Introduction to Theoretical Population Genetics
This book covers those areas of theoretical population genetics that can be investigated rigorously by elementary mathematical methods. An attempt has been made to formulate the various models fairly generally and to state the biological assumptions quite explicitly. The choice and treatment oftopics should enable the reader to understand and evaluate detailed analysesof many specific models and applications in the literature. The materialsuffices for a one-year course and is almost entirely self-contained. The little basic genetics needed for understanding it is presented in the text. Calculus and linear algebra are used freely. Previous exposure to elementary probability theory would be helpful. The major mathematical theme of the book is the dynamical analysis of recursion relations. Many exact and approximate techniques for investigating linear and nonlinear recursion relations in one dimension and in several dimensionsare developed and applied. The problems are an essential part of this book. Although some of them ask the reader merely to supply details of derivations in the text, many illuminate, rigorize, or extend these derivations. Some of the results in the problems are useful and important. They vary in difficulty; the harder ones offer a challenge even to good students.
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Selection at an Autosomal Locus
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AA x Aa adults AiAj allelic frequencies analysis approximation assortative mating assume Assumption autosomal calculate Chap chosen at random condition constant correlation deduce deme denote derive diallelic dioecious disassortative mating distribution eigenvalue epistasis fertilities formula gametes gametic frequencies gene frequencies gene-frequency change genetic variance genic genotypic frequencies hard selection Hardy-Weinberg proportions Hence heterozygotes homozygotes identical by descent implies inbreeding coefficient individuals Karlin Kimura and Crow linear linkage equilibrium locus Malecot matrix mean fitness monoecious multiallelic mutation rates Nagylaki niche number of loci obtain offspring overdominance panmictic panmixia parent pedigree positive Problem protected polymorphism Prove random drift random mating rate of convergence ratio recessive recombination recursion relations reduces regression relative respectively satisfy Sect selection coefficients selection intensity shows single-locus soft selection stochastically independent Substituting suppose underdominance variables viability weak selection whence Wright yields zero zygotes