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Unformatted text preview: Mutation models III: exotic models Peter Beerli September 19, 2005 Most of these exotic models are standard models in population genetics, where they dominate the field and finite-sites mutation models, such as HKY or GTR, are only recently used in the context of parameter inference using coalescence theory. 1 Infinitely many allele model This model was developed as an extension of the k-allele model, where k = 1 , 2 , , 3 .... . The k allele model allows back-mutations, so that A can mutate to a and also from a to A (see details of this model for k = 2 in the chapter about Mutation models I: basic nucleotide sequence mutation models ). The infinitely many allele model, or infinite allele model (IAM) for short, sets k = and so de facto does not allow any back-mutation: seeing two individuals with an A means that they must have a recent common ancestor and no mutation event happened since then. New mutations will results in a new allele. The rate matrix for the transitions between alleles A i and A j could be expressed as R = 1- k .... .... k .... 1- (1) In the program MIGRATE, I used a k allele approximation to the infinite allele model, that tries to lump all unobserved states into an additional k + 1 class. prob( A i | , t, A i ) = f A i e- t prob( A i | , t, A j ) = f A j e- t f A z = 1 k +1 if A z in sample , 1- k k +1 if A z not in sample 1 BSC5936-Fall 2005 Computational Evolutionary Biology Figure 1: Example of an electrophoretic marker: malate dehydrogenase (sMDH 1 ). In an electric field the enzyme moves according to the electric properties of the aminoacids. different electro- morphs (alleles) show different mobility. Ten individuals were scored, from left to right: a/a , a/a , c/c , c/c , c/c , a/a , a/a , a/a , a/c , a/a . The heterozygote a/c show three bands because sMDH is a dimer and a heterozygote individuals shows functional enzyme combinations of a/a, a/c, and c/c, in proportions of 1:2:1. The bands in the position slightly lower than the a-allele belong to sMDH that is monoporphic for these 10 individuals. 1 s stands for soluble in the cytosol and m stands for located in mitochondria This model was developed before genetic data could be analyzed and researchers started to use it to analyze protein electrophoresis results (Figure 1). Many results in population genetics were derived using the IAM and it is probably still the most often used model. 2 Infinitely many sites mutation model (ISM) The idea of the IAM was extended to sequences once they became available. When used with sequences IAM would not take into account multiple mutation on a sequence. We assume that a sequence of nucleotides (or aminoacids) is infinitely long and a mutation occurs at a random site, because the sequence is infinitely long every mutation happens at a different site. This mutation model is common assumption, for example haplotype networks where mutation separate haplotypes.model is common assumption, for example haplotype networks where mutation separate haplotypes....
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