4 ms·
Exactly. So suppose at some generation, the fraction of mosquitoes with the modified trait is p (and the unmodified fraction is 1 - p), and suppose that all mo
by jnhnum1 11y ago
Exactly. So suppose at some generation, the fraction of mosquitoes with the modified trait is p (and the unmodified fraction is 1 - p), and suppose that all mosquitoes are equally fit.
A random child in the next generation will have the modified trait if:
(a) both its parents are modified. This happens with probability p^2
(b) with probability .995 if one of its parents are modified. This happens with probability 2p(1-p), for a total probability of 1.99p(1-p).
Overall, the fraction of modified mosquitoes in the next generation will have p^2 + 1.99p(1-p).
Plotting this versus the identity function (http://www.wolframalpha.com/input/?i=%7Bp%2C+p%5E2+%2B+0.995*p*%281-p%29*2%7D+for+p+%3D+0+to+1 http://www.wolframalpha.com/input/?i=%7Bp%2C+p%5E2+%2B+0.995...), we see that this will increase monotonically to p = 1 (all mosquitoes have the modified trait).