Wesley R. Elsberry
Posts: 4991
Joined: May 2002
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"weasel" math
Given:
Base set size K (number of possible characters at each position)
Target string length L
Mutation rate (per site) u
Population size N
here are some basic probabilities to go with a "weasel" run.
Per base:
Pincorrect to correct = 1 / K
Pcorrect to incorrect = (K - 1) / K
Blind search:
Ptry is all correct = K-L
Pa try in the population is all correct = N * K-L
Expected number of correct bases when all bases are changed = L / K
Expected number of correct bases when a genome is produced via copy with mutation = u * L / K
In "weasel" run:
Expected number of correct bases given a partially matching string:
Given C as number of correct matching bases
expected correct bases after mutation = C + (u * (L - C) / K) - (u * C * (K - 1) / K)
There's a few more items to derive to pull in the population parameter, but I need to go now.
Edit: Equations for Ptry is all correct and dependencies per PT comment by Mike Elzinga.
Edited by Wesley R. Elsberry on Mar. 19 2009,19:40
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"You can't teach an old dogma new tricks." - Dorothy Parker
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