Inference from clines stabilized by frequency-dependent selection.

Abstract Frequency-dependent selection against rare forms can maintain clines. For weak selection, s, in simple linear models of frequency-dependence, single locus clines are stabilized with a maximum slope of between square root of s/square root of 8 sigma and square root of s/square root of 12 delta, where sigma is the dispersal distance. These clines are similar to those maintained by heterozygote disadvantage. Using computer simulations, the weak-selection analytical results are extended to higher selection pressures with up to three unlinked genes. Graphs are used to display the effect of selection, migration, dominance, and number of loci on cline widths, speeds of cline movements, two-way gametic correlations ("linkage disequilibria"), and heterozygote deficits. The effects of changing the order of reproduction, migration, and selection, are also briefly explored. Epistasis can also maintain tension zones. We show that epistatic selection is similar in its effects to frequency-dependent selection, except that the disequilibria produced in the zone will be higher for a given level of selection. If selection consists of a mixture of frequency-dependence and epistasis, as is likely in nature, the error made in estimating selection is usually less than twofold. From the graphs, selection and migration can be estimated using knowledge of the dominance and number of genes, of gene frequencies and of gametic correlations from a hybrid zone.

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Intruder colour and light environment jointly determine how nesting male stickleback respond to simulated territorial intrusions

Biology Letters ◽

10.1098/rsbl.2016.0467 ◽

2016 ◽

Vol 12 (8) ◽

pp. 20160467 ◽

Cited By ~ 10

Author(s):

Daniel I. Bolnick ◽

Kimberly Hendrix ◽

Lyndon Alexander Jordan ◽

Thor Veen ◽

Chad D. Brock

Keyword(s):

Frequency Dependence ◽

Three Dimensional ◽

Light Environment ◽

Depth Gradient ◽

Frequency Dependent ◽

Frequency Dependent Selection ◽

Negative Frequency Dependent Selection ◽

Colour Signals

Variation in male nuptial colour signals might be maintained by negative frequency-dependent selection. This can occur if males are more aggressive towards rivals with locally common colour phenotypes. To test this hypothesis, we introduced red or melanic three-dimensional printed-model males into the territories of nesting male stickleback from two optically distinct lakes with different coloured residents. Red-throated models were attacked more in the population with red males, while melanic models were attacked more in the melanic male lake. Aggression against red versus melanic models also varied across a depth gradient within each lake, implying that the local light environment also modulated the strength of negative frequency dependence acting on male nuptial colour.

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Zufallspaarung mit teilweiser Selbstung unter verschiedenen Modellen von häufigkeitsabhängiger Selektion /Mixed Random Mating and Selfing with Different Models of Frequency-Dependent Selection

Zeitschrift für Naturforschung C ◽

10.1515/znc-1978-9-1025 ◽

1978 ◽

Vol 33 (9-10) ◽

pp. 755-768 ◽

Cited By ~ 1

Author(s):

M. Hühn

Keyword(s):

Genetic Polymorphisms ◽

Population Genetic ◽

Random Mating ◽

Large Population ◽

Decisive Role ◽

Initial Population ◽

Special Importance ◽

Gene Frequencies ◽

Frequency Dependent ◽

Frequency Dependent Selection

Abstract Given a large population with mixed random mating and selfing (one locus-two alleles) different models of frequency-dependent selection were discussed - including a simple biometrical model for considering and analysing the competitive effects between neighbouring individuals in plant populations. For each model there were studied: changes in gene frequencies, population genetic equilibria, times until reaching these equilibria etc. - in dependence of the different parameters used: composition of the initial population, probability of selfing, selection-coefficients, competition-parameters.Apart from only few differing results it follows from the studies performed in these investigations, that the different composition of the initial population is of no particular importance as well for the gene frequencies p̂ at equilibrium as for the time t̂ until reaching these equilibria. This result is especially right for p̂.Different probabilities of selfing and different degrees of dominance in the selection coefficients are indeed of some influence on the existence and location of the population genetic equilibria, but here too we find an disproportionately stronger dependence with the time t̂ until reaching the equilibrium than with the gene frequency p̂ at equilibrium . The special importance of overdominance for the maintenance of genetic polymorphisms, which is well known in the case of non frequency-dependent selection (see: model 1 of the present studies) turn out to be of some other meaning in the models of frequency-dependent selection, which were analysed in the present paper: Depart from only few special situations (model 2 ; complete self-fertilization in models 5 and 6 ; extremely high probabilities of selfing in model 7) nontrivial equilibria are reached for all degrees of dominance. Therefore, the special importance of overdominance mentioned above, not proves right in the case of frequency-dependent selection.The investigations of the present paper have shown, that existence and location of the non trivial population genetic equilibria are determined not so much by degree of dominance and probability of selfing, but the equilibria are mainly determined by the model of the investigation used in the concerning studies.In the case of frequency-dependent selection, therefore, the explicit form of the fitness values as functions of the frequencies plays the decisive role in maintaining genetic polymorphisms.

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Introduction

Adaptive Diversification (MPB-48) ◽

10.23943/princeton/9780691128931.003.0001 ◽

2011 ◽

Author(s):

Michael Doebeli

Keyword(s):

Mathematical Modeling ◽

Frequency Dependence ◽

Biological Interactions ◽

Heritable Variation ◽

Evolutionary Trajectory ◽

Frequency Dependent ◽

Frequency Dependent Selection ◽

Suitable Parameter ◽

Space Frequency

This introductory chapter provides an overview of frequency-dependent selection—the phenomenon that the evolving population is part of the changing environment determining the evolutionary trajectory. Selection is frequency-dependent if the sign and magnitude of the correlations between heritable variation and reproductive variation change as a consequence of changes in the trait distribution that are themselves generated by such correlations. From the perspective of mathematical modeling, the realm of frequency dependence in evolution is larger than the realm of situations in which selection is not frequency dependent, because the absence of frequency dependence in a mathematical model of evolution essentially means that some parameters describing certain types of biological interactions are set to zero. Thus, in a suitable parameter space, frequency independence corresponds to the region around zero, while everything else corresponds to frequency dependence. In this way, frequency-dependent selection should therefore be considered the norm, not the exception, for evolutionary processes.

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Dodge, Duck, Dip, Dive & Dependence: Using Dodgeball to Explore Frequency Dependent Selection

The American Biology Teacher ◽

10.1525/abt.2016.78.7.603 ◽

2016 ◽

Vol 78 (7) ◽

pp. 603-606 ◽

Cited By ~ 1

Author(s):

Adam M. M. Stuckert ◽

Heather D. Vance-Chalcraft

Keyword(s):

High School ◽

Natural Selection ◽

Frequency Dependence ◽

Biological Processes ◽

Frequency Dependent ◽

Frequency Dependent Selection ◽

Predator Prey ◽

Biology Students ◽

Upper Level ◽

Evolution By Natural Selection

The term frequency dependence describes scenarios in which the likelihood of an event occurring is strongly tied to how common a particular trait is. Understanding frequency dependence is key to understanding numerous biological processes relevant to evolution by natural selection, such as predation, mimicry, disease, and effective vaccinations. We use dodgeball to demonstrate frequency dependent selection in a hypothetical predator–prey community, and provide possible extensions into other topics. This activity can be used with biology students in high school through upper-level undergraduate courses.

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Enzyme Kinetics, Substitutable Resources and Competition: From Biochemistry to Frequency-Dependent Selection in lac

Genetics ◽

10.1093/genetics/162.1.485 ◽

2002 ◽

Vol 162 (1) ◽

pp. 485-499 ◽

Cited By ~ 1

Author(s):

Mark Lunzer ◽

Arvind Natarajan ◽

Daniel E Dykhuizen ◽

Antony M Dean

Keyword(s):

Resource Utilization ◽

First Principles ◽

Narrow Range ◽

Catalytic Efficiency ◽

Weak Selection ◽

Frequency Dependent ◽

Frequency Dependent Selection ◽

Changing Environments ◽

Trade Offs ◽

Allozyme Polymorphisms

Abstract Trade-offs in catalytic efficiency at the lac permease of Escherichia coli produce alleles with different substrate specializations that are selectively favored on different galactosides. We show that differential resource utilization during competition for mixtures of galactosides produces frequency-dependent selection at lac. However, the polymorphism is protected only in a narrow range of galactoside ratios despite intense selection on the pure galactosides. Hence, stabilizing frequency-dependent selection protecting natural allozyme polymorphisms through differential resource utilization will be sporadic and ephemeral in randomly changing environments. A comparison of predictions, based on first principles, with experimental outcomes reveals an additional, unanticipated source of weak selection.

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