Coalescents

= Evolutionary Coalescent =

== Coalescent theory is used in population genetics to help map out the genetic history and relationships in the form of a phylogentic tree its better to use the term gene genealogy to emphasize that this is a tree for lineages within a population, and reserve phylogeny for a tree of species. When it comes to different populations within a species, we sometimes use phylogeny too... which is confusing. It traces back all of the alleles of one particular gene until it reaches the ancestral copy, the ‘most recent common ancestor' (MCRA), from which all of the alleles stemmed from. When two lineages are traced back to this point of origin they are said to have coalesced. Coalescents are important in terms of polymorphism due to the potential for mutations that is created. A coalescent provides two offspring with the same allele increasing the chance that one of them will mutate and potentially create a new phenotype, increasing polymorphism. This is confused. A coalescent event is simply a branching point in the genealogy. Mutations may happen at any point on the tree, and are not related to the coalescent events in this model. = =

Coalescent theory can be used to predict the level of heterozygosity within a population by using the probability of both a coalescent event and the probability of a mutation. The probability of a coalescent event is calculated as the likelihood that the two alleles shared the same parent. In a sample size of 10 there would be a possible 20 predecessor alleles, one paternal and one maternal for each individual, which equates to 2N lineages. This means that the probability that two alleles you will get confuse if you use the term 'allele' here (I know it is in the literature). I suggest using 'lineages'. have the same parent not quite. Two lineages can trace back the same parent but, different chromosomes... that would not be a coalescent event. is 1/(2N). The probability that they do not occur can then be calculated by subtracting the value from 1, giving the general rule of 1-1/(2N).

The probability of a mutation is calculated as the probability that a mutation could occur in either lineage of each allele: 2μ. The mutation rate from one specific generation would be analysed to generate the probability of the mutation. unclear what you mean here. This can be used to calculate the heterozygosity of a population, determining how much DNA variation there is I think you mean to say that the expected heterozygossity is a measure of how much variation would be observed at a loucs. The probability of a mutation is divided by the probability of an event, including all mutations and coalescences. You should specify that this ratio is the relative probability of a mutation each generation... but that since this is constant over the generations, it is the relative probability that the first event (tracing back in time from your sample) is a mutation. This gives us the equation: H = 2μ / (2μ + (1/2N)). By multiplying by 2N we can remove the fraction within the equation: H = 4Nμ / (1 + 4Nμ). Using this equation and our calculated probabilities we have calculated the heterozygosity.

Example: Sample size of 15 = 30 ancestral alleles Alleles 8 and 3 are mutations = =  Probability of coalescent: 1/(2N) = 1/30 Taking into account mutations 1/(2N) = 1/28 Probability of mutation: 2μ = 2 x 1/15 = 2/15

H = (4*28*(1/15))/(1+(4*28*(1/15))) H = 7.466666667/8.466666667 H = 0.881889764 H = 0.882