I was curious about the remark that simulation results differed from theoretical ones, so I tried some test runs. I think the difference is due to sexual reproduction.
Eliezer’s code uses random mating. I modified it to use asexual reproduction or assortative mating to see what difference that made.
Asexual reproduction:
mutation rate 0.1 gave 6 bits preserved
0.05 preserved 12-13 bits
0.025 preserved 27
increasing population size from 100 to 1000 bumped this to 28
decreasing the beneficial mutation rate brought it down to 27 again
so the actual preserved information is fairly consistently 0.6 times the theoretical value, with some sort of caveat about larger populations catching beneficial mutations.
Random mating:
mutation rate 0.1 gave 20 bits preserved (already twice the theoretical value)
Assortative mating:
mutation rate 0.1 gave 25-26 bits preserved
0.05 preserved 66 bits
increasing population size from 100 to 1000 bumped this to 73
So sexual reproduction helps in a big way, especially if mating is assortative and/or the population is large. Why? At least part of the explanation, as I understand it, is that it lets several bad mutations be shuffled into one victim. I don’t know the mathematics here, but there’s a book with the memorable title ‘Mendel’s Demon’ that I read some years ago, which proposed this (in addition to the usual explanation of fast adaptation to parasites) as an explanation for the existence of sex in the first place. These results would seem to support the theory.
I was curious about the remark that simulation results differed from theoretical ones, so I tried some test runs. I think the difference is due to sexual reproduction.
Eliezer’s code uses random mating. I modified it to use asexual reproduction or assortative mating to see what difference that made.
Asexual reproduction:
mutation rate 0.1 gave 6 bits preserved
0.05 preserved 12-13 bits
0.025 preserved 27
increasing population size from 100 to 1000 bumped this to 28
decreasing the beneficial mutation rate brought it down to 27 again
so the actual preserved information is fairly consistently 0.6 times the theoretical value, with some sort of caveat about larger populations catching beneficial mutations.
Random mating:
mutation rate 0.1 gave 20 bits preserved (already twice the theoretical value)
Assortative mating:
mutation rate 0.1 gave 25-26 bits preserved
0.05 preserved 66 bits
increasing population size from 100 to 1000 bumped this to 73
So sexual reproduction helps in a big way, especially if mating is assortative and/or the population is large. Why? At least part of the explanation, as I understand it, is that it lets several bad mutations be shuffled into one victim. I don’t know the mathematics here, but there’s a book with the memorable title ‘Mendel’s Demon’ that I read some years ago, which proposed this (in addition to the usual explanation of fast adaptation to parasites) as an explanation for the existence of sex in the first place. These results would seem to support the theory.