Unformatted text preview: .e., the
branching process becomes absorbed at 0?
Reverend Henry William Watson replied with a solution. Together, they then
wrote an 1874 paper entitled On the probability of extinction of families. For
this reason, these chains are often called Galton-Watson processes.
Example 1.9. Wright–Fisher model. Thinking of a population of N/2
diploid individuals who have two copies of each of their chromosomes, or of N
haploid individuals who have one copy, we consider a ﬁxed population of N
genes that can be one of two types: A or a. In the simplest version of this
model the population at time n + 1 is obtained by drawing with replacement
from the population at time n. In this case, if we let Xn be the number of A
alleles at time n, then Xn is a Markov chain with transition probability
✓ ◆ ✓ ◆j ✓
p(i, j ) =
since the right-hand side is the binomial distribution for N independent trials
with success probability i/N . 6 CHAPTER 1. MARKOV CHAINS In this model t...
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This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell.
- Spring '10
- The Land