Editing Quantitative genetics (section)

====Half-sib crossing (HS)====
Derivation of the ''half sib crossing'' takes a slightly different path to that for Full sibs. In the adjacent diagram, the two half-sibs at generation (t-1) have only one parent in common—parent "A" at generation (t-2). The ''cross-multiplier 1'' is used again, giving '''f<sub>Y</sub> = f<sub>(P1,P2)</sub> = (1/4) [ f<sub>AA</sub> + f<sub>AC</sub> + f<sub>BA</sub> + f<sub>BC</sub> ] '''. There is just one ''coefficient of parentage'' this time, but three ''co-ancestry coefficients'' at the (t-2) level (one of them—f<sub>BC</sub>—being a "dummy" and not representing an actual individual in the (t-1) generation). As before, the ''coefficient of parentage'' is '''(1/2)[1+f<sub>A</sub> ] ''', and the three ''co-ancestries'' each represent '''f<sub>(t-1)</sub> '''. Recalling that '' f<sub>A</sub> '' represents '' f<sub>(t-2)</sub> '', the final gathering and simplifying of terms gives ''' f<sub>Y</sub> = f<sub>t</sub> = (1/8) [ 1 + f<sub>(t-2)</sub> + 6 f<sub>(t-1)</sub> ] '''.<ref name="Crow & Kimura"/>{{rp|132–143}}<ref name="Falconer 1996"/>{{rp|82–92}} The graphs at left include this ''half-sib (HS) inbreeding'' over twenty successive generations. [[File:Inbreeding- Selfing.jpg|thumb|200px|right|Self fertilization inbreeding]] As before, this also quantifies the ''relatedness'' of the two half-sibs at generation (t-1) in its alternative form of '''f<sub>(P1, P2)</sub> '''.