Editing Quantitative genetics (section)

==== The progeny lines – dispersion====
The ''genotype frequencies'' of the five sample progenies are obtained from the usual quadratic expansion of their respective allele frequencies (''random fertilization''). The results are given at the diagram's ''white label'' "'''7'''" for the homozygotes, and at ''white label'' "'''8'''" for the heterozygotes. Re-arrangement in this manner prepares the way for monitoring inbreeding levels. This can be done either by examining the level of ''total'' homozygosis [('''p<sup>2</sup><sub>k</sub> + q<sup>2</sup><sub>k</sub>''') = ('''1 − 2p<sub>k</sub>q<sub>k</sub>''')], or by examining the level of heterozygosis  ('''2p<sub>k</sub>q<sub>k</sub>'''), as they are complementary.<ref>Both are used commonly.</ref>    Notice that samples ''k= 1, 3, 5'' all had the same level of heterozygosis, despite one being the "mirror image" of the others with respect to allele frequencies. The "extreme" allele-frequency case (k= ''2'') had the most homozygosis (least heterozygosis) of any sample. The "middle of the range" case (k= ''4'') had the least homozygosity (most heterozygosity): they were each equal at 0.50, in fact.

The ''overall summary'' can continue by obtaining the ''weighted average'' of the respective genotype frequencies for the progeny bulk. Thus, for '''AA''', it is <math display="inline"> p^2_\centerdot = \sum_k^s \omega_k \ p_k^2 </math>, for '''Aa''', it is <math display="inline"> 2p_\centerdot q_\centerdot = \sum_k^s \omega_k \ 2 p_k q_k </math> and for '''aa''', it is <math display="inline"> q_\centerdot^2 = \sum_k^s \omega_k \ q_k^2 </math>. The example results are given at ''black label'' "'''7'''" for the homozygotes, and at ''black label'' "'''8'''" for the heterozygote. Note that the heterozygosity mean is ''0.3588'', which the next section uses to examine inbreeding resulting from this genetic drift.

The next focus of interest is the dispersion itself, which refers to the "spreading apart" of the progenies' ''population means''. These are obtained as <math display="inline"> G_k = a (p_k - q_k) + 2p_k q_k d </math> [see section on the Population mean], for each sample progeny in turn, using the example gene effects given at ''white label'' "'''9'''" in the diagram. Then, each <math display="inline"> P_k = G_k + mp </math> is obtained also [at ''white label'' "'''10'''" in the diagram]. Notice that the "best" line (k = 2) had the ''highest'' allele frequency for the "more" allele ('''A''') (it also had the highest level of homozygosity). The ''worst'' progeny (k = 3) had the highest frequency for the "less" allele ('''a'''), which accounted for its poor performance. This "poor" line was less homozygous than the "best" line; and it shared the same level of homozygosity, in fact, as the two ''second-best'' lines (k = 1, 5). The progeny line with both the "more" and the "less" alleles present in equal frequency (k = 4) had a mean below the ''overall average'' (see next paragraph), and had the lowest level of homozygosity. These results reveal the fact that the alleles most prevalent in the "gene-pool" (also called the "germplasm") determine performance, not the level of homozygosity per se. Binomial sampling alone effects this dispersion.

The ''overall summary'' can now be concluded by obtaining <math display="inline"> G_{\centerdot} = \sum_k^s \omega_k \ G_k </math> and <math display="inline"> P_{\centerdot} = \sum_k^s \omega_k \ P_k </math>. The example result for '''P<sub>•</sub>''' is 36.94 (''black label'' "'''10'''" in the diagram). This later is used to quantify ''inbreeding depression'' overall, from the gamete sampling. [See the next section.] However, recall that some "non-depressed" progeny means have been identified already (k = 1, 2, 5). This is an enigma of inbreeding—while there may be "depression" overall, there are usually superior lines among the gamodeme samplings.