EVOLUTION OF DISPERSAL RATES IN METAPOPULATION MODELS: BRANCHING AND CYCLIC DYNAMICS IN PHENOTYPE SPACE (original) (raw)

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Zoology Institute University of Basel Rheinsprung 9, CH‐4051 Basel Switzerland

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Division of Environmental and Evolutionary Biology, Graham Kerr Building University of Glasgow Glasgow G12 8QQ UK

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Received:

13 December 1996

Published:

01 December 1997

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Abstract

We study the evolution of dispersal rates in a two patch metapopulation model. The local dynamics in each patch are given by difference equations, which, together with the rate of dispersal between the patches, determine the ecological dynamics of the metapopulation. We assume that phenotypes are given by their dispersal rate. The evolutionary dynamics in phenotype space are determined by invasion exponents, which describe whether a mutant can invade a given resident population. If the resident metapopulation is at a stable equilibrium, then selection on dispersal rates is neutral if the population sizes in the two patches are the same, while selection drives dispersal rates to zero if the local abundances are different. With non‐equilibrium metapopulation dynamics, non‐zero dispersal rates can be maintained by selection. In this case, and if the patches are ecologically identical, dispersal rates always evolve to values which induce synchronized metapopulation dynamics. If the patches are ecologically different, evolutionary branching into two coexisting dispersal phenotypes can be observed. Such branching can happen repeatedly, leading to polymorphisms with more than two phenotypes. If there is a cost to dispersal, evolutionary cycling in phenotype space can occur due to the dependence of selection pressures on the ecological attractor of the resident population, or because phenotypic branching alternates with the extinction of one of the branches. Our results extend those of Holt and McPeek (1996), and suggest that phenotypic branching is an important evolutionary process. This process may be relevant for sympatric speciation.

Literature Cited

Abrams

,

P. A.

,

H.

Matsuda

, and

Y.

Harada

.

1993

.

Evolutionary unstable fitness maxima and stable fitness minima of continuous traits

.

Evol. Ecol.

7

:

465

–

487

.

Bellows

,

T. S.

,Jr.

1981

.

The descriptive properties of some models for density dependence

.

J. Anim. Ecol.

50

:

139

–

156

.

Blarer

,

A.

, and

M.

Doebeli

.

1996

.

In the red zone

.

Nature

380

:

589

–

590

.

Cressman

,

R.

1992

.

The stability concept of evolutionary game theory

. Lect. Notes Biomath.

94

.

Springer

,

Berlin, Germany

.

Doebeli

,

M.

1995

.

Dispersal and dynamics

.

Theor. Popul. Biol.

47

:

82

–

106

.

Doebeli

,

M.

1996

.

A quantitative genetic competition model for sympatric speciation

.

J. Evol. Biol.

9

:

893

–

909

.

Doebeli

,

M.

1997

.

Invasion of rare mutants does not imply their evolutionary success: a counterexample from metapopulation theory

.

J. Evol. Biol.

In press.

Feder

,

J. L.

1995

.

The effects of parasitoids on sympatric host races of Rhagoletis pomonella (Diptera: Tephritidae)

.

Ecology

76

:

801

–

813

.

Geritz

,

S. A. H.

,

F. J. A.

Jacobs

,

J. S.

van Heerwaarden

,

E.

Kisdi

,

G.

Meszéna

, and

J. A. J.

Metz

.

1997

.

Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree

.

Evol. Ecol.

In press.

Gyllenberg

,

M.

,

G.

Söderbacka

, and

S.

Ericsson

.

1993

.

Does migration stabilize local population dynamics? Analysis of a discrete metapopulation model

.

Math. Biosci.

118

:

25

–

49

.

Hassell

,

M. P.

1975

.

Density‐dependence in single‐species models

.

J. Anim. Ecol.

44

:

283

–

296

.

Hastings

,

A.

1983

.

Can spatial variation alone lead to selection for dispersal?

Theor. Popul. Biol.

24

:

244

–

251

.

Hastings

,

A.

1993

.

Complex interactions between dispersal and dynamics: lessons from coupled logistic equations

.

Ecology

74

:

1362

–

1372

.

Holt

,

R. D.

1985

.

Population dynamics in two‐patch environments: some anomalous consequences of an optimal habitat distribution

.

Theor. Popul. Biol.

28

:

181

–

208

.

Holt

,

R. D.

, and

M. A.

McPeek

.

1996

.

Chaotic population dynamics favors the evolution of dispersal

.

Am. Nat.

148

:

709

–

718

.

Jánosi

,

I. M.

, and

I.

Scheuring

.

1997

.

On the evolution of density dependent dispersal in a spatially structured population model

.

J. theor. Biol.

187

:

397

–

408

.

Johnson

,

P. A.

,

F. C.

Hoppenstaedt

,

J. J.

Smith

, and

G. L.

Bush

.

1996

.

Conditions for sympatric speciation: a diploid model incorporating habitat fidelity and non‐habitat assortative mating

.

Evol. Ecol.

10

:

187

–

205

.

Kawecki

,

T. J.

1996

.

Sympatric speciation driven by beneficial mutations

.

Proc. R. Soc. Lond. B.

263

:

1515

–

1520

.

Lloyd

,

A. L.

1995

.

The coupled Logistic map—a simple model for the effects of spatial heterogeneity on population dynamics

.

J. theor. Biol.

173

:

217

–

230

.

May

,

R. M.

, and

G. F.

Oster

.

1976

.

Bifurcations and dynamic complexity in simple ecological models

.

Am. Nat.

110

:

573

–

599

.

Maynard Smith

,

J.

1982

. Evolution and the theory of games.

Cambridge Univ. Press

,

Cambridge, U.K.

Maynard Smith

,

J.

, and

M.

Slatkin

.

1973

.

The stability of predator‐prey systems

.

Ecology

54

:

384

–

391

.

McPeek

,

M. A.

, and

R. D.

Holt

.

1992

.

The evolution of dispersal in spatially and temporally varying environments

.

Am. Nat.

140

:

1010

–

1027

.

Metz

,

J. A. J.

,

R. M.

Nisbet

, and

S. A. H.

Geritz

.

1992

.

How should we define ‘fitness’ for general ecological scenarios? Trends Ecol

.

Evol.

7

:

198

–

202

.

Metz

,

J. A. J.

,

S. A. H.

Geritz

,

G.

Meszéna

,

F. J. A.

Jacobs

, and

J. S.

van Heerwaarden

.

1996

.

Adaptive dynamics: a geometrical study of the consequences of nearly faithful reproduction

. Pp.

183

–

231

in

S. J.

van Strien

and

S. M.

Verduyn Lunel

, eds. Stochastic and spatial structures of dynamical systems.

North Holland

,

Amsterdam, The Netherlands

.

Rand

,

D. A.

,

H. B.

Wilson

, and

J. M.

McGlade

.

1994

.

Dynamics and evolution: evolutionary stable attractors, invasion exponents and phenotype dynamics

.

Philos. Trans. R. Soc. Lond. B

343

:

261

–

283

.

Ricker

,

W. E.

1954

.

Stock and recruitment

.

J. Fish. Res. Board Can.

11

:

559

–

623

.

Roff

,

D. A.

1992

. The evolution of life histories.

Chapman and Hall

,

London

.

Rohani

,

P.

,

R. M.

May

, and

M. P.

Hassell

.

1996

.

Metapopulations and equilibrium stability—the effects of spatial structure

.

J. theor. Biol.

181

:

97

–

109

.

Schliewen

,

U. K.

,

D.

Tautz

, and

S.

Pääbo

.

1994

.

Sympatric speciation suggested by monophyly of Crater Lake cichlids

.

Nature

368

:

629

–

632

.

Schluter

,

D.

1994

.

Experimental evidence that competition promotes divergence in adaptive radiation

.

Science

266

:

798

–

801

.

Stearns

,

S. C.

1992

. The evolution of life histories.

Oxford Univ. Press

,

Oxford

.

Author notes

Corresponding Editor: E. Martins

© 2021, Society for the Study of Evolution

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