Population genetics occupies a central role in a number of important biological and social undertakings. It is fundamental to our understanding of evolutionary processes, of plant and animal breeding programs, and of various diseases of particular importance to mankind.

This is the first of a planned two-volume work discussing the mathematical aspects of population genetics, with an emphasis on the evolutionary theory. This first volume draws heavily from the author's classic 1979 edition, which appeared originally in Springer's Biomathematics series. It has been revised and expanded to include recent topics which follow naturally from the treatment in the earlier edition, e.g., the theory of molecular population genetics.

This book will appeal to graduate students and researchers in mathematical biology and other mathematically-trained scientists looking to enter the field of population genetics.

Advances in computers and biotechnology have had a profound impact on biomedical research, and as a result complex data sets can now be generated to address extremely complex biological questions. Correspondingly, advances in the statistical methods necessary to analyze such data are following closely behind the advances in data generation methods. The statistical methods required by bioinformatics present many new and difficult problems for the research community.

This book provides an introduction to some of these new methods. The main biological topics treated include sequence analysis, BLAST, microarray analysis, gene finding, and the analysis of evolutionary processes. The main statistical techniques covered include hypothesis testing and estimation, Poisson processes, Markov models and Hidden Markov models, and multiple testing methods.

The second edition features new chapters on microarray analysis and on statistical inference, including a discussion of ANOVA, and discussions of the statistical theory of motifs and methods based on the hypergeometric distribution. Much material has been clarified and reorganized.

The book is written so as to appeal to biologists and computer scientists who wish to know more about the statistical methods of the field, as well as to trained statisticians who wish to become involved with bioinformatics. The earlier chapters introduce the concepts of probability and statistics at an elementary level, but with an emphasis on material relevant to later chapters and often not covered in standard introductory texts. Later chapters should be immediately accessible to the trained statistician. Sufficient mathematical background consistsof introductory courses in calculus and linear algebra. The basic biological concepts that are used are explained, or can be understood from the context, and standard mathematical concepts are summarized in an Appendix. Problems are provided at the end of each chapter allowing the reader to develop aspects of the theory outlined in the main text.

Warren J. Ewens holds the Christopher H. Brown Distinguished Professorship at the University of Pennsylvania. He is the author of two books, Population Genetics and Mathematical Population Genetics. He is a senior editor of Annals of Human Genetics and has served on the editorial boards of Theoretical Population Biology, GENETICS, Proceedings of the Royal Society B and SIAM Journal in Mathematical Biology. He is a fellow of the Royal Society and the Australian Academy of Science.

Gregory R. Grant is a senior bioinformatics researcher in the University of Pennsylvania Computational Biology and Informatics Laboratory. He obtained his Ph.D. in number theory from the University of Maryland in 1995 and his Masters in Computer Science from the University of Pennsylvania in 1999.

Comments on the First Edition. "This book would be an ideal text for a postgraduate coursea ][and] is equally well suited to individual studya ]. I would recommend the book highly" (Biometrics). "Ewens and Grant have given us a very welcome introduction to what is behind those pretty [graphical user] interfaces" (Naturwissenschaften.). "The authors do an excellent job of presenting the essence of the material without getting bogged down in mathematical details" (Journal. American Staistical. Association). "The authors have restructured classical materialto a great extent and the new organization of the different topics is one of the outstanding services of the book" (Metrika).

This book describes the probability theory associated with frequently used statistical procedures and the relation between probability theory and statistical inference. The first third of the book is dedicated to probability theory including topics relating to events, random variables, and the Central Limit Theorem. Statistical topics then include parameter estimation with confidence intervals, hypothesis testing, chi-square tests, t tests, and several non-parametric tests. Flow charts are frequently used to facilitate an understanding of the material considered. The examples and problems in the book all concern simple data sets which can be analyzed with a simple calculator; however, the R code required to complete many examples and problems is provided as well for those that are interested.

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.

Advances in computers and biotechnology have had a profound impact on biomedical research, and as a result complex data sets can now be generated to address extremely complex biological questions. Correspondingly, advances in the statistical methods necessary to analyze such data are following closely behind the advances in data generation methods. The statistical methods required by bioinformatics present many new and difficult problems for the research community.

This book provides an introduction to some of these new methods. The main biological topics treated include sequence analysis, BLAST, microarray analysis, gene finding, and the analysis of evolutionary processes. The main statistical techniques covered include hypothesis testing and estimation, Poisson processes, Markov models and Hidden Markov models, and multiple testing methods.

The second edition features new chapters on microarray analysis and on statistical inference, including a discussion of ANOVA, and discussions of the statistical theory of motifs and methods based on the hypergeometric distribution. Much material has been clarified and reorganized.

The book is written so as to appeal to biologists and computer scientists who wish to know more about the statistical methods of the field, as well as to trained statisticians who wish to become involved with bioinformatics. The earlier chapters introduce the concepts of probability and statistics at an elementary level, but with an emphasis on material relevant to later chapters and often not covered in standard introductory texts. Later chapters should be immediately accessible to the trained statistician. Sufficient mathematical background consists of introductory courses in calculus and linear algebra. The basic biological concepts that are used are explained, or can be understood from the context, and standard mathematical concepts are summarized in an Appendix. Problems are provided at the end of each chapter allowing the reader to develop aspects of the theory outlined in the main text.

Warren J. Ewens holds the Christopher H. Brown Distinguished Professorship at the University of Pennsylvania. He is the author of two books, Population Genetics and Mathematical Population Genetics. He is a senior editor of Annals of Human Genetics and has served on the editorial boards of Theoretical Population Biology, GENETICS, Proceedings of the Royal Society B and SIAM Journal in Mathematical Biology. He is a fellow of the Royal Society and the Australian Academy of Science.

Gregory R. Grant is a senior bioinformatics researcher in the University of Pennsylvania Computational Biology and Informatics Laboratory. He obtained his Ph.D. in number theory from the University of Maryland in 1995 and his Masters in Computer Science from the University of Pennsylvania in 1999.

Comments on the first edition:

"This book would be an ideal text for a postgraduate course... and] is equally well suited to individual study.... I would recommend the book highly." (Biometrics)

"Ewens and Grant have given us a very welcome introduction to what is behind those pretty graphical user] interfaces." (Naturwissenschaften)

"The authors do an excellent job of presenting the essence of the material without getting bogged down in mathematical details." (Journal American Statistical Association)

"The authors have restructured classical material to a great extent and the new organization of the