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1.
The consequences of gene flow for local adaptation and differentiation: a twolocus twodeme model
Open Access
Title:
The consequences of gene flow for local adaptation and differentiation: a twolocus twodeme model
Author:
Ada Akerman
;
Reinhard Bürger
Ada Akerman
;
Reinhard Bürger
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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 supersymmetric 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 migrationselection balance facilitates invasion. Hence, loci of much smaller effect can invade than predicted by onelocus 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 twoway migration on the effective migration rate at a linked neutral locus is explored. Numerical work complements our analytical results.
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Publisher:
Springer Berlin Heidelberg
Year of Publication:
20140401
Source:
Journal of Mathematical Biology, 20140401, Volume 68, pp 11351198
Journal of Mathematical Biology, 20140401, Volume 68, pp 11351198
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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
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URL:
http://dx.doi.org/10.1007/s002850130660z
http://dx.doi.org/10.1007/s002850130660z
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Springer Open Choice
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2.
Multilocus Selection . . . I. Convergence properties for weak or strong migration
Open Access
Title:
Multilocus Selection . . . I. Convergence properties for weak or strong migration
Author:
Reinhard Bürger
Reinhard Bürger
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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 socalled weakselection limit, a simple dynamical system for suitably averaged allele frequencies. Under nondegeneracy assumptions on this weakselection limit which are generic, every equilibrium of the full dynamics is a perturbation of an equilibrium of the weakselection limit and has the same stability
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Contributors:
The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20130320
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
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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.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.221.9499
http://www.ped.fas.harvard.edu/publications/PEDpublications/2009/Burger_JMB09.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.221.9499
http://www.ped.fas.harvard.edu/publications/PEDpublications/2009/Burger_JMB09.pdf
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3.
Mathematical Biology Digital Object Identifier (DOI):
Open Access
Title:
Mathematical Biology Digital Object Identifier (DOI):
Author:
Reinhard Bürger
Reinhard Bürger
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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
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Contributors:
The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20120507
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
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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.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.221.8639
http://www.fas.harvard.edu/%7Eped/publications/PEDpublications/2005/buerger_jmathbiol05.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.221.8639
http://www.fas.harvard.edu/%7Eped/publications/PEDpublications/2005/buerger_jmathbiol05.pdf
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4.
The TwoLocus Model of Gaussian Stabilizing Selection
Open Access
Title:
The TwoLocus Model of Gaussian Stabilizing Selection
Author:
Martin Willensdorfer
;
Reinhard Bürger
Martin Willensdorfer
;
Reinhard Bürger
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Description:
We study the equilibrium structure of a wellknown twolocus 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 wellknown twolocus 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.
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Contributors:
The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20110404
Source:
http://www.esi.ac.at/preprints/esi1274.pdf
http://www.esi.ac.at/preprints/esi1274.pdf
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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.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.149.3729
http://www.esi.ac.at/preprints/esi1274.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.149.3729
http://www.esi.ac.at/preprints/esi1274.pdf
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5.
The TwoLocus Model of Gaussian Stabilizing Selection
Open Access
Title:
The TwoLocus Model of Gaussian Stabilizing Selection
Author:
Martin Willensdorfer
;
Reinhard Bürger
Martin Willensdorfer
;
Reinhard Bürger
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Description:
We study the equilibrium structure of a wellknown twolocus 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 wellknown twolocus 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.
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Contributors:
The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20110404
Source:
ftp://ftp.esi.ac.at:/pub/Preprints/esi1274.ps.gz
ftp://ftp.esi.ac.at:/pub/Preprints/esi1274.ps.gz
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Document Type:
text
Language:
en
Subjects:
Key words ; quantitative genetics ; stabilizing selection ; twolocus model ; recombination ; linkage disequilibrium ; symmetric viability model
Key words ; quantitative genetics ; stabilizing selection ; twolocus model ; recombination ; linkage disequilibrium ; symmetric viability model
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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.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.57.7572
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.57.7572
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6.
Evolution of dominance under frequencydependent intraspecific competition
Open Access
Title:
Evolution of dominance under frequencydependent intraspecific competition
Author:
Stephan Peischl
;
Reinhard Bürger
Stephan Peischl
;
Reinhard Bürger
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Contributors:
The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20130320
Source:
http://www.fas.harvard.edu/%7Eped/publications/PEDpublications/2008/
Reinhard
.pdf
http://www.fas.harvard.edu/%7Eped/publications/PEDpublications/2008/
Reinhard
.pdf
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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.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.221.9119
http://www.fas.harvard.edu/%7Eped/publications/PEDpublications/2008/Reinhard.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.221.9119
http://www.fas.harvard.edu/%7Eped/publications/PEDpublications/2008/Reinhard.pdf
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7.
A Multilocus Analysis of Intraspecific . . .
Open Access
Title:
A Multilocus Analysis of Intraspecific . . .
Author:
Reinhard Bürger
Reinhard Bürger
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Description:
The equilibrium structure of an additive, diallelic multilocus model of a quantitative trait under frequency and densitydependent 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 densitydependent 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
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Contributors:
The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20110404
Source:
http://www.esi.ac.at/preprints/esi1472.pdf
http://www.esi.ac.at/preprints/esi1472.pdf
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Document Type:
text
Language:
en
DDC:
519 Probabilities & applied mathematics
(computed)
;
612 Human physiology
(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.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.143.1277
http://www.esi.ac.at/preprints/esi1472.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.143.1277
http://www.esi.ac.at/preprints/esi1472.pdf
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8.
Polymorphism in the twolocus Levene model with nonepistatic . . .
Open Access
Title:
Polymorphism in the twolocus Levene model with nonepistatic . . .
Author:
Reinhard Bürger
Reinhard Bürger
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The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20130320
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
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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.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.222.4886
http://www.ped.fas.harvard.edu/publications/PEDpublications/2009/Burger_TPB09.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.222.4886
http://www.ped.fas.harvard.edu/publications/PEDpublications/2009/Burger_TPB09.pdf
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9.
Multilocus selection in subdivided populations II. Maintenance of polymorphism under weak or strong migration
Open Access
Title:
Multilocus selection in subdivided populations II. Maintenance of polymorphism under weak or strong migration
Author:
Reinhard Bürger
Reinhard Bürger
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The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20130320
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
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text
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en
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.222.3145
http://www.ped.fas.harvard.edu/publications/PEDpublications/2009/Burger2_JMB09.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.222.3145
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10.
THE MUTATION MATRIX AND THE EVOLUTION OF EVOLVABILITY
Title:
THE MUTATION MATRIX AND THE EVOLUTION OF EVOLVABILITY
Author:
Adam G. Jones
;
Stevan J. Arnold
;
Reinhard Bürger
;
C. Goodnight
Adam G. Jones
;
Stevan J. Arnold
;
Reinhard Bürger
;
C. Goodnight
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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 Gmatrix, which describes the standing additive genetic variances and covariances for a suite of traits, and the Mmatrix, which describes the effects of new mutations on genetic variances and covariances. A population's immediate response to selection is governed by the Gmatrix. However, evolvability is also concerned with the ability of mutational processes to produce adaptive variants, and consequently the Mmatrix is a crucial quantitative genetic parameter. Here, we explore the evolution of evolvability by using analytical theory and simulationbased 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 twotrait 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 Mmatrix 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 Mmatrix tends to increase stability of the Gmatrix under most circumstances. Previous studies of Gmatrix stability, which assume nonevolving Mmatrices, 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 Gmatrix, the Mmatrix, and the adaptive landscape, and that such evolution tends to stabilize the Gmatrix over evolutionary time.
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Publisher:
The Society for the Study of Evolution
Contributors:
Adam G. Jones ; Stevan J. Arnold ; Reinhard Bürger ; C. Goodnight
Year of Publication:
20070401
Source:
10.1111/j.15585646.2007.00071.x
10.1111/j.15585646.2007.00071.x
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Document Type:
text
Language:
English
DDC:
612 Human physiology
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All rights reserved.
All rights reserved.
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URL:
http://www.bioone.org/doi/full/10.1111/j.15585646.2007.00071.x
http://www.bioone.org/doi/full/10.1111/j.15585646.2007.00071.x
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(1) Goeckingk, Leopold Friedrich Günther von von...
(1) Hampel, Harald
(1) Heidtmann, B.
(1) Heun, Reinhard
(1) Hisashi Ohtsuki C
(1) Holl, Reinhard W.
(1) Holterhus, P. M.
(1) Horst Buerger
(1) Jessen, Frank
(1) Josef Loidl
(1) Jörg Fuchs
(1) Karges, Beate Maria
(1) Kiess, Wieland
(1) Knerr, I.
(1) Kordonouri, O.
(1) Lange, K.
(1) Lepler, R.
(1) Levine, Jonathan M.
(1) Loeschcke, V.
(1) Loeschcke, Volker
(1) Loidl, Josef
(1) Lorenz, Alexander
(1) M. Rausher
(1) Maier, Wolfgang
(1) Manapat, Michael
(1) Manapat, Michael L.
(1) Marg, W.
(1) Marije M. Vleugel
(1) Martin A. Nowak A
(1) Michael Manapat A
(1) Möller, Dietmar P. F.
(1) Möller, HansJürgen
(1) Neu, Andreas
(1) Novak, Mark
(1) Nowak, Martin
(1) Nowak, Martin A
(1) Näke, A.
(1) Outi R. Saramäki
(1) Papassotiropoulos, Andreas
(1) Paul A. Hohenlohe
(1) Paul J. van Diest
(1) Peischl, Stephan
(1) Petersen, M.
(1) Petra van der Groep
(1) Podeswik, A.
(1) Ptok, U.
(1) Rao, Marie Luise
(1) Reinhard Bos
(1) Reinhard Bürger D
Author:
Subject
(13) article
(6) biologie
(6) ddc 570
(5) mate choice
(5) mathematical model
(5) premating isolation
(5) secondary contact
(5) sexual selection
(5) speciation
(3) 510 mathematics
(3) investigations
(3) quantitative biology populations and evolution
(2) recombination
(2) research article
(1) 050
(1) 34c60
(1) 34d05
(1) 34d30
(1) 37n25
(1) 39a60 secondary
(1) 43a15
(1) 46e99
(1) 570 life sciences biology
(1) 92d10 primary 92d15
(1) 92d15
(1) angewandte mathematik
(1) applied mathematics
(1) assortative mating competitive divergence costs...
(1) biological sciences
(1) computational biology
(1) computer sciences
(1) evolution
(1) evolutionary biology
(1) evolutionary dynamics
(1) fixation index
(1) genetic architecture
(1) informatik
(1) key words
(1) linkage disequilibrium
(1) mathematica
(1) mathematics
(1) mathematics dynamical systems
(1) mathematik
(1) migration
(1) multilocus polymorphism
(1) natural sciences
(1) naturwissenschaften
(1) origin of life
(1) population subdivision
(1) prelife
(1) quantitative biology genomics
(1) quantitative genetics
(1) replication
(1) selection
(1) stabilizing selection
(1) symmetric viability model
(1) two locus model
(1) öfos
Subject:
Dewey Decimal Classification (DDC)
(16) Medicine & health [61*]
(12) Mathematics [51*]
(2) Economics [33*]
(2) Life sciences; biology [57*]
(2) Engineering [62*]
(1) Geography & travel [91*]
Dewey Decimal Classification (DDC):
Year of Publication
(11) 2014
(10) 2013
(5) 2011
(5) 2012
(4) 2008
(3) 2006
(3) 2007
(3) 2009
(3) 2010
(2) 1981
(2) 1992
(2) 1993
(2) 2003
(2) 2004
(1) 1773
(1) 1980
(1) 1982
(1) 1990
(1) 1994
(1) 2015
Year of Publication:
Content Provider
(19) PubMed Central
(13) CiteSeerX
(6) Munich LMU: Open Access
(5) DataCite Metadata Store
(3) ArXiv.org
(3) DigiZeitschriften
(3) Vienna Univ.: u:scholar
(2) BioOne (USA)
(2) Harvard Univ.: DASH
(1) Project Euclid
(1) Göttingen Univ.: GOEDOC
(1) Göttingen Center for Retrospective Digitization...
(1) Hindawi Publishing Corporation
(1) Lausanne Ecole Polytechnique Fed.: Infoscience
(1) Aachen RWTH: Publications
(1) Springer Open Choice
(1) Basel Univ.: edoc
(1) Bern Univ.: BORIS
Content Provider:
Language
(44) English
(18) Unknown
(3) German
Language:
Document Type
(45) Text
(9) Article, Journals
(5) Primary Data
(3) Unknown
(2) Books
(1) Reports, Papers, Lectures
Document Type:
Access
(36) Open Access
(29) Unknown
Access:
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