We could do that, or we could set up a scheme where fitter individuals were more probable to reproduce, and less fit less probable, as follows.
p = my fitness --------------------------------- sum of fitnesses of all creatures
If fitness is positive, then p is a number between 0 and 1, and the sum of all these probabilities is 1. A separate page shows how to make a choice according to probabilities.
One problem with the above is if there is a large population. Let there be one individual with fitness 1, and 100 individuals with fitness 0.2. Then the probability of the fit individual being chosen is only 1/21. One way around this is the following:
The Boltzmann or "soft max" distribution gives us a flexible way of choosing who reproduces.
Let individual i have fitness f(i). Then its probability of reproducing, p(i), is:
By varying the temperature T, we can change it from only the very fittest reproduce (perhaps towards the end of run) to almost everybody has a chance, probabilities are almost equal (start of run). To be precise, T large at start of run, small towards end of run. The fittest will always be strictly more probable.
Fitter individuals reproduce. If we allow the number of children they have to vary, we may get a variable population size.
Q. As a programmer, what could happen if we have a variable population size?
If we do this, make the population size even.repeat (population size / 2) times { pick individual from whole population according to probabilities pick individual from whole population according to probabilities (may be the same individual!) construct 2 new individuals from these 2 parents } entire old population is now replaced by the new population (keep constant population size)
p = my fitness --------------------------------- sum of fitnesses of all creatures
Q. Consider if one individual has fitness 1, and n individuals have fitness 0.2.
As n goes to infinity, prove that number of times the fit individual is picked goes to just 5 (out of huge n).