A—
EVE-PQ
To correct for this, we computed an expected number v of mutations that the parents should have in common. This is given by v = (T1 T2)/S where T1 = the total number of mutations possessed by one parent, T2 = the total number of mutations possessed by the other parent, and S = the total number acquired by the entire population. (The
NUMBER OF GENERATIONS Fig. 3.
total S is accumulated as each individual in each generation has the probability a of acquiring a new mutation. If Ns is the average population in each generation, after k generations, Sis approximately N . k · a.)
We allotted this number v to the children for certain and then played a game of chance for additional mutations using the reduced binomial distribution centered at the midpoint of the total count of independent mutations possessed by the parents. In this manner, we count more correctly, the number in common only once.
This method leads to a slower rate of acquisition; it is still exponential in the beginning but tails off to something like a quadratic function, as more mutations must of necessity be held in common. Results from four problems are plotted in Fig. 4 on a semilog scale. The
NUMBER OF GENERATIONS Fig. 4.
cases PQ1 and PQ2 have N = 100, a = .02 and y = .1 and .05 respectively. The case PQ3 is the same as PQ2 except that the sample size was doubled, N = 200. It had a somewhat higher value for p,, but the slopes are like those of PQ2. The last case, PQ4, had the same parameters as PQ3 except that a was cut to .01. This problem was run to 290 generations and showed a definite bending over of the curve to almost a linear rate of acquisition after 230 generations as the population had more and more mutations in common.