** ** 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.

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Population genetics is increasingly relevant to real-world problems such as mapping of genes associated with human diseases, conservation of endangered species, and antibiotic and drug resistance. This book is an attempt to explain the principles of population genetics to biology students, most of whom will not be come population geneticists. I have tried to show the applications of population genetics by using real-world examples from a variety of disciplines, including ecology, evolutionary biology, conservation biology, molecular biology, medicine, human genetics, and epidemiology.

Students bring a wide range of interests and backgrounds to a population genetics course. Some of the existing texts are elementary, designed to provide only a basic background; others are advanced, intended primarily for graduate students and specialists. This book tries to steer a middle ground. It is intended for advanced undergraduates and beginning graduate students who have taken a course in genetics and have some background in probability and statistics. The mathematics is not particularly advanced. A good working knowledge of algebra and familiarity with logarithmic and exponential functions are assumed. Calculus and linear algebra are used only occasionally. Basic probability theory is used extensively; Appendix A provides a review of the probability theory used in the book.

Mathematical models are an essential part of population genetics, and students often have trouble with them. Three features of the book are intended to help students understand and appreciate mathematical models in population genetics. First, they are presented as "what-if" exercises—as hypotheses that can be tested and modified by looking at real populations, as opposed to unrealistic mathematical descriptions of some hypothetical population. Second, I have emphasized the biological rationale and assumptions of the models and have tried to explain their biological implications in nonmathematical language. Third, I have tried to explain the equations and the steps in the derivations carefully, without sacrificing (much) mathematical rigor. Secondary mathematical details are often segregated into boxes, which can be read or skipped, as desired. My experience has been that students can do most of the math in this book if they are led through the steps slowly and carefully.

An important feature of this book is the emphasis on using a spreadsheet as a learning tool. I believe that one of the best ways to learn population genetics is to simulate models and analyze data with a spreadsheet. Boxes throughout the text provide detailed examples of data analysis, which students can replicate on their own computers and use as guides to working the end of chapter problems. Many problems require students to analyze models with spreadsheet simulations.

The organization of the book is mostly traditional. Chapter 1 is an overview of population genetics, and a gentle introduction to mathematical modeling. Chapter 2 introduces the ideas of genotype frequency, allele frequency, and observed heterozygosity. It then provides an extensive overview of the different kinds of genetic variation found in natural populations, including various kinds of molecular markers. These sections can be read at the beginning of a course, or referred to as needed.

The heart of the book is Chapters 3 through 10. Chapter 3 is an introduction to the Hardy-Weinberg principle and the idea of expected heterozygosity. F is introduced in its most general meaning, as a measure of the difference between the expected and observed heterozygosity. Chapter 4 introduces linkage and gametic disequilibrium and the approach to equilibrium, along with some applications. Sections 4.4 and 4.5 introduce the principles of human gene mapping and disease diagnosis based on linkage disequilibrium. I cover these topics because my students are interested in them; however, they can be skipped without loss of continuity. Chapters 5 through 9 cover the basic evolutionary processes of population genetics: natural selection, mutation, genetic drift, nonrandom mating, and gene flow. Each is introduced as a process acting alone, then interactions with other processes are discussed. Many examples, both conventional and molecular, are described.

Molecular population genetics and the neutral theory are discussed throughout the text. Chapter 10 is a detailed discussion of the neutral theory and its predictions, relevant observations from experimental and natural populations, and ways to detect natural selection on protein and DNA sequences.

The last three chapters contain material not usually covered in a first course on population genetics. They are included here as introductions to advanced topics for students and instructors who wish to pursue them. Chapter 11 is an introduction to methods of molecular phylogenetics. Chapter 12 reviews various kinds of natural selection beyond the simple one-locus, two-allele model. Chapter 13 is an introduction to quantitative genetics, with some emphasis on evolutionary quantitative genetics. Only a few sections in these chapters should be considered essential; for example, most instructors will want to cover Section 11.3 (Gene genealogies and coalescence) and 12.9 (Sexual selection). Students with some prior knowledge of quantitative genetics will want to read Section 13.6 (Evolutionary quantitative genetics). Instructors may wish to cover other sections depending on the interests of their class.

The problems at the end of each chapter include simple derivations, applications of formulas, data analysis, and simulation exercises. Many of them require students to investigate models or analyze data with a spreadsheet. Several require written analysis or short essays.

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