Genome Evolution Course 2009-2010

www.yanaiweb.com/genome

Itai Yanai, Technion – Israel Institute of Technology

Problem Set #2 assigned October 25^th, 2009

To be submitted as hard-copy in English or Hebrew on November 1^st, 2009 (at the beginning of class, 9:30am).

E-mail submissions will not be accepted.

Problem 1. Make up 4 different DNA sequences, each of length 20, that have a nucleotide diversity of 0.10 .

Problem 2. In class, we saw that co-dominant selection increases the frequency of one allele at the expense of the other. From the graph of the change in frequencies of q, note that co-dominant selection is not as efficient at low frequencies of q as it is in higher frequencies. Explain the reason for this in terms of the fractions of homozygotes and heterozygotes as q increases.

Problem 3: Genetic drift

Given the simple stochastic model of evolution presented, imagine a new mutation in a population of 1,000. Calculate the probability that in the next generation the mutation will:

1) Be lost in the next generation?

2) Maintain its frequency (1 in a thousand)?

3) Jump to fixation?

Problem 4: Homozygotic selection.

Imagine a situation where it is advantageous not to be heterozygous.

                        w₁₁       w₁₂       w₂₂

Weights            1+s      1          1+s

Compute the for such a situation and describe its behavior with time.

Problem 5: A popularity contest.

There are more SNPs with low frequencies (say 10%) than SNPs with high frequencies (say 45%). Rationalize this distribution in terms of genetic drift.