This book covers those areas of theoretical population genetics that can be investigated rigorously by elementary mathematical methods. I have tried to formulate the various models fairly generally and to state the biological as sumptions quite explicitly. I hope the choice and treatment of topics will en able the reader to understand and evaluate detailed analyses of many specific models and applications in the literature. Models in population genetics are highly idealized, often even over idealized, and their connection with observation is frequently remote. Further more, it is not practicable to measure the parameters and variables in these models with high accuracy. These regrettable circumstances amply justify the use of appropriate, lucid, and rigorous approximations in the analysis of our models, and such approximations are often illuminating even when exact solu tions are available. However, our empirical and theoretical limitations justify neither opaque, incomplete formulations nor unconvincing, inadequate analy ses, for these may produce uninterpretable, misleading, or erroneous results. Intuition is a principal source of ideas for the construction and investigation of models, but it can replace neither clear formulation nor careful analysis. Fisher (1930; 1958, pp. x, 23-24, 38) not only espoused similar ideas, but he recognized also that our concepts of intuition and rigor must evolve in time. The book is neither a review of the literature nor a compendium of results. The material is almost entirely self-contained. The first eight chapters are a thoroughly revised and greatly extended version of my published lecture notes (Nagylaki, 1977a).

This is the first of a planned two-volume work discussing the mathematical aspects of population genetics with an emphasis on evolutionary theory. This volume draws heavily from the author’s 1979 classic, but it has been revised and expanded to include recent topics which follow naturally from the treatment in the earlier edition, such as the theory of molecular population genetics.

Tracing the development of population genetics through the writings of such luminaries as Darwin, Galton, Pearson, Fisher, Haldane, and Wright, William B. Provine sheds light on this complex field as well as its bearing on other branches of biology.

The rise of the neutral theory of molecular evolution seems to have aroused a renewed interest in mathematical population genetics among biologists, who are primarily experimenters rather than theoreticians. This has encouraged me to set out the mathematics of the evolutionary process in a manner that, I hope, will be comprehensible to those with only a basic knowledge of calculus and matrix algebra. I must acknowledge from the start my great debt to my students. Equipped initially with rather limited mathematics, they have pursued the subject with much enthusiasm and success. This has enabled me to try a number of different approaches over the years. I was particularly grateful to Dr L. J. Eaves and Professor W. E. Nance for the opportunity to give a one-semester course at the Medical College of Virginia, and I would like to thank them, their colleagues and their students for the many kindnesses shown to me during my visit. I have concentrated almost entirely on stochastic topics, since these cause the greatest problems for non-mathematicians. The latter are particularly concerned with the range of validity of formulae. A sense of confidence in applying these formulae is, almost certainly, best gained by following their derivation. I have set out proofs in fair detail, since, in my experience, minor points of algebraic manipulation occasionally cause problems. To avoid loss of continuity, I have sometimes put material in notes at the end of chapters.

This text book, originally published in 1970, presents the field of population genetics, starting with elementary concepts and leading the reader well into the field. It is concerned mainly with population genetics in a strict sense and deals primarily with natural populations and less fully with the rather similar problems that arise in breading live stock and cul t i vat ed plans . The emphasis is on the behavior of genes and population attributes under natural selection where the most important measure is Darwinian fitness. This text is intended for graduatestudents and advanced undergraduates in genetics and population biology. This book steers a middle course between completely verbal biological arguments and the rigor of the mathematician. The first two-thirds of the book do not require advanced mathematical background. An ordinary knowledge of calculus will suffice. The latter parts of the book, which deal with population stochastically, use more advanced methods.

Making the theory of population genetics relevant to readers, this book explains the related mathematics with a logical organization. It presents the quantitative aspects of population genetics, and employs examples of human genetics, medical evolution, human evolution, and endangered species. For an introduction to, and understanding of, population genetics.

This book covers both classical population genetics theory developed in terms of allele and haplotype frequencies and modern population genetics theory developed in terms of coalescent theory. It features applications of theory to problems that arise in the study of human and other populations and assumes little prior knowledge of mathematics.