2015-07-08

The mating algorithm

We have a population of animals. Each individual can be associated with a certain "value", expressing his "fit level to the environment". We want to design a simple algorithm in the animal's genes that would make the individuals to mate close to optimal.

Let's say that resulting value for the mating is the product of the "value" of the two involved individuals. We will study the case when each individual can only be involved in mating with a single other individual.

In this conditions, the close to optimum mating is reached when mating is realized between individuals with very close values. Mathematically, we have a set of positive numbers (the values) and we want to create the pairs of numbers so that the sum of products of each pair will be maximal. This happens when we sort the numbers and we pair each number with the one next to it.


If we add sexes it would be similar. We have the 2 groups by sexes ordered by value. We start with the highest value, than just pair with the closest available value from the other sex. Some with low "value" will remain without a mate of course.

However, in an animal population we cannot create such sorting, we need to rely on a swarm behavior: a simple rule that applied globally results is a higher level of organization.

Such simple rule is to level the individuals into "social" classes based on "value", and do the pairing inside the classes. However, it is still a little too complex to define these classes in genes.

One solution could be that each individual will try to mate to the most valuable partner he could get. When all the individuals are applying the same strategy, the mating will not be normally possible between very different "values", because the more valuable will not settle for a way lower value partner.

How can be this implemented in individuals in a simple way? Even the relative value between individuals is not something very easy to define, it takes time to evaluate it. There are also geographical and age constraints on reaching a very close value partner. There is for sure a limited time to evaluate potential partners and take a decision.

One strategy would be to try partners until the individual finds the best affordable partner. It will be a hard task, because the individual will not be able to measure the "number" defining it's value and the  "number" of the potential partner. It can only compare relative values of partners and maybe eliminate some very clear cases of "out of my league" or "out of his league".

When not being able to evaluate the relative value between itself and possible partners, the rational approach might be to try increasing valuable partners until finding the best affordable one. It will fight to conquer each even valuable partner until finding one that refuses the mating because he has a way higher value; than settle with the next best potential partner.

Individuals that don't have a clear value of itself would then reject partners that are too willing to mate with him. The high desire to mate would be interpreted as a lower relative value of the partner. In the same time, partners that needs a big conquer fight would seem to be more valuable, so then be a more desirable partners.

Good that this happens only with this fictional animals... ;)

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