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

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

Amount of heterozygosity is directly proportional …

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

1. Allele frequency (p) changes over generations via process of random mating
2. Changes till it reaches fixation (non-segregating) or extinction
3. More generations reduce genetic variation in a population
   1. Rate it goes down is inversely proportional to population size (N)
      1. lose variation faster with small N
      2. lose variation slower with large N
4. Markov chain with absorbing boundary (math model)
5. pi(p) = p : the probability an allele with frequency p will go to fixation

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

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

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

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

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