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The origin of species has fascinated both biologists and the general public since the publication of Darwin's Origin of Species in 1859. Significant progress in understanding the process was achieved in the "modern synthesis," when Theodosius Dobzhansky, Ernst Mayr, and others reconciled Mendelian genetics with Darwin's natural selection. Although evolutionary biologists have developed significant new theory and data about speciation in the years since the modern synthesis, this book represents the first systematic attempt to summarize and generalize what mathematical models tell us about the dynamics of speciation.

Fitness Landscapes and the Origin of Species presents both an overview of the forty years of previous theoretical research and the author's new results. Sergey Gavrilets uses a unified framework based on the notion of fitness landscapes introduced by Sewall Wright in 1932, generalizing this notion to explore the consequences of the huge dimensionality of fitness landscapes that correspond to biological systems.

In contrast to previous theoretical work, which was based largely on numerical simulations, Gavrilets develops simple mathematical models that allow for analytical investigation and clear interpretation in biological terms. Covering controversial topics, including sympatric speciation and the effects of sexual conflict on speciation, this book builds for the first time a general, quantitative theory for the origin of species.

Endorsements

"A landmark work. This is the first systematic summary of the mathematical theory of speciation, and Dr. Gavrilets, whose work has changed the field in recent years, is the most qualified person to have written it. There is no comparable book."—Günter Paul Wagner, Yale University

"Undoubtedly a significant contribution. The book will be valuable not only in speciation theory but beyond the theoretical realm, to empirical scientists working on speciation, to evolutionary biologists more broadly, and to mathematicians interested in the applications. The scholarship is excellent, and the logical organization is impeccable."—Roger Butlin, University of Leeds

"This is a book that has been needed for a long time, but it required someone of Sergey Gavrilets's breadth and depth of understanding of both evolutionary biology and mathematical modeling. Gavrilets has already infused evolutionary biology with highly innovative ways of thinking about the structure of natural selection and the dynamics of evolution, using novel mathematical models to probe difficult ideas. Here he analyzes past work critically and adopts a clear viewpoint of his own, complete with a rich set of models that support that viewpoint. He does so in a way that makes the ideas accessible both to empirical evolutionary researchers and applied mathematicians."—John N. Thompson, University of California, Santa Cruz

"This is the first book I have read about speciation that actually presents the topic in an objective way, rather than carrying on the fifty-year tradition of strong opinions without critical evidence. Gavrilets does a splendid job of building all of the models and discussing their implications."—John A. Endler, University of California, Santa Barbara

Preface xiii
Mathematical symbols xv
Common abbreviations xviii
1 Introduction 1
1.1 General structure of the book 7
1.2 Some biological ideas and notions 9
1.2.1 Species definition and the nature of reproductive isolation 9
1.2.2 Geographic modes of speciation 10
1.2.3 Some speciation scenarios and patterns 14
Part I
Fitness landscapes
2 Fitness landscapes 21
2.1 Working example: one-locus, two-allele model of viability selection 22
2.2 Fitness landscape as fitness of gene combinations 25
2.3 Fitness landscape as the mean fitness of populations 30
2.4 The metaphor of fitness landscapes 33
2.4.1 Wright's rugged fitness landscapes 34
2.4.2 Fisher's single-peak fitness landscapes 36
2.4.3 Kimura's flat fitness landscapes 38
2.5 Fitness landscapes for mating pairs 40
2.6 Fitness landscapes for quantitative traits 41
2.6.1 Fitness landscape as fitness of trait combinations 41
2.6.2 Fitness landscape as the mean fitness of populations 42
2.6.3 Fitness landscapes for mating pairs 45
2.7 General comment on fitness landscapes 46
2.8 Summary 47
2.9 Conclusions 48
Box 2.1. Dynamics of allele frequencies in one-locus, multiallele population 49
Box 2.2. Hill climbing on a rugged fitness landscape 50
Box 2.3. Evolution on flat landscapes 51
3 Steps toward speciation on rugged fitness landscapes 53
3.1 Stochastic transitions between isolated fitness peaks 53
3.1.1 Fixation of an underdominant mutation 54
3.1.2 Peak shift in a quantitative character 60
3.1.3 Fixation of compensatory mutations in a two-locus haploid population 62
3.2 Some consequences of spatial subdivision and density fluctuations 66
3.2.1 Spatial subdivision 66
3.2.2 Stochastic transitions in a growing population 71
3.3 Peak shifts by selection 75
3.4 Summary 76
3.5 Conclusions 77
Box 3.1. Diffusion theory: the probability of fixation 78
Box 3.2. Diffusion theory: the time to fixation 79
Box 3.3. Diffusion theory: the duration of transition 80
4 Nearly neutral networks and holey fitness landscapes 81
4.1 Simple models 82
4.1.1 Russian roulette model in two dimensions 83
4.1.2 Russian roulette model on hypercubes 86
4.1.3 Generalized Russian roulette model 89
4.1.4 Multiplicative fitnesses 90
4.1.5 Stabilizing selection on an additive trait 91
4.1.6 Models based on the Nk-model 92
4.2 Neutral networks in RNA landscapes 95
4.3 Neutral networks in protein landscapes 97
4.4 Other evidence for nearly neutral networks 99
4.5 The metaphor of holey fitness landscapes 100
4.6 Deterministic evolution on a holey landscape 105
4.6.1 Error threshold 105
4.6.2 Genetic canalization 106
4.7 Stochastic evolution on a holey landscape 108
4.7.1 Random walks 108
4.7.2 Dynamics of haploid populations 112
4.8 Summary 113
4.9 Conclusions 114
Part II
The Bateson-Dobzhansky-Muller model
5 Speciation in the BDM model 117
5.1 The BDM model of reproductive isolation 117
5.1.1 Fitness landscapes in the BDM model 119
5.1.2 The mechanisms of reproductive isolation in the BDM model 121
5.2 Population genetics in the BDM model 124
5.2.1 Haploid population 125
5.2.2 Diploid population 128
5.3 Dynamics of speciation in the BDM model 130
5.3.1 Allopatric speciation 131
5.3.2 Parapatric speciation 137
5.4 Summary 143
5.5 Conclusions 145
Box 5.1. Hitting probability and hitting time in discrete-time Markov chains 146
Box 5.2. Genetic barrier to gene flow 147
6 Multidimensional generalizations of the BDM model 149
6.1 One- and two-locus, multiallele models 149
6.2 Multilocus models 151
6.2.1 The Walsh model 152
6.2.2 Divergent degeneration of duplicated genes 154
6.2.3 Three- and four-locus models 155
6.2.4 Accumulation of genetic incompatibilities 158
6.2.5 Allopatric speciation 174
6.2.6 Parapatric speciation 184
6.3 Summary 192
6.4 Conclusions 194
7 Spatial patterns in the BDM model 195
7.1 Individual-based models: spread of mutually incompatible neutral genes 197
7.1.1 Model 197
7.1.2 Parameters 198
7.1.3 Numerical procedure 199
7.1.4 Results 200
7.1.5 Interpretations 205
7.2 Deme-based models: spread of mutually incompatible neutral genes 207
7.2.1 Model 207
7.2.2 Parameters and dynamic characteristics 210
7.2.3 Results 211
7.2.4 Interpretations 219
7.3 Deme-based models: spread of mutually incompatible advantageous genes 221
7.4 Comment on adaptive radiation 228
7.5 Summary 228
7.6 Conclusions 230
Part III
Speciation via the joint action of disruptive natural selection and nonrandom mating
8 Maintenance of genetic variation under disruptive natural selection 233
8.1 Spatially heterogeneous selection 235
8.1.1 The Levene model 235
8.1.2 Two-locus, two-allele haploid version of the Levene model 238
8.1.3 Restricted migration between two niches 240
8.1.4 Spatial gradients in selection 242
8.1.5 Coevolutionary clines 249
8.2 Spatially uniform disruptive selection 251
8.2.1 Migration-selection balance: the Karlin-McGregor model 251
8.2.2 Migration-selection balance: the Bazykin model 252
8.3 Temporal variation in selection 254
8.4 Frequency-dependent selection in a single population 255
8.4.1 Phenomenological approach 256
8.4.2 Intraspecific competition 257
8.4.3 Spatially heterogeneous selection and competition 263
8.4.4 Adaptive dynamics approach 265
8.5 Summary 277
8.6 Conclusions 278
9 Evolution of nonrandom mating 279
9.1 A general framework for modeling nonrandom mating and fertilization 280
9.1.1 Random mating within mating pools joined preferentially 282
9.1.2 Preferential mating within mating pools joined randomly 284
9.2 Similarity-based nonrandom mating 287
9.2.1 Single locus 287
9.2.2 Multiple loci 299
9.2.3 General conclusions on similarity-based nonrandom mating 309
9.3 Matching-based nonrandom mating 309
9.3.1 Two loci 311
9.3.2 Two polygenic characters 321
9.3.3 One locus, one character 325
9.3.4 General conclusions on matching-based nonrandom mating 326
9.4 Nonrandom mating controlled by a culturally transmitted trait 327
9.5 Summary 328
9.6 Conclusions 330
10 Interaction of disruptive selection and nonrandom mating 331
10.1 Disruptive selection and similarity-based nonrandom mating 332
10.1.1 Single locus 333
10.1.2 Single quantitative character 352
10.1.3 Sympatric speciation with culturally transmitted mating preferences 356
10.2 Disruptive selection and matching-based nonrandom mating 359
10.2.1 Two loci 359
10.2.2 Two polygenic characters 364
10.3 "Magic trait" models 368
10.3.1 Single locus 369
10.3.2 Two loci: speciation by sexual conflict 370
10.3.3 Single polygenic character 374
10.3.4 Two polygenic characters: speciation by sexual selection 384
10.4 Disruptive selection and modifiers of mating 387
10.5 Summary 396
10.6 Conclusions 398
11 General conclusions 399
11.1 The structure of fitness landscapes and speciation 399
11.2 Allopatric speciation 401
11.3 Parapatric speciation 401
11.4 Sympatric speciation 403
11.5 Some speciation scenarios and patterns 406
11.6 General rules of evolutionary diversification 412
11.7 Why species? 414
11.8 Some open theoretical questions 416
11.9 Final thoughts 417
References 419
Index 457
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