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

Format:

Book

Author/Creator:

Rosenberg, Noah A.

Series:

Princeton Series in Theoretical and Computational Biology Series

Language:

English

Subjects (All):

Population biology--Mathematics.

Population biology.

Genetics--Mathematics.

Genetics.

Physical Description:

1 online resource (216 pages)

Edition:

1st ed.

Place of Publication:

Princeton : Princeton University Press, 2025.

Summary:

"A pedagogical monograph showing how to use the mathematical properties of population-genetic statistics to better interpret genetic data"-- Provided by publisher.

"A powerful new approach to interpreting population-genetic data in evolution and ecologyPopulation 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"-- Provided by publisher.

Contents:

Cover

Contents

Preface

Acknowledgments

1. Mathematical and Biological Introduction

1.1. Interpreting Population-Genetic Statistics

1.2. A Note about Assumed Background

1.3. Definitions

1.4. Standard Inequalities

1.5. Genetic Diversity and Genetic Homogeneity

1.6. Genetic Differentiation and Genetic Similarity

1.7. Do Statistics "Depend" on Allele Frequencies?

1.8. Exercises

2. Homozygosity and the Most Frequent Allele

2.1. Arbitrarily Many Distinct Alleles

2.2. A Fixed Value I for the Number of Distinct Alleles

2.3. Example from Human Populations

2.4. Implications

2.5. Exercises

3. Variations on Homozygosity: JA, JB, and JC

3.1. Bounds on JC/JB in Terms of JA

3.2. Example from Drosophila

3.3. Implications

3.4. Exercises

4. The ith Most Frequent Allele

4.1. Lower Bound on J in Terms of pi

4.2. Upper Bound on J in Terms of pi

4.3. Lower and Upper Bounds on pi in Terms of J

4.4. Example from Human Populations

4.5. Implications

4.6. Exercises

5. α-homozygosity

5.1. Convexity Inequalities

5.2. Arbitrarily Many Distinct Alleles

5.3. A Fixed Value I for the Number of Distinct Alleles

5.4. Example from Human Populations

5.5. Implications

5.6. Exercises

6. Estimated Homozygosity

6.1. Samples

6.2. Number of Distinct Alleles Constrained by Sample Size

6.3. A Fixed Value I for the Number of Distinct Alleles

6.4. Example from Human Populations

6.5. Implications

6.6. Exercises

7. Conclusions

7.1. Summary of Mathematical Results

7.2. Summary of Mathematical Methods

7.3. Benefits of the Mathematical Bounds Approach

7.4. The Continuing Importance of Summary Statistics

7.5. Strategies for Improved Use of Summary Statistics

Notation

Solutions to Exercises

Bibliography

Author Index

Subject Index.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

0-691-26157-1

OCLC:

1513420821