Thought up a genetic model on holiday. I always call my automata “bugs”. So each bug has two binary genes. Gene1 decides whether on seeing a predator the individual signals to the group or not, giving us a brave allele and a cowardly allele. Gene2 decides who you wish to mate with a brave or a coward.
The bugs were distributed in a 15x15 grid, with a 10% chance of moving to adjacent squares randomly, and with a 1% chance of mutation in the genes. Bugs died if they were preyed upon or ran out of energy. The total amount of energy in the group was kept constant by scaling each bug up when the energy fell.
The chance of being caught was determined by the number of braves in your square. Let a solitary individual not see a predator (and get predated) on 70% of occasions (p=0.7) then a group of B braves will be predated on 0.7^B of occasions. If you are a coward in a group of braves you benefit from the braves and yourself so 0.7^(B+1) the extra protection is the benefit of cheating.
2DO-- Originally I wanted to create an expression in the classic style of economics and ecology to express the marginal point at which cheating became less beneficial to being brave. A coward having a lot of non-mobile cowardly children will not benefit as much as a brave having lots of brave children so a dispersal factor will be needed to determine the probability of meeting your offspring.
Instead I did a model. Interestingly being 11 or 00 means that you can produce a self sustaining population since 11 are braves who breed with braves, and 00 are cowards which breed with coward. However as explained under heavy predation groups of braves do much better than groups of cowards.
If you are 01 or 10 then you wish to breed with a different type from yourself. This means that only a mixed population strategy works and is more complex and liable to failure than the simple 11 or 00 strategies.
In the few test runs I performed the 11 quickly became the most dominant type, but then entered population dynamics due to other factors. This eventually gave an opportunity for other types to take over, which usually lead to extinction of all the bugs. One notable feature is the prevalence of type 10 i.e. brave bugs who seek to mate with cowards. As the 11 population falls away and cowards become more frequent it is beneficial to mate with a coward. However under heavy predation large groups of cowards get decimated, so braves are selected for which benefits 10s. However as the cowards fall away 10 run out of mates and if 11s can’t respond fast enough the system collapses.
The program worked by setting the probabilities of each bug, and then throwing dice to select individuals into the next generation. Thus it was not that whole squares got selected for (as in reality) but rather than probability of being selected was increased in good squares. I thought this would reflect general dynamics better.
2Do The model doesn’t have proper diploid sex. A proper diploid genome with sex (genetic mixing) and dominance effects will complicate this logic.
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