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3 How to use MIGRATE or why are Markov chain Monte Carlo programs difficult to use?
 POPULATION GENETICS FOR ANIMAL CONSERVATION
, 2009
"... Population genetic analyses often require the estimation of parameters such as population size and migration rates. In the 1960s, enzyme electrophoresis was developed; it was the first method to gather codominant data from many individuals in many populations relatively easily. Summary statistics m ..."
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Population genetic analyses often require the estimation of parameters such as population size and migration rates. In the 1960s, enzyme electrophoresis was developed; it was the first method to gather codominant data from many individuals in many populations relatively easily. Summary statistics methods, such as allelefrequency based Fstatistics (Wright 1951), were used to estimate population genetics parameters from these data sets. These methods matured and expanded into many variants that were enthusiastically accepted by many researchers. Fstatistics are still a hallmark of any population genetic study, especially in conservation genetics, although over the years, limitations have become evident (Neigel 2002). Many of these methods use restrictive assumptions, for example, disallowing mutation. Fstatistics, such as FST methods, are often employed on pairs of populations; this can lead to biased parameter estimates (cf. Beerli 2004; Slatkin 2005) and the reuse of data in these pairwise methods is undesirable from a statistical viewpoint. In 1982, Sir John Kingman developed the coalescence theory (Kingman 1982a, b). His overview of the developments of this theory (Kingman 2000) gives an interesting insight into the development of new ideas. This new development opened the door to methods in population genetics that go beyond the Fstatistics methods and have led to several theoretical breakthroughs (Hein et al. 2005; although inferences based on coalescence theory were not practicable until about 1995 because of computational constraints). In recent years, computerintensive programs that can estimate parameters using genetic data under various coalescent models have been developed; for example, programs that estimate gene...
In Bertorelle, Giorgio, Bruford, M W, Hauffe, Heidi C, Rizzoli, A, & Vernesi, C (Eds.), Population Genetics for Animal Conservation (pp. 4279). Cambridge University Press, Cambridge UK.
Microsatellite evolution: Markov transition functions for a suite of models
 Theor. Popul. Biol
, 2007
"... This paper takes from the collection of models considered by Whittaker et. al. (2003) derived from direct observation of microsatellite mutation in parentchild pairs and provides analytical expressions for the probability distributions for the change in number of repeats over any given number of ge ..."
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This paper takes from the collection of models considered by Whittaker et. al. (2003) derived from direct observation of microsatellite mutation in parentchild pairs and provides analytical expressions for the probability distributions for the change in number of repeats over any given number of generations. The mathematical framework for this analysis is the theory of Markov processes. We find these expressions using two approaches, approximating by circulant matrices and solving a partial differential equation satisfied by the generating function. The impact of the differing choice of models is examined using likelihood estimates for time to most recent common ancestor. The analysis presented here may play a role in elucidating the connections between these two approaches and shows promise in reconciling differences between estimates for mutation rates based on Whittaker’s approach and methods based on phylogenetic analyses. Key words and phrases: microsatellites, Markov process, generating functions 1.
REPEAT DISTRIBUTIONS FROM UNEQUAL CROSSOVERS
, 803
"... Abstract. It is a wellknown fact that genetic sequences may contain sections with repeated units, called repeats, that differ in length over a population, with a length distribution of geometric type. A simple class of recombination models with single crossovers is analysed that result in equilibri ..."
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Abstract. It is a wellknown fact that genetic sequences may contain sections with repeated units, called repeats, that differ in length over a population, with a length distribution of geometric type. A simple class of recombination models with single crossovers is analysed that result in equilibrium distributions of this type. Due to the nonlinear and infinitedimensional nature of these models, their analysis requires some nontrivial tools from measure theory and functional analysis, which makes them interesting also from a mathematical point of view. In particular, they can be viewed as quadratic, hence nonlinear, analogues of Markov chains.
Lump it or Loose it! Population genetic inference with the ncoalescent experiments graph within a phylogenomic lineage
, 2009
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RESEARCH ARTICLE Open Access Research article
"... Influence of mutation rate on estimators of genetic differentiation lessons from Arabidopsis thaliana ..."
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Influence of mutation rate on estimators of genetic differentiation lessons from Arabidopsis thaliana
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"... Vol. 26 ECCB 2010, pages i440–i445 doi:10.1093/bioinformatics/btq367 Maximum likelihood estimation of locusspecific mutation rates in Ychromosome short tandem repeats ..."
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Vol. 26 ECCB 2010, pages i440–i445 doi:10.1093/bioinformatics/btq367 Maximum likelihood estimation of locusspecific mutation rates in Ychromosome short tandem repeats
Contents lists available at ScienceDirect Journal of Theoretical Biology
"... journal homepage: www.elsevier.com/locate/yjtbi A Markov chain description of the stepwise mutation model: Local and global ..."
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journal homepage: www.elsevier.com/locate/yjtbi A Markov chain description of the stepwise mutation model: Local and global
Distributed under Creative Commons CCBY 4.0 OPEN ACCESS
, 2016
"... Declarations can be found on page 21 ..."
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