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Title:

The consequences of gene flow for local adaptation and differentiation: a two-locus two-deme model

Description:

We consider a population subdivided into two demes connected by migration in which selection acts in opposite direction. We explore the effects of recombination and migration on the maintenance of multilocus polymorphism, on local adaptation, and on differentiation by employing a deterministic model with genic selection on two linked diallelic l...

We consider a population subdivided into two demes connected by migration in which selection acts in opposite direction. We explore the effects of recombination and migration on the maintenance of multilocus polymorphism, on local adaptation, and on differentiation by employing a deterministic model with genic selection on two linked diallelic loci (i.e., no dominance or epistasis). For the following cases, we characterize explicitly the possible equilibrium configurations: weak, strong, highly asymmetric, and super-symmetric migration, no or weak recombination, and independent or strongly recombining loci. For independent loci (linkage equilibrium) and for completely linked loci, we derive the possible bifurcation patterns as functions of the total migration rate, assuming all other parameters are fixed but arbitrary. For these and other cases, we determine analytically the maximum migration rate below which a stable fully polymorphic equilibrium exists. In this case, differentiation and local adaptation are maintained. Their degree is quantified by a new multilocus version of $$F_\mathrm{ST}$$ and by the migration load, respectively. In addition, we investigate the invasion conditions of locally beneficial mutants and show that linkage to a locus that is already in migration-selection balance facilitates invasion. Hence, loci of much smaller effect can invade than predicted by one-locus theory if linkage is sufficiently tight. We study how this minimum amount of linkage admitting invasion depends on the migration pattern. This suggests the emergence of clusters of locally beneficial mutations, which may form ‘genomic islands of divergence’. Finally, the influence of linkage and two-way migration on the effective migration rate at a linked neutral locus is explored. Numerical work complements our analytical results. Minimize

Publisher:

Springer Berlin Heidelberg

Year of Publication:

2014-04-01

Source:

Journal of Mathematical Biology, 2014-04-01, Volume 68, pp 1135-1198

Journal of Mathematical Biology, 2014-04-01, Volume 68, pp 1135-1198 Minimize

Language:

En

Subjects:

Selection ; Migration ; Recombination ; Population subdivision ; Genetic architecture ; Multilocus polymorphism ; Fixation index ; 92D15 ; 34C60

Selection ; Migration ; Recombination ; Population subdivision ; Genetic architecture ; Multilocus polymorphism ; Fixation index ; 92D15 ; 34C60 Minimize

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Title:

Evolution of dominance under frequency-dependent intraspecific competition

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-03-20

Source:

http://www.fas.harvard.edu/%7Eped/publications/PEDpublications/2008/Reinhard.pdf

http://www.fas.harvard.edu/%7Eped/publications/PEDpublications/2008/Reinhard.pdf Minimize

Document Type:

text

Language:

en

Rights:

Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

A Multilocus Analysis of Intraspecific . . .

Description:

The equilibrium structure of an additive, diallelic multilocus model of a quantitative trait under frequency- and density-dependent selection is derived. The trait is under stabilizing selection and mediates intraspecific competition as induced, for instance, by differential resource utilization. It is assumed that stabilizing selection is weak,...

The equilibrium structure of an additive, diallelic multilocus model of a quantitative trait under frequency- and density-dependent selection is derived. The trait is under stabilizing selection and mediates intraspecific competition as induced, for instance, by differential resource utilization. It is assumed that stabilizing selection is weak, but the strength of competition may be arbitrary relative to it. Density dependence is caused by population regulation, which may be of a very general kind. Number and effects of loci are arbitrary and stabilizing selection is not necessarily symmetric with respect to the range of phenotypic values. All previously studied models of intraspecific competition for a continuum of resources known to the author reduce to a special case of the present model if overall selection is weak. Therefore, in this case our results are applicable as approximations to all these models. Our central result is the (nearly) complete characterization of the equilibrium structure in terms of all parameters. It is derived under the sole assumption that selection is weak enough relative to recombination to ignore linkage disequilibrium. In particular, necessary and sufficient conditions on the strength of competition relative to stabilizing selection are found that ensure the maintenance of multilocus polymorphism and the occurrence of disruptive selection. In this case, explicit Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2011-04-04

Source:

http://www.esi.ac.at/preprints/esi1472.pdf

http://www.esi.ac.at/preprints/esi1472.pdf Minimize

Document Type:

text

Language:

en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

The Two-Locus Model of Gaussian Stabilizing Selection

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Description:

We study the equilibrium structure of a well-known two-locus model in which two diallelic loci contribute additively to a quantitative trait that is under Gaussian stabilizing selection. The population is assumed to be infinitely large, randomly mating, and having discrete generations. The two loci may have arbitrary effects on the trait, the st...

We study the equilibrium structure of a well-known two-locus model in which two diallelic loci contribute additively to a quantitative trait that is under Gaussian stabilizing selection. The population is assumed to be infinitely large, randomly mating, and having discrete generations. The two loci may have arbitrary effects on the trait, the strength of selection and the recombination rate may also be arbitrary. We find that sixteen different equilibrium patterns exist, having up to eleven equilibria; up to seven interior equilibria may coexist, and up to four interior equilibria, three in negative and one in positive linkage disequilibrium, may be simultaneously stable. Also, two monomorphic and two fully polymorphic equilibria may be simultaneously stable. Therefore, the result of evolution may be highly sensitive to perturbations in the initial conditions or in the underlying genetic parameters. For the special case of equal effects, global stability results are proved. In the general case, we rely in part on numerical computations. The results are compared with previous analyses of the special case of extremely strong selection, of an approximate model that assumes linkage equilibrium, and of the much simpler quadratic optimum model. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2011-04-04

Source:

http://www.esi.ac.at/preprints/esi1274.pdf

http://www.esi.ac.at/preprints/esi1274.pdf Minimize

Document Type:

text

Language:

en

DDC:

519 Probabilities & applied mathematics *(computed)*

Rights:

Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

The Two-Locus Model of Gaussian Stabilizing Selection

Author:

Description:

We study the equilibrium structure of a well-known two-locus model in which two diallelic loci contribute additively to a quantitative trait that is under Gaussian stabilizing selection. The population is assumed to be in nitely large, randomly mating, and having discrete generations. The two loci may have arbitrary eects on the trait, the stren...

We study the equilibrium structure of a well-known two-locus model in which two diallelic loci contribute additively to a quantitative trait that is under Gaussian stabilizing selection. The population is assumed to be in nitely large, randomly mating, and having discrete generations. The two loci may have arbitrary eects on the trait, the strength of selection and the recombination rate may also be arbitrary. We nd that sixteen dierent equilibrium patterns exist, having up to eleven equilibria; up to seven interior equilibria may coexist, and up to four interior equilibria, three in negative and one in positive linkage disequilibrium, may be simultaneously stable. Also, two monomorphic and two fully polymorphic equilibria may be simultaneously stable. Therefore, the result of evolution may be highly sensitive to perturbations in the initial conditions or in the underlying genetic parameters. For the special case of equal eects, global stability results are proved. In the general case, we rely in part on numerical computations. The results are compared with previous analyses of the special case of extremely strong selection, of an approximate model that assumes linkage equilibrium, and of the much simpler quadratic optimum model. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2011-04-04

Source:

ftp://ftp.esi.ac.at:/pub/Preprints/esi1274.ps.gz

ftp://ftp.esi.ac.at:/pub/Preprints/esi1274.ps.gz Minimize

Document Type:

text

Language:

en

Subjects:

Key words ; quantitative genetics ; stabilizing selection ; two-locus model ; recombination ; linkage disequilibrium ; symmetric viability model

Key words ; quantitative genetics ; stabilizing selection ; two-locus model ; recombination ; linkage disequilibrium ; symmetric viability model Minimize

DDC:

519 Probabilities & applied mathematics *(computed)*

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Title:

Multilocus selection in subdivided populations II. Maintenance of polymorphism under weak or strong migration

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-03-20

Source:

http://www.ped.fas.harvard.edu/publications/PEDpublications/2009/Burger2_JMB09.pdf

http://www.ped.fas.harvard.edu/publications/PEDpublications/2009/Burger2_JMB09.pdf Minimize

Document Type:

text

Language:

en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

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Title:

Multilocus Selection . . . I. Convergence properties for weak or strong migration

Description:

The dynamics and equilibrium structure of a deterministic populationgenetic model of migration and selection acting on multiple multiallelic loci is studied. A large population of diploid individuals is distributed over finitely many demes connected by migration. Generations are discrete and nonoverlapping, migration is irreducible and aperiodic...

The dynamics and equilibrium structure of a deterministic populationgenetic model of migration and selection acting on multiple multiallelic loci is studied. A large population of diploid individuals is distributed over finitely many demes connected by migration. Generations are discrete and nonoverlapping, migration is irreducible and aperiodic, all pairwise recombination rates are positive, and selection may vary across demes. It is proved that, in the absence of selection, all trajectories converge at a geometric rate to a manifold on which global linkage equilibrium holds and allele frequencies are identical across demes. Various limiting cases are derived in which one or more of the three evolutionary forces, selection, migration, and recombination, are weak relative to the others. Two are particularly interesting. If migration and recombination are strong relative to selection, the dynamics can be conceived as a perturbation of the so-called weak-selection limit, a simple dynamical system for suitably averaged allele frequencies. Under nondegeneracy assumptions on this weak-selection limit which are generic, every equilibrium of the full dynamics is a perturbation of an equilibrium of the weak-selection limit and has the same stability Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-03-20

Source:

http://www.ped.fas.harvard.edu/publications/PEDpublications/2009/Burger_JMB09.pdf

http://www.ped.fas.harvard.edu/publications/PEDpublications/2009/Burger_JMB09.pdf Minimize

Document Type:

text

Language:

en

DDC:

519 Probabilities & applied mathematics *(computed)*

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

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Title:

Mathematical Biology Digital Object Identifier (DOI):

Description:

A multilocus analysis of intraspecific competition and stabilizing selection on a quantitative trait

A multilocus analysis of intraspecific competition and stabilizing selection on a quantitative trait Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-05-07

Source:

http://www.fas.harvard.edu/%7Eped/publications/PEDpublications/2005/buerger_jmathbiol05.pdf

http://www.fas.harvard.edu/%7Eped/publications/PEDpublications/2005/buerger_jmathbiol05.pdf Minimize

Document Type:

text

Language:

en

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Title:

Polymorphism in the two-locus Levene model with nonepistatic . . .

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-03-20

Source:

http://www.ped.fas.harvard.edu/publications/PEDpublications/2009/Burger_TPB09.pdf

http://www.ped.fas.harvard.edu/publications/PEDpublications/2009/Burger_TPB09.pdf Minimize

Document Type:

text

Language:

en

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Title:

THE MUTATION MATRIX AND THE EVOLUTION OF EVOLVABILITY

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Description:

Abstract Evolvability is a key characteristic of any evolving system, and the concept of evolvability serves as a unifying theme in a wide range of disciplines related to evolutionary theory. The field of quantitative genetics provides a framework for the exploration of evolvability with the promise to produce insights of global importance. With...

Abstract Evolvability is a key characteristic of any evolving system, and the concept of evolvability serves as a unifying theme in a wide range of disciplines related to evolutionary theory. The field of quantitative genetics provides a framework for the exploration of evolvability with the promise to produce insights of global importance. With respect to the quantitative genetics of biological systems, the parameters most relevant to evolvability are the G-matrix, which describes the standing additive genetic variances and covariances for a suite of traits, and the M-matrix, which describes the effects of new mutations on genetic variances and covariances. A population's immediate response to selection is governed by the G-matrix. However, evolvability is also concerned with the ability of mutational processes to produce adaptive variants, and consequently the M-matrix is a crucial quantitative genetic parameter. Here, we explore the evolution of evolvability by using analytical theory and simulation-based models to examine the evolution of the mutational correlation, rμ, the key parameter determining the nature of genetic constraints imposed by M. The model uses a diploid, sexually reproducing population of finite size experiencing stabilizing selection on a two-trait phenotype. We assume that the mutational correlation is a third quantitative trait determined by multiple additive loci. An individual's value of the mutational correlation trait determines the correlation between pleiotropic effects of new alleles when they arise in that individual. Our results show that the mutational correlation, despite the fact that it is not involved directly in the specification of an individual's fitness, does evolve in response to selection on the bivariate phenotype. The mutational variance exhibits a weak tendency to evolve to produce alignment of the M-matrix with the adaptive landscape, but is prone to erratic fluctuations as a consequence of genetic drift. The interpretation of this result is that the evolvability of the population is capable of a response to selection, and whether this response results in an increase or decrease in evolvability depends on the way in which the bivariate phenotypic optimum is expected to move. Interestingly, both analytical and simulation results show that the mutational correlation experiences disruptive selection, with local fitness maxima at –1 and +1. Genetic drift counteracts the tendency for the mutational correlation to persist at these extreme values, however. Our results also show that an evolving M-matrix tends to increase stability of the G-matrix under most circumstances. Previous studies of G-matrix stability, which assume nonevolving M-matrices, consequently may overestimate the level of instability of G relative to what might be expected in natural systems. Overall, our results indicate that evolvability can evolve in natural systems in a way that tends to result in alignment of the G-matrix, the M-matrix, and the adaptive landscape, and that such evolution tends to stabilize the G-matrix over evolutionary time. Minimize

Publisher:

The Society for the Study of Evolution

Contributors:

Adam G. Jones ; Stevan J. Arnold ; Reinhard Bürger ; C. Goodnight

Year of Publication:

2007-04-01

Source:

10.1111/j.1558-5646.2007.00071.x

10.1111/j.1558-5646.2007.00071.x Minimize

Document Type:

text

Language:

English

DDC:

612 Human physiology *(computed)*

Rights:

All rights reserved.

All rights reserved. Minimize

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