Editing Quantitative genetics (section)

====Meiosis determination – reproductive path analysis====
[[File:ReproDetmntn.jpg|thumb|200px|right|Reproductive coefficients of determination and inbreeding]]
[[File:ReproPaths.jpg|thumb|300px|left|Path analysis of sexual reproduction.]]

The '''meiosis determination (b<sup>2</sup>)''' is the ''coefficient of determination'' of meiosis, which is the cell-division whereby parents generate gametes. Following the principles of ''standardized partial regression'', of which '''path analysis''' is a pictorially oriented version, Sewall Wright analyzed the paths of gene-flow during sexual reproduction, and established the "strengths of contribution" (''coefficients of determination'') of various components to the overall result.<ref name="Wright 1921 a"/><ref name="Wright 1951"/> Path analysis includes ''partial correlations'' as well as ''partial regression coefficients'' (the latter are the ''path coefficients''). Lines with a single arrow-head are directional ''determinative paths'', and lines with double arrow-heads are ''correlation connections''. Tracing various routes according to ''path analysis rules'' emulates the algebra of standardized partial regression.<ref name="Li 1977"/>

The path diagram to the left represents this analysis of sexual reproduction. Of its interesting elements, the important one in the selection context is ''meiosis''. That's where segregation and assortment occur—the processes that partially ameliorate the truncation of the phenotypic variance that arises from selection.  The path coefficients '''b''' are the meiosis paths. Those labeled '''a''' are the fertilization paths. The correlation between gametes from the same parent ('''g''') is the ''meiotic correlation''. That between parents within the same generation is '''r<sub>A</sub>'''. That between gametes from different parents ('''f''') became known subsequently as the ''inbreeding coefficient''.<ref name="Crow & Kimura"/>{{rp|64}}  The primes ( ' ) indicate generation '''(t-1)''', and the ''un''primed indicate generation '''t'''. Here, some important results of the present analysis are given. Sewall Wright interpreted many in terms of inbreeding coefficients.<ref name="Wright 1921 a"/><ref name="Wright 1951"/>

The meiosis determination ('''b<sup>2</sup>''') is ''{{sfrac|1|2}} (1+g)'' and equals '''{{sfrac|1|2}} (1 + f<sub>(t-1)</sub>) ''', implying that '''g = f<sub>(t-1)</sub>'''.<ref>Notice that this '''b<sup>2</sup>''' is the ''coefficient of parentage ('''f<sub>AA</sub>''')'' of ''Pedigree analysis'' re-written with a "generation level" instead of an "A" inside the parentheses.</ref> With non-dispersed random fertilization, f<sub>(t-1)</sub>) = 0, giving '''b<sup>2</sup> = {{sfrac|1|2}}''', as used in the selection section above. However, being aware of its background, other fertilization patterns can be used as required. Another determination also involves inbreeding—the fertilization determination ('''a<sup>2</sup>''') equals '''1 / [ 2 ( 1 + f<sub>t</sub> ) ]''' . Also another correlation is an inbreeding indicator—'''r<sub>A</sub>''' = '''2 f<sub>t</sub> / ( 1 + f<sub>(t-1)</sub> )''', also known as the ''coefficient of relationship''. [Do not confuse this with the ''coefficient of kinship''—an alternative name for the ''co-ancestry coefficient''. See introduction to "Relationship" section.] This '''r<sub>A</sub>''' re-occurs in the sub-section on dispersion and selection.

These links with inbreeding reveal interesting facets about sexual reproduction that are not immediately apparent. The graphs to the right plot the ''meiosis'' and ''syngamy (fertilization)'' coefficients of determination against the inbreeding coefficient. There it is revealed that as inbreeding increases, meiosis becomes more important (the coefficient increases), while syngamy becomes less important. The overall role of reproduction [the product of the previous two coefficients—'''r<sup>2</sup>'''] remains the same.<ref>There is a small "wobble" arising from the fact that ''b<sup>2</sup>'' alters one generation behind ''a<sup>2</sup>''—examine their inbreeding equations.</ref> This ''increase in '''b<sup>2</sup>''''' is particularly relevant for selection because it means that the ''selection truncation of the Phenotypic variance'' is offset to a lesser extent during a sequence of selections when accompanied by inbreeding (which is frequently the case).