Fitness Landscapes and the Origin of Species

Sergey Gavrilets
Princeton University Press, 2004
Monographs in Population Biology

Paper: ISBN: 0-691-11983-X
Cloth: ISBN: 0-691-11758-6

Table of Contents

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