Editing Quantitative genetics (section)

=== Mendel's research cross – a contrast===

Mendel's pea experiments were constructed by establishing true-breeding parents with "opposite" phenotypes for each attribute.<ref name="Mendel Bateson"/> This meant that each opposite parent was homozygous for its respective allele only. In our example, "tall ''vs'' dwarf", the tall parent would be genotype '''''TT''''' with '''''p''''' = '''1''' (and '''''q''''' = '''0'''); while the dwarf parent would be genotype '''''tt''''' with '''''q''''' = '''1''' (and '''''p''''' = '''0'''). After controlled crossing, their hybrid is '''''Tt''''', with '''''p''''' = '''''q''''' = '''{{sfrac|1|2}}'''. However, the frequency of this heterozygote = '''1''', because this is the F1 of an artificial cross: it has not arisen through random fertilization.<ref name="Gordon 1999">{{cite journal|last1=Gordon|first1=Ian L.|title=Quantitative genetics of intraspecies hybrids.|journal=Heredity|date=1999|volume=83|issue=6|pages=757–764|doi=10.1046/j.1365-2540.1999.00634.x|pmid=10651921|doi-access=free}}</ref> The F2 generation was produced by natural self-pollination of the F1 (with monitoring against insect contamination), resulting in '''''p''''' = '''''q''''' = '''{{sfrac|1|2}}''' being maintained. Such an F2 is said to be "autogamous". However, the genotype frequencies (0.25 '''''TT''''', 0.5 '''''Tt''''', 0.25 '''''tt''''') have arisen through a mating system very different from random fertilization, and therefore the use of the quadratic expansion has been avoided. The numerical values obtained were the same as those for random fertilization only because this is the special case of having originally crossed homozygous opposite parents.<ref name="Gordon 2001">{{cite journal|last1=Gordon|first1=Ian L.|title=Quantitative genetics of autogamous F2.|journal=Hereditas|date=2001|volume=134|pages=255–262|doi=10.1111/j.1601-5223.2001.00255.x|pmid=11833289|issue=3|doi-access=free}}</ref> We can notice that, because of the dominance of '''''T-''''' [frequency (0.25 + 0.5)] over '''''tt''''' [frequency 0.25], the 3:1 ratio is still obtained.

A cross such as Mendel's, where true-breeding (largely homozygous) opposite parents are crossed in a controlled way to produce an F1, is a special case of hybrid structure. The F1 is often regarded as "entirely heterozygous" for the gene under consideration. However, this is an over-simplification and does not apply generally—for example when individual parents are not homozygous, or when ''populations'' inter-hybridise to form ''hybrid swarms''.<ref name="Gordon 1999"/> The general properties of intra-species hybrids (F1) and F2 (both "autogamous" and "allogamous") are considered in a later section.