%0 Book %1 akin1979geometry %A Akin, Ethan %B Lecture Notes in Biomathematics %D 1979 %I Springer-Verlag, Berlin-New York %K cycling dynamical_systems epistasis large_populations population_genetics review selection %P iv+205 %T The geometry of population genetics %V 31 %X This book describes S. Shahshahani's use of differential geometry in population genetics. The differential geometry illuminates many aspects of the nonlinear differential equations which model the action of selection and recombination. Fisher's fundamental theorem of natural selection (which says that along the solution curves of the selection differential equation, mean fitness is constantly increasing) and Kimura's maximal principle (the direction of motion of the mean fitness is the direction of greatest increase; i.e., the gradient) are proved. The effect of recombination on entropy is clarified and the relationship between two classic measures of genetic distance, the chi-squared measure and the arc-cosine measure, is described. Two applications are described: the definition of degree of epistasis which applies to general forms of selection and the appearance of cycling in the two-locus-two-allele model of selection plus recombination. MR: The book is divided into four chapters. Chapter I contains a general description of the entire work. Chapters II and IV contain the heart of the mathematics describing the geometry of epistasis and the Hopf bifurcation. Chapter III contains a description of position effects. %@ 3-540-09711-2

@book{akin1979geometry, abstract = {This book describes S. Shahshahani's use of differential geometry in population genetics. The differential geometry illuminates many aspects of the nonlinear differential equations which model the action of selection and recombination. Fisher's fundamental theorem of natural selection (which says that along the solution curves of the selection differential equation, mean fitness is constantly increasing) and Kimura's maximal principle (the direction of motion of the mean fitness is the direction of greatest increase; i.e., the gradient) are proved. The effect of recombination on entropy is clarified and the relationship between two classic measures of genetic distance, the chi-squared measure and the arc-cosine measure, is described. Two applications are described: the definition of degree of epistasis which applies to general forms of selection and the appearance of cycling in the two-locus-two-allele model of selection plus recombination. [MR:] The book is divided into four chapters. Chapter I contains a general description of the entire work. Chapters II and IV contain the heart of the mathematics describing the geometry of epistasis and the Hopf bifurcation. Chapter III contains a description of position effects. }, added-at = {2014-10-10T06:14:24.000+0200}, author = {Akin, Ethan}, biburl = {https://www.bibsonomy.org/bibtex/29e7d1ac455da23dc8fbe9f68f7c17e56/peter.ralph}, interhash = {f9ed5ea48a5f506ce324338428d96737}, intrahash = {9e7d1ac455da23dc8fbe9f68f7c17e56}, isbn = {3-540-09711-2}, keywords = {cycling dynamical_systems epistasis large_populations population_genetics review selection}, mrclass = {92A10 (58F40)}, mrnumber = {559137 (80m:92007)}, mrreviewer = {Howard B. Stauffer}, pages = {iv+205}, publisher = {Springer-Verlag, Berlin-New York}, series = {Lecture Notes in Biomathematics}, timestamp = {2014-10-10T06:14:24.000+0200}, title = {The geometry of population genetics}, volume = 31, year = 1979 }