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Wesley R. Elsberry

Posts: 4991
Joined: May 2002

"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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