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Quantitative genetics
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==== Total dispersed genic variance β Ο<sup>2</sup><sub>A(f)</sub> and Ξ²<sub>f</sub> ==== Previous sections found that the '''within line''' ''genic variance'' is based upon the ''substitution-derived'' genic variance '''( Ο<sup>2</sup><sub>A</sub> )'''βbut the ''amongst line'' ''genic variance'' is based upon the ''gene model'' allelic variance '''( Ο<sup>2</sup><sub>a</sub> )'''. These two cannot simply be added to get ''total genic variance''. One approach in avoiding this problem was to re-visit the derivation of the ''average allele substitution effect'', and to construct a version, '''( Ξ²<sub> ''f'' </sub> )''', that incorporates the effects of the dispersion. Crow and Kimura achieved this<ref name ="Crow & Kimura"/> {{rp|130β131}} using the re-centered allele effects ('''aβ’, dβ’, (-a)β’ ''') discussed previously ["Gene effects re-defined"]. However, this was found subsequently to under-estimate slightly the ''total Genic variance'', and a new variance-based derivation led to a refined version.<ref name="Gordon 2003"/> The ''refined'' version is: ''' Ξ²<sub> ''f'' </sub> = { a<sup>2</sup> + [(1β''f'' ) / (1 + ''f'' )] 2(q β p ) ad + [(1-''f'' ) / (1 + ''f'' )] (q β p )<sup>2</sup> d<sup>2</sup> } <sup>(1/2)</sup>''' Consequently, '''Ο<sup>2</sup><sub>A(f)</sub> = (1 + ''f'' ) 2pq Ξ²<sub>f</sub> <sup>2</sup> ''' does now agree with '''[ (1-f) Ο<sup>2</sup><sub>A(0)</sub> + 2f Ο<sup>2</sup><sub>a(0)</sub> ]''' exactly.
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