scholarly journals Geographical variation in a quantitative character.

Genetics ◽  
1994 ◽  
Vol 136 (1) ◽  
pp. 361-381
Author(s):  
T Nagylaki
Keyword(s):  
Local Population ◽  
Weighted Average ◽  
Two Dimensions ◽  
Quantitative Character ◽  
Stabilizing Selection ◽  
Convergence To Equilibrium ◽  
Stepping Stone ◽  
Evolutionary Forces ◽  
Local Averages ◽  
Stepping Stone Model

Abstract A model for the evolution of the local averages of a quantitative character under migration, selection, and random genetic drift in a subdivided population is formulated and investigated. Generations are discrete and nonoverlapping; the monoecious, diploid population mates at random in each deme. All three evolutionary forces are weak, but the migration pattern and the local population numbers are otherwise arbitrary. The character is determined by purely additive gene action and a stochastically independent environment; its distribution is Gaussian with a constant variance; and it is under Gaussian stabilizing selection with the same parameters in every deme. Linkage disequilibrium is neglected. Most of the results concern the covariances of the local averages. For a finite number of demes, explicit formulas are derived for (i) the asymptotic rate and pattern of convergence to equilibrium, (ii) the variance of a suitably weighted average of the local averages, and (iii) the equilibrium covariances when selection and random drift are much weaker than migration. Essentially complete analyses of equilibrium and convergence are presented for random outbreeding and site homing, the Levene and island models, the circular habitat and the unbounded linear stepping-stone model in the diffusion approximation, and the exact unbounded stepping-stone model in one and two dimensions.

Isolation by distance in a quantitative trait.

Genetics ◽  
1991 ◽  
Vol 128 (2) ◽  
pp. 443-452 ◽  
Author(s):  
R Lande
Keyword(s):  
Genetic Drift ◽  
Genetic Variance ◽  
Two Dimensions ◽  
Quantitative Character ◽  
Stabilizing Selection ◽  
Neighborhood Size ◽  
Phenotypic Variance ◽  
Two Dimensional ◽  
Random Genetic Drift ◽  
Dispersal Function

Abstract Random genetic drift in a quantitative character is modeled for a population with a continuous spatial distribution in an infinite habitat of one or two dimensions. The analysis extends Wright's concept of neighborhood size to spatially autocorrelated sampling variation in the expected phenotype at different locations. Weak stabilizing selection is assumed to operate toward the same optimum phenotype in every locality, and the distribution of dispersal distances from parent to offspring is a (radially) symmetric function. The equilibrium pattern of geographic variation in the expected local phenotype depends on the neighborhood size, the genetic variance within neighborhoods, and the strength of selection, but is nearly independent of the form of the dispersal function. With all else equal, geographic variance is smaller in a two-dimensional habitat than in one dimension, and the covariance between expected local phenotypes decreases more rapidly with the distance separating them in two dimensions than in one. The equilibrium geographic variance is less than the phenotypic variance within localities, unless the neighborhood size is small and selection is extremely weak, especially in two dimensions. Nevertheless, dispersal of geographic variance created by random genetic drift is an important mechanism maintaining genetic variance within local populations. For a Gaussian dispersal function it is shown that, even with a small neighborhood size, a population in a two-dimensional habitat can maintain within neighborhoods most of the genetic variance that would occur in an infinite panmictic population.

scholarly journals Relationship between migration and DNA polymorphism in a local population.

Genetics ◽  
1990 ◽  
Vol 126 (1) ◽  
pp. 231-234 ◽  
Author(s):  
F Tajima
Keyword(s):  
Dna Sequences ◽  
Migration Rate ◽  
Dna Polymorphism ◽  
Local Population ◽  
Island Model ◽  
Marginal Populations ◽  
Stepping Stone ◽  
Stepping Stone Model

Abstract The expected amount of DNA polymorphism, measured in terms of the number of nucleotide differences between the two DNA sequences randomly sampled from subpopulations, was studied by using the stepping-stone model and the finite island model, under the assumption that the migration rate is not the same among different subpopulations. The results obtained indicate that the expected amount of DNA polymorphism in the subpopulation with lower migration rate is smaller than that of higher migration rate. This suggests that marginal populations tend to have lower level of DNA polymorphism than central populations if the migration rate in the marginal populations is lower than that of the central populations.

Stepping stone models of finite length

1970 ◽  
Vol 2 (02) ◽  
pp. 229-258 ◽  
Author(s):  
Takeo Maruyama
Keyword(s):  
Monte Carlo ◽  
Population Structure ◽  
Finite Length ◽  
Correlation Coefficients ◽  
Gene Frequencies ◽  
Explicit Formulas ◽  
Stepping Stone ◽  
Monte Carlo Experiments ◽  
Stepping Stone Models ◽  
Stepping Stone Model

The stepping stone model of population structure, of finite length, is analysed with special reference to the variance, and correlation coefficients of gene frequencies. Explicit formulas for these quantities are obtained. The model is also analysed for the genetic variability maintained in the population. In order to check the validity of the analytical results, several numerical computations were carried out using two different methods: iterations and Monte Carlo experiments. The values obtained by these numerical methods agree well with the theoretical values obtained by formulas derived analytically.

scholarly journals Quantitative genetic variability maintained by mutation-stabilizing selection balance: sampling variation and response to subsequent directional selection

1989 ◽  
Vol 54 (1) ◽  
pp. 45-58 ◽  
Author(s):  
Peter D. Keightley ◽  
William G. Hill
Keyword(s):  
Genetic Variance ◽  
Directional Selection ◽  
Quantitative Character ◽  
Stabilizing Selection ◽  
Effective Population ◽  
Selection Responses ◽  
Quantitative Genetic ◽  
Before And After ◽  
Cage Population ◽  
Selection Of

SummaryA model of genetic variation of a quantitative character subject to the simultaneous effects of mutation, selection and drift is investigated. Predictions are obtained for the variance of the genetic variance among independent lines at equilibrium with stabilizing selection. These indicate that the coefficient of variation of the genetic variance among lines is relatively insensitive to the strength of stabilizing selection on the character. The effects on the genetic variance of a change of mode of selection from stabilizing to directional selection are investigated. This is intended to model directional selection of a character in a sample of individuals from a natural or long-established cage population. The pattern of change of variance from directional selection is strongly influenced by the strengths of selection at individual loci in relation to effective population size before and after the change of regime. Patterns of change of variance and selection responses from Monte Carlo simulation are compared to selection responses observed in experiments. These indicate that changes in variance with directional selection are not very different from those due to drift alone in the experiments, and do not necessarily give information on the presence of stabilizing selection or its strength.

The expected probabilities of identity for the circular stepping-stone model

1986 ◽  
Vol 28 (6) ◽  
pp. 1048-1050
Author(s):  
Curtis Strobeck
Keyword(s):  
Population Ecology ◽  
Identity By Descent ◽  
Model Population ◽  
Stepping Stone ◽  
Expected Values ◽  
Stepping Stone Model

The expected values of the probabilities of identity by descent are derived for the circular stepping-stone model. The results are more easily interpreted than those derived previously.Key words: model, population, ecology.

scholarly journals Spontaneous mutations and the origin and maintenance of quantitative genetic variation

eLife ◽  
2016 ◽  
Vol 5 ◽  
Author(s):  
Wen Huang ◽  
Richard F Lyman ◽  
Rachel A Lyman ◽  
Mary Anna Carbone ◽  
Susan T Harbison ◽  
...  
Keyword(s):  
Genetic Variation ◽  
Natural Selection ◽  
Quantitative Traits ◽  
Spontaneous Mutation ◽  
Natural Populations ◽  
Empirical Work ◽  
Stabilizing Selection ◽  
Spontaneous Mutation Rate ◽  
Evolutionary Forces ◽  
Quantitative Genetic

Mutation and natural selection shape the genetic variation in natural populations. Here, we directly estimated the spontaneous mutation rate by sequencing new Drosophila mutation accumulation lines maintained with minimal natural selection. We inferred strong stabilizing natural selection on quantitative traits because genetic variation among wild-derived inbred lines was much lower than predicted from a neutral model and the mutational effects were much larger than allelic effects of standing polymorphisms. Stabilizing selection could act directly on the traits, or indirectly from pleiotropic effects on fitness. However, our data are not consistent with simple models of mutation-stabilizing selection balance; therefore, further empirical work is needed to assess the balance of evolutionary forces responsible for quantitative genetic variation.

scholarly journals Selection constrains high rates of satellite DNA mutation in Daphnia pulex

2017 ◽  
Author(s):  
Jullien M. Flynn ◽  
Ian Caldas ◽  
Melania E. Cristescu ◽  
Andrew G. Clark
Keyword(s):  
Satellite Dna ◽  
Related Species ◽  
Rapid Evolution ◽  
Daphnia Pulex ◽  
Selective Constraint ◽  
Mutation Rates ◽  
Stabilizing Selection ◽  
Closely Related Species ◽  
Dna Mutation ◽  
Evolutionary Forces

AbstractA long-standing evolutionary puzzle is that all eukaryotic genomes contain large amounts of tandemly-repeated satellite DNA whose composition varies greatly among even closely related species. To elucidate the evolutionary forces governing satellite dynamics, quantification of the rates and patterns of mutations in satellite DNA copy number and tests of its selective neutrality are necessary. Here we used whole-genome sequences of 28 mutation accumulation (MA) lines of Daphnia pulex in addition to six isolates from a non-MA population originating from the same progenitor to both estimate mutation rates of abundances of satellite sequences and evaluate the selective regime acting upon them. We found that mutation rates of individual satellite sequence “kmers” were both high and highly variable, ranging from additions/deletions of 0.29 – 105 copies per generation (reflecting changes of 0.12 - 0.80 percent per generation). Our results also provide evidence that new kmer sequences are often formed from existing ones. The non-MA population isolates showed a signal of either purifying or stabilizing selection, with 33 % lower variation in kmer abundance on average than the MA lines, although the level of selective constraint was not evenly distributed across all kmers. The changes between many pairs of kmers were correlated, and the pattern of correlations was significantly different between the MA lines and the non-MA population. Our study demonstrates that kmer sequences can experience extremely rapid evolution in abundance, which can lead to high levels of divergence in genome-wide satellite DNA composition between closely related species.

scholarly journals GENE FLOW AND GENETIC DIFFERENTIATION

Genetics ◽  
1974 ◽  
Vol 78 (3) ◽  
pp. 961-965
Author(s):  
P T Spieth
Keyword(s):  
Gene Flow ◽  
Genetic Differentiation ◽  
Population Size ◽  
Local Population ◽  
Biological Significance ◽  
Island Model ◽  
Genetic Identity ◽  
Biological Interpretation ◽  
Different Populations ◽  
Stepping Stone Model

ABSTRACT A brief analysis is presented for the effects of gene flow upon genetic differentiation within and between populations generated by mutation and drift. Previous results obtained with the "island" model are developed into a form that lends itself to biological interpretation. Attention is focused upon the effective local population size and the ratio of the genetic identity of two genes in different populations to that of two genes in the same population. The biological significance of this ratio, which is independent of population size, is discussed. Similarities between the results of this model and those of the "stepping-stone" model are noted.

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