Banana Slug Genomics

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===== BME 235 notes 5/1/2015 =====

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
Banana Slug Genomics

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