Editing Quantitative genetics (section)

====Relationship through ancestral genepools====
Individuals descended from a common ancestral genepool obviously are related. This is not to say they are identical in their genes (alleles), because, at each level of ancestor, segregation and assortment will have occurred in producing gametes. But they will have originated from the same pool of alleles available for these meioses and subsequent fertilizations. [This idea was encountered firstly in the sections on pedigree analysis and relationships.]  The genepool contributions [see section above] of their '''nearest common ancestral genepool'''(an ''ancestral node'') can therefore be used to define their relationship. This leads to an intuitive definition of relationship which conforms well with familiar notions of "relatedness" found in family-history; and permits comparisons of the "degree of relatedness" for complex patterns of relations arising from such  genealogy.

The only modifications necessary (for each individual in turn) are in Γ and are due to the shift to "shared '''common''' ancestry" rather than "individual '''total''' ancestry". For this, define '''Ρ''' (in lieu of '''Γ'''); ''' m = number of ancestors-in-common''' at the node (i.e. m = 1 or 2 only); and an "individual index" '''k'''. Thus:

<math display="block"> \begin{align}
\Rho_k & = \sum_{m=1} ^{1 , 2} {\gamma_n} \\
& = \sum_{m=1} ^{1 , 2} {\left( \frac{1}{2} \right) ^n}
\end{align} </math>

where, as before,  ''n = number of sexual generations''  between the individual and the ancestral node.

An example is provided by two first full-cousins. Their nearest common ancestral node is their grandparents which gave rise to their two sibling parents, and they have both of these grandparents in common. [See earlier pedigree.] For this case, ''m=2'' and ''n=2'', so for each of them

<math display="block"> \begin{align}
\Rho_k & = \sum_{m=1} ^{2} {\gamma_2} \\
& = \sum_{m=1} ^{2} { \left( \frac{1}{2} \right) ^2} \\
& = \frac{1}{2} 
\end{align} </math>

In this simple case, each cousin has numerically the same Ρ .

A second example might be between two full cousins, but one (''k=1'') has three generations back to the ancestral node (n=3), and the other (''k=2'') only two (n=2) [i.e. a second and first cousin relationship].  For both, m=2 (they are full cousins).

<math display="block"> \begin{align}
\Rho_1 & = \sum_{m=1} ^{2} {\gamma_3} \\
& = \sum_{m=1} ^{2} {\left( \frac{1}{2}\right) ^3} \\
& = \frac{1}{4} 
\end{align} </math>

and

<math display="block"> \begin{align}
\Rho_2 & = \sum_{m=1} ^{2} {\gamma_2} \\
& = \sum_{m=1} ^{2} {\left( \frac{1}{2}\right) ^2} \\
& = \frac{1}{2} 
\end{align} </math>

Notice each cousin has a different Ρ <sub>k</sub>.