The assortative mating matrix

A grid of allowed crosses

The Assortative Mating page offers three mating rules. This module generalises them. You mark, cross by cross, which female by male pairings are allowed, and the module iterates the genotype frequencies under that rule.

There are six distinct crosses at one locus: AA×AA, AA×Aa, AA×aa, Aa×Aa, Aa×aa and aa×aa. The grid is symmetric, so AA×Aa and Aa×AA switch together. That gives 2^6 = 64 patterns, and 14 of them match a named model. Models 1, 2 and 3 are the three rules of the Assortative Mating page. Only the 14 presets run. A pattern with no match, random mating included, shows "Invalid mating pattern".

The second choice is the variant, which says what a forbidden cross does. Both variants use the same Mendelian offspring ratios, and both renormalise the offspring to sum to 1. They differ in who loses out.

Two edge cases follow from the rules. A genotype with frequency below 10⁻¹² counts as absent, so a vanished allele does not return. If no fertile mating is possible at all, for example Model 3 in a population that is all AA, the population is returned unchanged and no error appears.

Forbidden: females choose again

In the forbidden variant a forbidden cross never happens. A female of genotype i mates with an allowed male j with probability f_j divided by the total frequency of the males allowed for her, so the cross frequency is f_i × f_j / (sum of allowed f_k). Every female with an allowed partner present leaves offspring. Only a female with no allowed partner at all is left out.

Take Model 1 (A-carriers mate with A-carriers, aa with aa) at D = 0.04, H = 0.32, R = 0.64. The realised mating frequencies are aa×aa 0.6400, Aa×Aa 0.2844, AA×Aa 0.0356 (and 0.0356 for Aa×AA), AA×AA 0.0044. Under random mating aa×aa would be 0.64² = 0.4096. The aa females all find aa males, so the cross is more common than chance. The next generation is D′ = 0.1111, H′ = 0.1778 and R′ = 0.7111, and p stays at 0.2000.

Sterile: wasted matings

In the sterile variant mating is random, with cross frequency f_i × f_j for all nine ordered pairs, but a forbidden cross produces no offspring. The mating happens and is wasted.

Run the same Model 1 grid as sterile. A-carriers have frequency 0.36 and aa has 0.64, so A- × aa pairings take up 2 × 0.36 × 0.64 = 0.4608 of all matings, and 46% of matings are wasted. The surviving offspring come mostly from aa×aa. The next generation is D′ = 0.0742, H′ = 0.1187 and R′ = 0.8071.

Allele frequency now falls, because the fertile crosses are mostly aa×aa, which produce only a. In the forbidden variant of the same grid p stayed at 0.2000. Here it is 0.1335 in generation 1, 0.0374 in generation 2 and 0.0020 in generation 3. By generation 4 A is gone.