Editing Quantitative genetics (section)

==== Selfing within random fertilization====
[[File:RF Inbreeding B.jpg|thumb|300px|right|Random fertilization compared to cross-fertilization]]
It is easy to overlook that ''random fertilization'' includes self-fertilization. Sewall Wright showed that a proportion '''1/N''' of ''random fertilizations'' is actually ''self fertilization'' <math> \left( \bigotimes \right) </math>, with the remainder '''(N-1)/N''' being ''cross fertilization'' <math> \left( \mathsf{X} \right) </math>.  Following path analysis and simplification, the new view  ''random fertilization inbreeding'' was found to be: <math display="inline"> f_t = \Delta f \left( 1 + f_{t-1} \right) + \tfrac {N-1}{N} f_{t-1} </math>.<ref name="Wright 1921 a"/><ref name="Wright 1951">{{cite journal|last1=Wright|first1=Sewall|title=The genetical structure of populations.|journal=Annals of Eugenics|date=1951|volume=15|issue=4|pages=323–354|doi=10.1111/j.1469-1809.1949.tb02451.x|pmid=24540312}}</ref> Upon further rearrangement, the earlier results from the binomial sampling were confirmed, along with some new arrangements. Two of these were potentially very useful, namely: '''(A)''' <math display="inline"> f_t = \Delta f \left[ 1 + f_{t-1} \left( 2N-1 \right) \right] </math>; and '''(B)''' <math display="inline"> f_t = \Delta f \left( 1 - f_{t-1} \right) + f_{t-1} </math>.

The recognition that selfing may  ''intrinsically be a part of'' random fertilization leads to some issues about the use of the previous ''random fertilization'' 'inbreeding coefficient'. Clearly, then, it is inappropriate for any species incapable of ''self fertilization'', which includes plants with self-incompatibility mechanisms, dioecious plants, and [[bisexual animals]]. The equation of Wright was modified later to provide a version of random fertilization that involved only ''cross fertilization'' with no ''self fertilization''. The proportion '''1/N''' formerly due to ''selfing'' now defined the ''carry-over'' gene-drift inbreeding arising from the previous cycle. The new version is:<ref name="Crow & Kimura"/>{{rp|166}}
<math display="block"> f_{\mathsf{X}_{t}} = f_{t-1} + \Delta f \left( 1 + f_{t-2} - 2 f_{t-1} \right) </math>.

The graphs to the right depict the differences between standard ''random fertilization''  '''RF''', and random fertilization adjusted for "cross fertilization alone" '''CF'''. As can be seen, the issue is non-trivial for small gamodeme sample sizes.

"Panmixia' is ''not'' synonymous with 'random fertilization,' nor is "random fertilization" synonymous with 'cross fertilization'.{{citation needed|date=January 2025}}