Theoretical Evolutionary Genetics

383 Pages·2003·2.465 MB·English

by  Felsenstein J.

THEORETICAL
EVOLUTIONARY GENETICS
JOSEPH FELSENSTEIN

Theoretical Evolutionary Genetics
GENOME 562
Joseph Felsenstein
Department of Genome Sciences
University of Washington
Box 357730
Seattle, Washington 98195-7730
April, 2003
Copyright (c) 1978, 1983, 1988, 1991, 1992, 1994, 1995, 1997, 1999, 2001, 2003
by Joseph Felsenstein. All rights reserved.
Not to be reproduced without author’s permission.

Contents
PREFACE ix
1 RANDOM MATING POPULATIONS 1
I.1 Asexual inheritance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
I.2 Haploid inheritance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
I.3 Diploids with two alleles: Hardy-Weinberg laws. . . . . . . . . . . . . . . . . . . . . 4
I.4 Multiple alleles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
I.5 Overlapping generations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
I.6 Di(cid:11)erent Gene Frequencies in the Two Sexes . . . . . . . . . . . . . . . . . . . . . . 12
I.7 Sex linkage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
I.8 Linkage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
I.9 Estimating Gene Frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
I.10 Testing Hypotheses about Frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Complements/Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2 NATURAL SELECTION 33
II.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
II.2 Selection in Asexuals - Discrete Generations . . . . . . . . . . . . . . . . . . . . . . 34
II.3 Selection in Asexuals - Continuous Reproduction . . . . . . . . . . . . . . . . . . . . 39
II.4 Selection in Diploids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
II.5 Rates of Change of Gene Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
II.6 Overdominance and Underdominance . . . . . . . . . . . . . . . . . . . . . . . . . . 58
II.7 Selection and Fitness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
II.8 Selection and Fitness : Multiple Alleles . . . . . . . . . . . . . . . . . . . . . . . . . 73
II.9 Selection Dependent on Population Density . . . . . . . . . . . . . . . . . . . . . . . 77
II.10 Temporal Variation in Fitnesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
II.11 Frequency-Dependent Fitnesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
II.12 Kin selection: a speci(cid:12)c case of frequency - dependence . . . . . . . . . . . . . . . . 91
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Complements/Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
3 MUTATION 103
III.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
III.2 E(cid:11)ect of Mutation on Gene Frequencies . . . . . . . . . . . . . . . . . . . . . . . . . 104
v
III.3 Mutation with Multiple Alelles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
III.4 Mutation versus Selection: Haploids . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
III.5 Mutation vs. Selection: E(cid:11)ects of Dominance . . . . . . . . . . . . . . . . . . . . . . 110
III.6 Mutational Load. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
III.7 Mutation and Linkage Disequilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . 121
III.8 History and References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Complements/Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
4 MIGRATION 127
IV.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
IV.2 The E(cid:11)ect of Migration on Gene Frequencies . . . . . . . . . . . . . . . . . . . . . . 127
IV.3 Migration and Genotype Frequencies: Gene Pools . . . . . . . . . . . . . . . . . . . 128
IV.4 Estimating Admixture. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
IV.5 Recurrent Migration: Models of Migration . . . . . . . . . . . . . . . . . . . . . . . 132
IV.6 Recurrent Migration: E(cid:11)ects on Gene Frequencies . . . . . . . . . . . . . . . . . . . 135
IV.7 History and References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
IV.8 Migration vs. Selection: Patches of Adaptation . . . . . . . . . . . . . . . . . . . . . 137
IV.9 Two-Population Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
IV.10The Levene Model: Large Amounts of Migration . . . . . . . . . . . . . . . . . . . . 145
IV.11Selection-Migration Clines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
IV.12The Wave of Advance of an Advantageous Allele . . . . . . . . . . . . . . . . . . . . 157
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
Complements/Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
5 INBREEDING 161
V.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
V.2 Inbreeding Coe(cid:14)cients and Genotype Frequencies . . . . . . . . . . . . . . . . . . . 162
V.3 The Loop Calculus: A Simple Example. . . . . . . . . . . . . . . . . . . . . . . . . . 164
V.4 The Loop Calculus: A Pedigree With Several Loops.. . . . . . . . . . . . . . . . . . 166
V.5 The Loop Calculus: Sex Linkage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
V.6 The Method of Coe(cid:14)cients of Kinship. . . . . . . . . . . . . . . . . . . . . . . . . . 169
V.7 The Complication of Linkage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
V.8 More Elaborate Probabilities of Identity. . . . . . . . . . . . . . . . . . . . . . . . . 172
V.9 Regular Systems of Inbreeding: Sel(cid:12)ng. . . . . . . . . . . . . . . . . . . . . . . . . . 174
V.10 Regular Systems of Inbreeding: Full Sib Mating . . . . . . . . . . . . . . . . . . . . 175
V.11 Regular Systems of Inbreeding: Matrix Methods . . . . . . . . . . . . . . . . . . . . 179
V.12 Repeated double (cid:12)rst cousin mating. . . . . . . . . . . . . . . . . . . . . . . . . . . 181
V.13 The E(cid:11)ects of Inbreeding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
V.14 Some Comments About Pedigrees . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
Complements/Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
6 FINITE POPULATION SIZE 191
VI.1 Genetic Drift and Inbreeding: their relationship . . . . . . . . . . . . . . . . . . . . 191
VI.2 Inbreeding due to (cid:12)nite population size . . . . . . . . . . . . . . . . . . . . . . . . . 192
VI.3 Genetic drift: the Wright model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
VI.4 Inbreeding coe(cid:14)cients, variances, and (cid:12)xation probabilities. . . . . . . . . . . . . . . 198
VI.5 E(cid:11)ective population number: avoidance of sel(cid:12)ng, two sexes, monogamy. . . . . . . 201
VI.6 Varying population size, varying o(cid:11)spring number. . . . . . . . . . . . . . . . . . . . 205
VI.7 Other e(cid:11)ects on e(cid:11)ective population number. . . . . . . . . . . . . . . . . . . . . . . 209
VI.8 Hierarchical population structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
Complements/Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
7 GENETIC DRIFT AND OTHER EVOLUTIONARY FORCES 215
VII.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
VII.2 Drift Versus Mutation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
VII.3 Genetic distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
VII.4 Drift Versus Migration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
VII.5 Drift vs. Migration: the Island Model . . . . . . . . . . . . . . . . . . . . . . . . . . 229
VII.6 Drift vs. Migration: the stepping stone model. . . . . . . . . . . . . . . . . . . . . . 236
VII.7 Drift versus Selection: Probability of Fixation of a Mutant . . . . . . . . . . . . . . 242
VII.8 The Di(cid:11)usion Approximation to Fixation Probabilities. . . . . . . . . . . . . . . . . 247
VII.9 Di(cid:11)usion Approximation to Equilibrium Distributions. . . . . . . . . . . . . . . . . 258
VII.10The Relative Strength of Evolutionary Forces . . . . . . . . . . . . . . . . . . . . . 272
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
Complements/Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
8 MULTIPLE LINKED LOCI 279
VIII.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
VIII.2 A Haploid 2-locus Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
VIII.2.1 Selection with no recombination . . . . . . . . . . . . . . . . . . . . . . . . . 280
VIII.2.2 Epistasis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
VIII.2.3 Selection and recombination . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
VIII.2.4 Interaction and Linkage { An Example . . . . . . . . . . . . . . . . . . . . . 284
VIII.3 Linkage and Selection in Diploids . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
VIII.4 Lewontin and Kojima’s symmetric model. . . . . . . . . . . . . . . . . . . . . . . . 289
VIII.4.1 Fitness and Disequilibrium: Moran’s Counterexample . . . . . . . . . . . . 294
VIII.4.2 Coadapted Gene Complexes and Recombination . . . . . . . . . . . . . . . 294
VIII.5 The General Symmetric Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
9 QUANTITATIVE CHARACTERS 299
IX.1 What is a Quantitative Character? . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
IX.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
IX.3 Means . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304
IX.4 Additive and Dominance Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308
IX.5 Covariances Between Relatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318
IX.6 Regression of O(cid:11)spring on Parents . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322
IX.7 Estimating variance components and heritability.. . . . . . . . . . . . . . . . . . . . 325
IX.8 History and References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328
IX.9 Response to arti(cid:12)cial selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
IX.10History and References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337
Complements/Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339
10 MOLECULAR POPULATION GENETICS 341
X.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341
X.2 Mutation models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341
X.3 The Coalescent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343
Problems/Complements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346
11 POLYGENIC CHARACTERS IN NATURAL POPULATIONS 349
XI.1 Phenotypic Evolution Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349
XI.2 Kimura’s model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350
XI.3 Lande’s model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350
XI.4 Bulmer’s model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354
XI.5 Other models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
Complements/Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356
REFERENCES 357
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PREFACE
These are chapters I-XI of a set of notes which when completed will serve as a text for Genome
Sciences 562 (Population Genetics). The material omitted will complete chapter VIII on the in-
teraction of linkage and selection and cover some additional topics in chapters X and XI, such as
quantitative characters in natural populations and coalescents.
Each chapter ends with two sets of problems. Those labeled Exercises are intended to be
relativelystraightforwardapplicationofprinciplesgiveninthetext. Theyusuallyinvolvenumerical
calculationorsimplealgebra. ThesetlabeledProblems/Complementsaremorealgebraic,andoften
involve extension or re-examination of the material in the text.
The level of mathematics required to read this text is not high, although the volume of algebra
is sometimes heavy. It is probably su(cid:14)cient to know elementary Calculus, and parts of elementary
statistics and probability. Matrix algebra is used in several places, but these can be skipped
without much loss. The most relevant mathematical technique for population genetics is probably
factorization of simple polynomial expressions, which most people are taught in high school.
Many people have contributed to the production of these notes, particularly students in earlier
years of the course who caught many errors in earlier versions. The presentations were heavily
in(cid:13)uenced by lecture notes and courses on this subject by J. F. Crow and R. C. Lewontin. The
cover illustration is adapted from an original by Helen Leung. Sean Lamont wrote the plotting
program that producedthe majority of the (cid:12)gures. I am indebtedto many studentsfor suggestions
and corrections, particularly to Eric Anderson and Max Robinson. But most of all, I must thank
Nancy Gamble and Martha Katz for doing the enormous job of typing out these notes, and Nancy
Gamble for drawing some of the (cid:12)gures for earlier editions.
I am still hoping to complete this set of notes one day.
Joe Felsenstein
Department of Genome Sciences
University of Washington
Seattle
[email protected]
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