Editing Quantitative genetics (section)

=== Self fertilization – an alternative===

Having noticed that the pea is naturally self-pollinated, we cannot continue to use it as an example for illustrating random fertilization properties. Self-fertilization ("selfing") is a major alternative to random fertilization, especially within Plants. Most of the Earth's cereals are naturally self-pollinated (rice, wheat, barley, for example), as well as the pulses. Considering the millions of individuals of each of these on Earth at any time, it is obvious that self-fertilization is at least as significant as random fertilization. Self-fertilization is the most intensive form of ''inbreeding'', which arises whenever there is restricted independence in the genetical origins of gametes. Such reduction in independence arises if parents are already related, and/or from genetic drift or other spatial restrictions on gamete dispersal. Path analysis demonstrates that these are tantamount to the same thing.<ref name="Wright 1917">{{cite journal|last1=Wright|first1=S.|title=The average correlation within subgroups of a population.|journal=J. Wash. Acad. Sci.|date=1917|volume=7|pages=532–535}}</ref><ref name="Wright 1921 a">{{cite journal|last1=Wright|first1=S.|title=Systems of mating. I. The biometric relations between parent and offspring.|journal=Genetics|date=1921|volume=6|issue=2|pages=111–123|doi=10.1093/genetics/6.2.111|pmc=1200501|pmid=17245958}}</ref> Arising from this background, the ''inbreeding coefficient'' (often symbolized as '''F''' or '''''f''''') quantifies the effect of inbreeding from whatever cause. There are several formal definitions of '''''f''''', and some of these are considered in later sections. For the present, note that for a long-term self-fertilized species '''''f''''' = '''1'''.
Natural self-fertilized populations are not single " ''pure lines'' ", however, but mixtures of such lines. This becomes particularly obvious when considering more than one gene at a time. Therefore, allele frequencies ('''''p''''' and '''''q''''') other than '''1''' or '''0''' are still relevant in these cases (refer back to the Mendel Cross section). The genotype frequencies take a different form, however.
 
In general, the genotype frequencies become <math display="inline">[p^2(1-f)+pf]</math> for '''AA''' and <math display="inline">2pq(1-f)</math> for '''Aa''' and <math display="inline">[q^2(1-f)+qf]</math> for '''aa'''.<ref name="Crow & Kimura" />{{rp|65}}

Notice that the frequency of the heterozygote declines in proportion to '''''f'''''. When '''''f'' = 1''', these three frequencies become respectively '''p''', '''0''' and '''q''' Conversely, when '''f = 0''', they reduce to the random-fertilization quadratic expansion shown previously.