The aim of this experiment is to see how I can mathematically model a simple evolutionary scenario.
Now, the point is that this initially heterogenous population soon expresses a very simple evolutionary path. What I'd like is to find out what properties I can pick and put into some equations to show this.
What I need to find, in fact, is a little complicated. The evolutionary path of any particular simulation is not relevant. What I need is the probability of all possible evolutionary paths. Since that is really difficult to represent graphically, a related graph that would be useful is to show the probability that a continuous valued gene has some value r at some time t, given only the starting conditions. The graph would be an intensity map, where intensity represents probability.
Each agent genome, at the start of the simulation, has a probability for reproducing between 0 and 1, distributed uniformly. Reproductions do not guarantee a new child agent appearing in the next generation; rather, the probability of having a new child in the next generation given a reproduction will be 10/(number of total repros). The probability of a given agent having a child in the next gen in their first cycle of life will be the probability of reproduction * 10/(number of total repros). i.e. P_a(Reproduction)*10/(Total Reproductions). If we assume Total Reproductions refers to reproductions for the entire generation, then this also represents the probability of having a child in any given cycle that will end up in the next gen. So, we can just multiply this by the length of an agent's life to find the probability of any giving