'''" in the diagram.] The two samples (k = 1, 5), with the allele frequencies the same as in the ''potential gamodeme'', had higher "chances" of occurring than the other samples. Their binomial probabilities did differ, however, because of their different sample sizes (2N<sub>k</sub>). The "reversal" sample (k = 3) had a very low Probability of occurring, confirming perhaps what might be expected. The "extreme" allele frequency gamodeme (k = 2) was not "rare", however; and the "middle of the range" sample (k=4) ''was'' rare. These same Probabilities apply also to the progeny of these fertilizations.
  
Here, some ''summarizing'' can begin. The ''overall allele frequencies'' in the progenies bulk are supplied by weighted averages of the appropriate frequencies of the individual samples. That is: <math display="inline"> p_{\centerdot} = \sum_{k}^s \omega_{k} \ p_{k} </math> and <math display="inline"> q_{\centerdot} = \sum_{k}^s \omega_{k} \ q_{k} </math>. (Notice that '''k''' is replaced by '''•''' for the overall result—a common practice.)<ref name="S & T"/> The results for the example are '''p<sub>•</sub>''' = 0.631 and '''q<sub>•</sub>''' = 0.369 [''black label'' "'''5'''" in the diagram]. These values are quite different to the starting ones ('''p<sub>g</sub>''' and '''q<sub>g</sub>''') [''white label'' "'''1'''"]. The sample allele frequencies also have variance as well as an average. This has been obtained using the ''sum of squares (SS)'' method <ref>This is outlined subsequently in the genotypic variances section.</ref> [See to the right of ''black label'' "'''5'''" in the diagram]. [Further discussion on this variance occurs in the section below on Extensive genetic drift.]