Mating systems in which the least related individuals are mated have been designated by Wright as having maximum avoidance of inbreeding. For such systems the initial rate of decrease in heterozygosity is minimum. However, some other systems have a lower rate of decrease in later generations.

Circular mating, in which each individual is mated with the one to his right and to his left, leads to an asymptotic rate of decrease in heterozygosity of 1– λ ˜ π2/(2N + 4)2 compared with 1/4N for maximum avoidance systems. Circular pair mating, in which for example each male progeny is moved one cage to the right, leads to 1– λ ~ π2/(N + 12)2. Other similar systems are discussed.

For minimum gene frequency drift, a mating system should have a constant number of progeny per parent and the population should be broken up as rapidly as possible into the maximum number of lines. The gene frequency variance at generation T within a line is

where N is the number in the line and Ht is the proportion of heterozygotes in generation t. Although the three mating systems, circular, circular pair, and maximum avoidance (and many others) have the same amount of random drift ultimately, at any generation circular mating has the smallest drift variance, VT, and circular pair next smallest.