Mathematical Structures in Population Genetics (Biomathematics, 22)

Hardcover, translated from the Russian, x + 373 pages, NOT ex-library. Printed in the USA. Owner's name concealed with a blank sticker inside the front board. Book is clean, bright, untanned, with unmarked text, free of stamps, firmly bound. Issued without a dust jacket. -- An advanced mathematical exploration of the genetic dynamics within populations. The book integrates classical genetics with modern algebraic and biomathematical approaches to examine population genetics through the lens of evolutionary equations, algebraic structures, and genetic recombination processes. Lyubich introduces foundational concepts in population genetics, such as classical genetic equations, Mendelian laws, and selection dynamics, while advancing into complex topics like nonassociative algebras, gene structure modeling, and quadratic evolutionary operators. The book emphasizes algebraic structures - such as Bernstein and genetic algebras - that allow for a mathematical representation of evolutionary processes, highlighting their role in understanding genetic variability, mutation, and selection dynamics. Key topics include the stability of genetic systems, convergence to equilibrium states, and recombination processes across loci and alleles. Lyubich also delves into the solution of Bernstein's problem and the application of algebraic tools to model selection dynamics and evolutionary operators. With a blend of theoretical discussions, mathematical models, and rigorous proofs, Mathematical Structures in Population Genetics serves as an essential resource for geneticists, mathematicians, and theoretical biologists seeking a deep understanding of the mathematical frameworks underlying evolutionary genetics. -- "In the theory of population genetics, fundamental results on its dynamical processes and equilibrium laws have emerged during the last few decades. This monograph systematically reviews these developments, beginning from elementary examples and explanations. Mathematically, the main emphasis of the book is the investigation of iterations of a quadratic or fractional quadratic operator in the simplex. By the use of some non-associative algebra, many results can be obtained in explicit form eg. the explicit description (Bernstein problem) of stationary quadratic operators, and the explicit solutions of a nonlinear evolutionary equation in the absence of selection, as well as general theorems on convergence to equilibrium in the presence of selection. Some of the algebraic theory used is interesting for its own sake. The reader can use this book either to obtain a thorough and comprehensive coverage of the present state of knowledge of the subject, and to learn new methods from it, or else to obtain an elementary introduction to the field.".…