Mathematical Properties of Population-Genetic Statistics: Quadratic Forms Most Beautiful

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Noah A. Rosenberg

Mathematical Properties of Population-Genetic Statistics

Quadratic Forms Most Beautiful

Noah A. Rosenberg

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Hardback

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English

Princeton University Press
27 August 2025

Probability & statistics; Evolution; Genetics (non-medical)

Series: Princeton Series in Theoretical and Computational Biology

A powerful new approach to interpreting population-genetic data in evolution and ecology

Population genetics uses statistical analysis to catalog genetic variation among populations and species. Summary statistics computed from allele frequencies-mathematical functions that measure features of genetic similarity and diversity-are key to this global effort. Yet despite their widespread use in evolutionary biology, ecology, and conservation biology, their mathematical properties have largely been overlooked. This book shows how to use the mathematical bounds on summary statistics to make better interpretations of population-genetic data.

Noah Rosenberg discusses how the behavior of these statistics depends not only on the biology of the populations they seek to describe but also on the mathematical properties of the functions used to compute them, properties that produce constraints on the values of the statistics and influence their interpretation. Focusing on the concept of homozygosity-a quadratic function of allele frequencies in a population-he demonstrates how to account for mathematical constraints when measuring genetic similarity and diversity. Rosenberg illustrates the results using examples from empirical data and shares strategies that readers can use to apply this mathematical perspective to different kinds of summary statistics, including those for measuring biodiversity in ecological communities.

Drawing inspiration from Charles Darwin, who marveled at evolution's ""endless forms most beautiful and most wonderful,"" this book presents a groundbreaking approach to the study of genetic variation. It is sure to stimulate new research in population biology and deeper thinking about the meaning and interpretation of essential measurements of the world's genomes.

By: Noah A. Rosenberg
Imprint: Princeton University Press
Country of Publication: United States [Currently unable to ship to USA: see Shipping Info]
Dimensions: Height: 254mm, Width: 178mm,
ISBN: 9780691261560
ISBN 10: 0691261563
Series: Princeton Series in Theoretical and Computational Biology
Pages: 184
Publication Date: 27 August 2025
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Hardback
Publisher's Status: Active

Noah A. Rosenberg is Professor of Biology at Stanford University, where he holds the Stanford Professorship in Population Genetics and Society.