Titlebook: An Operator Semigroup in Mathematical Genetics; Adam Bobrowski,Marek Kimmel Book 2015 The Author(s) 2015 Differential Lyapunov Equation.Mi

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Motivating Example: Population Bottlenecks in the History of Modern Humans, Use of the Imbalance Inex they introduced. Three major groups of population, Asians, Africans, and Europeans, were considered for this purpose. The analysis shows that the data are consistent with a population bottleneck in modern humanity history and gradual settling of Europe and Asia.

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Mathematical Tools,ups of operators related to Markov chains at the end of the chapter. Since these semigroups act in the space of absolutely summable sequences, which is a particularly simple Banach space, some results of the theory of semigroups of operators can be proved in a simpler way here.

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Epilogue, recombination. The principles are simple, and encompass various versions of the Wright-Fisher and Moran Models of drift, with Markovian mutations, Haldane model for recombination and several types of selection. However, when combined, these principles lead to very complicated and frequently puzzling models some with very interesting mathematics.

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