lecture_notes:05-01-2015

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+ Can learn species demographic info from a single genome + Not sequencing 1 genome but 2 (for a diploid organism), so can compare genomes to each other

- Each is composed of a segment of the genome of an individual from previous generations
- Looking further and further back you are sampling 1000s of individuals

+ Amount of heterozygosity is directly proportional …

+ Wright-Fischer model of reproduction

- Finite and constant population (N)
- Random mating with respect to the gene of the locus you are looking at
- Non-overlapping / discrete generations

+ Genetic drift

- Allele frequency (p) changes over generations via process of random mating
- Changes till it reaches fixation (non-segregating) or extinction
- More generations reduce genetic variation in a population

+ rate it goes down is inversely proportional to population size (N)

- lose variation faster with small N
- lose variation slower with large N
- Markov chain with absorbing boundary (math model)
- pi(p) = p : the probability an allele with frequency p will go to fixation

+ Heterozygosity, H

- rate of differences per base pair in the genome
- can be measured extremely precisely
- Ht = H0*(1 - (1/(2N)))^t : heterozygosity over time

+ Mutation

- Adds genetic variation to a population
- Works to counter allele fixation through genetic drift
- Enters population at rate mu, per generation
- deltaHmu = 2mu*(1 - H)
- Independent of population size

+ Mutation - drift equilibrium

- deltaH = -(1/(2N))*H + 2mu*(1 - H)
- to determine stable heterozygosity, assume deltaH is 0 and solve for H (assuming mutation - drift equilibrium)
- H = (4N*mu) / (1 + (4N*mu))
- 4N*mu is typically pretty small
- becomes H ~= 4Ne*mu where Ne is the effective population size

+ Molecular evolution

- what is rate of fixation of new mutations over evolutionary time?
- 2N*mu new alleles per generation, each of which starts life at frequency 1/2N
- change of fixation is the allele frequency
- rate of fixation per generation = number of new alleles * chance that each goes to fixation = 1/2N * 2N*mu = mu
- molecular clock

+ PMSC

- pairwise sequentially Markovian coalescent model
- used to predict local time to the most recent common ancestor (TMRCA) based on local density of heterozygotes
- hidden markov model where observations is diploid sequence, hidden states are discretized TMCRA, and transitions represent ancestral recombination events

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lecture_notes/05-01-2015.1430511652.txt.gz · Last modified: 2015/05/01 13:20 by nsaremi