“The Effect of Assortative Mating on the Genetic Composition of a Population”, 1968 ():
There are two classic papers on assortative mating, written by Sewall 1921 and R. A. 1918. The approach in the two papers is quite different, although the general qualitative conclusions are similar. Fisher’s paper is notoriously difficult to read, although this is remedied to some extent by the publication of an annotated version by 1966. Our object is mainly a review of these classic results. Included is a derivation of Fisher’s main conclusions, using a method rather similar to Wright’s. It is thereby possible to obtain Fisher’s results using only elementary methods.
…Assortative mating, as does inbreeding, causes an increase in homozygosity and an increase in the population variance. However, with multiple factors the increase in homozygosity is very slight while the increase in variance is large. There is an association between genes of like effect and the resulting gametic phase (linkage) disequilibrium explains the large variance increase.
A trait determined by homozygosity for a rare recessive gene eventually has its incidence multiplied ~by a factor (1 − rp2)−1, where 1 − p is the recessive gene frequency and r is the correlation between mates. Exact formulae are given for any generation.
A multifactorial trait with complete heritability (additive gene effects and no environmental influence) has at equilibrium an average inbreeding coefficient:
f = r ⁄ (2ne(1 − r) + r)
where ne is the effective number of loci. The variance is increased by a factor (1 − rQ)−1 where Q = (2ne − l)⁄2ne. The methods used are similar to those of 1921.
Extensions of these formulae are given to include dominance and environmental effects for a trait determined by a large number of loci. The effect of assortative mating on the correlation between certain relatives is also given. These were all shown earlier by 1918, but are derived here by a more elementary method.