MATH 19A Midterm: MATH191 Harvard Practice1191 Fall 01
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X j=1 xjfj(~x)qji xi i = 1, , n i=1 fjixi and = pi xifi. with fj(~x) = pn. Let qii = q for all i = 1n. let qij = (1 q)/(n 1) for all i 6= j. Let fii = 1 for all i = 1n. let fij = a for all i 6= j. Consider an evolutionary graph, g, with n vertices. At time 0, all vertices are occupied by individuals of type a. In each reproductive event, a can mutate into b with probability u. B has relative tness r. this stochastic process has only one absorbing state: all-b. We are interested in nding a graph g that minimizes the time to reach this absorbing state. Let n = 10, u = 10 4 and r = 1. Do at least 1000 runs for each graph. Compute the average time until absorption into all-b.
