This is an old revision of the document!
==== 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
