Fitness Landscapes and the Origin of Species

by Sergey Gavrilets

Overview

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.

Product Details

ISBN-13:	9780691119830
Publisher:	Princeton University Press
Publication date:	07/26/2004
Series:	Monographs in Population Biology , #41
Edition description:	New Edition
Pages:	480
Product dimensions:	5.50(w) x 8.50(h) x (d)

About the Author

Sergey Gavrilets is Professor of Ecology and Evolutionary Biology and Mathematics at the University of Tennessee. His many scientific articles have appeared in Nature, Proceedings of the National Academy of Sciences, Proceedings of the Royal Society of London, and other publications.

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	185
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	229
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 and fertilization	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	327
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

What People are Saying About This

Roger Butlin

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

Endler

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

From the Publisher

"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

Gunter Paul Wagner

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.
— Gunter Paul Wagner, Yale University

Thompson

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

Editorial Reviews

"This is a . . . rich book, full of sober, well-considered insights, and there is a sense of real progress in understanding the variety of situations in which speciation can occur. Any investment in this book is well rewarded."—-Brett Calcott, Austral Ecology

From the Publisher

This is a . . . rich book, full of sober, well-considered insights, and there is a sense of real progress in understanding the variety of situations in which speciation can occur. Any investment in this book is well rewarded.

Austral Ecology - Brett Calcott

This is a . . . rich book, full of sober, well-considered insights, and there is a sense of real progress in understanding the variety of situations in which speciation can occur. Any investment in this book is well rewarded.
— Brett Calcott

Austral Ecology