Eliezer, the simulation is a great idea. I’ve used it to test the following hypothesis: given sufficiently large population and genome size, the number of useful bits that a sexual species can maintain against a mutation probability (per base) of m is O(1/m^2). The competing hypothesis is the one given in your opening post, namely that it’s O(1/m).
To do this, I set Number=1000, Genome=1000, Beneficial=0, and let Mutation range from 0.03 to 0.14 in steps of 0.01. Then I plotted Fitness (which in the program equals the number of useful bits in the genome) against both 1/Mutation and 1/Mutation^2. I think the results [1] are pretty clear: when 1/Mutation^2 is small compared to Number and Genome, Fitness is linear in 1/Mutation^2, not 1/Mutation.
Eliezer, the simulation is a great idea. I’ve used it to test the following hypothesis: given sufficiently large population and genome size, the number of useful bits that a sexual species can maintain against a mutation probability (per base) of m is O(1/m^2). The competing hypothesis is the one given in your opening post, namely that it’s O(1/m).
To do this, I set Number=1000, Genome=1000, Beneficial=0, and let Mutation range from 0.03 to 0.14 in steps of 0.01. Then I plotted Fitness (which in the program equals the number of useful bits in the genome) against both 1/Mutation and 1/Mutation^2. I think the results [1] are pretty clear: when 1/Mutation^2 is small compared to Number and Genome, Fitness is linear in 1/Mutation^2, not 1/Mutation.
Oh, I rewrote the simulation code in C++ to make it run faster. It’s available at http://www.weidai.com/fitness/adhoc.cpp.
[1] http://www.weidai.com/fitness/fitness.htm, first plot is Fitness vs 1/Mutation, second is Fitness vs 1/Mutation^2.