Population Genetics vdxiaovd Population Genetics A Concise Guide John H.vvvspie THEJOHNS HOPKINS UNIVERSITYPRESS Baltimore and London ._./,.,.I.,.,_,_,,.,,... ...l,.,ll.”_.~....,.,.,., ,.*..I .....I..., ..... ,..I.......,.. ,’. , , ’ 0 1998 The JohnsHopkine University Press All rights reserved. Published 1998 Printed in the United Statesof America on acid-free paper 9876543 The JohnsHopkins University Press 2715 North Charles Street Baltimore, Maryland 21218-4363 www.press.jhu.edu Library of Congress Cataloging-in-Publication Data will be'found at the endof this book. A catalog record for this book is available from the British Library. ISBN 0-8018-5764-6 ISBN 0-8018-5755-4(pbk.) To Robin Gordon Contents List of Figures ix Preface xi 1 The Hardy-Weinberg Law 1 1.1 DNA variationin Drosophila .................... 2 1.2 Loci and alleles ............................ 5 1.3 Genotypeand allele frequencies ................... 9 1.4 Randomly matingpopulations .................... 11 1.5 Answers to problems ......................... 17 2 Genetic Drift 19 2.1 A computersimulation ........................ 20 2.2 The decay of heterozygosity ..................... 22 2.3 Mutationand drift .......................... 27 2.4 Theneutral theory .......................... 32 2.5 Effective population size ....................... 35 2.6 The coalescent ............................ 38 2.7 Binomial sampling .......................... 42 2.8 Answers to problems ......................... 47 Natural Selection 3 Natural 49 3.1 The fundamental model ....................... 51 3.2 Relative fitness ............................ 52 3.3 Three kinds of selection ....................... 55 3.4 Mutation-selectionbalance ..................... 60 3.5 The heterozygous effects of alleles .................. 62 3.6 Changingenvironments ....................... 71 3.7 Selection and drift .......................... 77 3.8 Derivation of the fixationprobability ................ 80 3.9 Answers to problems ......................... 83 vii .....I\~,~-lI.,-_,.YI,IXOI*",.IIIY,'~I-,~"~~.'',~~,~I ...................................................... x ............................. ... Vlll Contents 4 Nonrandom Mating 85 4.1 Generalized Hardy-Weinberg .................... 86 4.2 Identity by descent .......................... 87 4.3 Inbreeding ............................... 90 4.4 Subdivision .............................. 96 4.5Answers to problems ......................... 101 5 Quantitative Genetics 103 5.1Correlation between relatives .................... 103 5.2 Response to selection ......................... 114 5.3 Evolutionaryquantitative genetics .................118 5.4 Dominance .............................. 124 5.5 The intensity of selection ...................... 130 5.6Answers to problems ......................... 131 6 The Evolutionary Advantage of Sex 133 6.1 Genetic segregation .......................... 134 6.2 Crossing-over ............................. 137 6.3 Muller’s ratchet ............................ 141 6.4 Kondrashov’s hatchet ......................... 145 6.5 Answers to problems ......................... 149 Appendix A Mathematical Necessities 151 Appendix B Probability 155 Bibliography 167 Index 171 List of Figures 1.1 The ADH coding sequence ...................... 3 1.2 Two ADH sequences .......................... 6 1.3 Differences between alleles ...................... 8 1.4 Proteinheterozygosities ....................... 16 2.1 Simulation of geneticdrift ...................... 21 2.2 Driftwith N = 1 ........................... 22 2.3 The derivation of g' ......................... 24 2.4 Neutralevolution ........................... 31 2.5 Hemoglobin evolution ........................ 33 2.6 The effective population size ..................... 36 2.7 A coalescent .............................. 39 2.8 Simulation of heterozygosity ..................... 43 2.9 Distributions of allele frequencies .................. 45 3.1 The rnedionigm allele in Paneda .................. 50 3.2 A simple lifecycle .......................... 51 3.3 Directional selection ......................... 54 3.4 Balancing selection .......................... 57 3.5 Hiddenvariation crosses ....................... 63 3.6 Drosophila viability ......................... 65 3.7 Atypical Greenberg and Crow locus ................ 67 3.8 A model of dominance ........................ 69 3.9 Spatial variationin selection ..................... 73 4.1 Coefficient of kinship ......................... 87 4.2 Shared alleles ............................. 88 4.3 Effects of inbreeding ......................... 90 4.4 Evolution of selfing .......................... 94 4.5 The island model ........................... 99 5.1 The height of evolution students .................. 104 5.2 Quantitative genetics model ..................... 105 5.3 Regression of Y on X ........................ 112 5.4 A selective breedingexperiment ...................114 ix ..........- ... ............. .. X List of Figures 5.5 The response to selection ...................... 116 5.6 The selection intensity ........................ 117 5.7 Selection of different intensities ................... 119 5.8 Additive and dominance effects ...................125 6.1 Sex versus parthenogenesis ...................... 134 6.2 Evolution in parthenogens ...................... 135 6.3. Asexual directional selection ..................... 137 6.4 Two loci ................................ 138 6.5 Muller’s ratchet ............................ 142 6.6 Recombination ............................ 145 6.7 Synergistic epistasis ......................... 146 6.8 Asexual mutation distribution .................... 147 Preface At various times I have taught population genetics in two- to five-week chunks. This is precious little time in which to teach a subject, like population genetics, that stands quite apartfrom the rest of biology in the way that itmakes scientific progress. As there are no textbooks short enough for these chunks, I wrote a Minimalist's Guide to Population Genetics. In this 21-page guide I attempted to distill population genetics down to itsessence. This guide was, for me, a central canon of the theoretical side of the field. The minimalist approach of the guide has been retained in this, its expanded incarnation. My goal has been to focus on that part of population genetics that is central and incontrovertible. I feel strongly that a student who understands well the core of population genetics is much better equipped to understand evolution than is one who understands less well each of a greater number of topics. If this book is mastered, then the rest of population genetics should be approachable. Population genetics is concerned with the genetic basis of evolution. It differs from much of biology in that its importantinsights are theoretical rather than observational or experimental. It could hardly be otherwise. The objects of study are primarily the frequencies and fitnesses of genotypes in natural populations. Evolution is the change in the frequencies of genotypes through time, perhaps due to their differences in fitness. While genotype frequencies are easily measured, their change is not. The time scale of change of most naturally occurring genetic variants is very long, probably on the order of tens of thousands to millions of years. Changes this slow are impossible to observe directly. Fitness differences between genotypes,. which may be responsible for some of the frequency changes, are so extraordinarily small, probably less than 0.01 percent, that they too areimpossible to measure directly. Although we can observe the state of a population, there really is no way to explore directly the evolution of a population. Rather, progress is made in population genetics by constructing mathemati- cal models of evolution, studying their behavior, and then checking whether the states of populations are compatible with this behavior. Early in the history of population genetics, certain models exhibited dynamics that were of such obvi- ous universal importance that thefact that they could not be directly verified in a natural setting seemed unimportant. There is no better example than genetic drift, the small random changes in genotype frequencies caused by variation in offspring number between individuals and, in diploids, genetic segregation. Ge- xi xii Preface netic drift is known to operate on a time scale that is proportional to thesize of the population. In a species with a million individuals, it takes roughly a million generations for genetic drift to change allele frequencies appreciably. There is no conceivable way of verifying that genetic drift changes allele frequencies in most natural populations. Our understanding that itdoes is entirely theoretical. Most population geneticists not only are comfortable with this state of affairs but also revel in the fact that they can demonstrate on the back of an envelope, rather than in the laboratory, how a significant evolutionary force operates. As most of the important insights of population genetics came initially from theory, so too is this text driven by theory. Although many of the chapters begin with an observation that sets the biological context for what follows, the signif- icant concepts first appear as ideas about how evolution ought to proceed when certain assumptions are met. Only after the theoretical ideas are in hand does the text focus on the application of the theory to an issue raised by experiments or observations. The discussions of many of these issues are