MATH 396 Lecture Notes - Lecture 10: Genetic Drift, Hypergeometric Distribution, Random Variable
Document Summary
So a new genetic variant (y = 1) has probability 1/2n of eventual fixation. Transition and extinction/fixation probabilities in the wright-fisher model (iii) so, as var(yk) increases without limit, eventually, yk = 0 or yk = 2n. Also var(yk) = var(e(yk|yk 1)) + e(var(yk|yk 1)) = var(yk 1) + e(2n. (yk 1/2n). (1 yk 1/2n)) (cid:951) var(yk 1) + (1 . So 1 y is the probability a gene curently at count y is eventually lost from the population: yk = 0. So e(y ) = e(y0) = y gives y = 2n. y + 0. (1 y) or y = y/2n. (i) in the wright-fisher model, the step sizes xk = (yk yk 1) may be large. Then also p(yk = y 1 | yk 1 = y) = (y/2n). (1 (y/2n)) = py. So then p(yk = y | yk 1 = y) = 1 2py (same type dies as duplicates).
