Mutational order: a major stochastic process in evolution

1990 ◽  
Vol 240 (1297) ◽  
pp. 29-37 ◽  
Keyword(s):  
Stochastic Process ◽  
Computer Simulations ◽  
Genetic Drift ◽  
Molecular Clock ◽  
Quantitative Character ◽  
Evolutionary Divergence ◽  
Random Genetic Drift ◽  
Random Drift ◽  
Large Populations ◽  
Different Populations

Computer simulations in which selection acts on a quantitative character show that the randomness of mutations can contribute significantly to evolutionary divergence between populations. In different populations, different advantageous mutations occur, and are selected to fixation, so that the populations diverge even when they are initially identical, and are subject to identical selection. This stochastic process is distinct from random genetic drift. In some circumstances (large populations or strong selection, or both) mutational order can be greatly more important than random drift in bringing about divergence. It can generate a ‘disconnection’ between evolution at the phenotypic and genotypic levels, and can give rise to a rough ‘molecular clock’, albeit episodic, that is driven by selection. In the absence of selection, mutational order has little or no effect.

The geometry of random drift II. The symmetry of random genetic drift

1977 ◽  
Vol 9 (2) ◽  
pp. 250-259 ◽  
Author(s):  
Peter L. Antonelli ◽  
Jared Chapin ◽  
G. Mark Lathrop ◽  
Kenneth Morgan
Keyword(s):  
Velocity Field ◽  
Genetic Drift ◽  
Gene Frequency ◽  
Radial Symmetry ◽  
Divergence Times ◽  
Random Genetic Drift ◽  
Initial State ◽  
Random Drift ◽  
Arithmetic Average ◽  
Frequency Space

It has been conjectured that a certain transformation of gene frequency space due to Fisher and Bhattacharyya will map the random genetic drift process, or its diffusion approximation, into one with radial symmetry. This paper proves rigorously that the Fisher–Bhattacharyya mapping does not do this. This implies that the initial state of an evolving ensemble can only be unbiasedly estimated from the means of a sample if we weight by the proper divergence times. If the ensemble is known not to have begun at the centroid of frequency space, the estimate of the initial state vector is not simply the arithmetic average, as symmetry analysis of the Christoffel velocity field shows.

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.

Frequency-dependent selection, metrical characters and molecular evolution

1988 ◽  
Vol 319 (1196) ◽  
pp. 631-640 ◽  
Keyword(s):  
Molecular Evolution ◽  
Genetic Drift ◽  
Random Order ◽  
Quantitative Character ◽  
Stabilizing Selection ◽  
Molecular Clocks ◽  
Random Genetic Drift ◽  
Stochastic Effects ◽  
Frequency Dependent ◽  
Frequency Dependent Selection

Computer models of selection acting on a quantitative character show that a combination of frequency-dependent and stabilizing selection can maintain many polymorphisms among the genes that determine the character. The models also show that the random order of mutations can give rise to selectively driven stochastic effects that are sometimes more important than random genetic drift. They suggest simple explanations for patterns of divergence between populations and species, and for apparent discrepancies between the rates of morphological and molecular evolution. They point towards a selective theory of ‘molecular clocks’

scholarly journals Linkage disequilibrium due to random genetic drift

1969 ◽  
Vol 13 (1) ◽  
pp. 47-55 ◽  
Author(s):  
Tomoko Ohta ◽  
Motoo Kimura
Keyword(s):  
Stochastic Process ◽  
Linkage Disequilibrium ◽  
Genetic Drift ◽  
Recombination Fraction ◽  
Random Genetic Drift ◽  
Effective Population ◽  
Finite Populations ◽  
Population Number ◽  
Backward Equation ◽  
Expected Values

The behaviour of linkage disequilibrium between two segregating loci in finite populations has been studied as a continuous stochastic process for different intensity of linkage, assuming no selection. By the method of the Kolmogorov backward equation, the expected values of the square of linkage disequilibrium z2, and other two quantities, xy(1 − x) (1 − y) and z(1 − 2x) (1 − 2y), were obtained in terms of T, the time measured in Ne as unit, and R, the product of recombination fraction (c) and effective population number (Ne). The rate of decrease of the simultaneous heterozygosity at two loci and also the asymptotic rate of decrease of the probability for the coexistence of four gamete types within a population were determined. The eigenvalues λ1, λ2 and λ3 related to the stochastic process are tabulated for various values of R = Nec.

The geometry of random drift II. The symmetry of random genetic drift

1977 ◽  
Vol 9 (02) ◽  
pp. 250-259 ◽  
Author(s):  
Peter L. Antonelli ◽  
Jared Chapin ◽  
G. Mark Lathrop ◽  
Kenneth Morgan
Keyword(s):  
Velocity Field ◽  
Genetic Drift ◽  
Gene Frequency ◽  
Radial Symmetry ◽  
Divergence Times ◽  
Random Genetic Drift ◽  
Initial State ◽  
Random Drift ◽  
Arithmetic Average ◽  
Frequency Space

It has been conjectured that a certain transformation of gene frequency space due to Fisher and Bhattacharyya will map the random genetic drift process, or its diffusion approximation, into one with radial symmetry. This paper proves rigorously that the Fisher–Bhattacharyya mapping does not do this. This implies that the initial state of an evolving ensemble can only be unbiasedly estimated from the means of a sample if we weight by the proper divergence times. If the ensemble is known not to have begun at the centroid of frequency space, the estimate of the initial state vector is not simply the arithmetic average, as symmetry analysis of the Christoffel velocity field shows.

scholarly journals Multinomial-Sampling Models for Random Genetic Drift

Genetics ◽  
1997 ◽  
Vol 145 (2) ◽  
pp. 485-491
Author(s):  
Thomas Nagylaki
Keyword(s):  
Population Regulation ◽  
Finite Population ◽  
Small Populations ◽  
Random Genetic Drift ◽  
Random Drift ◽  
Diploid Population ◽  
Fisher Model ◽  
Multinomial Sampling ◽  
Large Populations ◽  
Monoecious Population

Three different derivations of models with multinomial sampling of genotypes in a finite population are presented. The three derivations correspond to the operation of random drift through population regulation, conditioning on the total number of progeny, and culling, respectively. Generations are discrete and nonoverlapping; the diploid population mates at random. Each derivation applies to a single multiallelic locus in a monoecious or dioecious population; in the latter case, the locus may be autosomal or X-linked. Mutation and viability selection are arbitrary; there are no fertility differences. In a monoecious population, the model yields the Wright-Fisher model (i.e., multinomial sampling of genes) if and only if the viabilities are multiplicative. In a dioecious population, the analogous reduction does not occur even for pure random drift. Thus, multinomial sampling of genotypes generally does not lead to multinomial sampling of genes. Although the Wright-Fisher model probably lacks a sound biological basis and may be inaccurate for small populations, it is usually (perhaps always) a good approximation for genotypic multinomial sampling in large populations.

The geometry of random drift III. Recombination and diffusion

1977 ◽  
Vol 9 (02) ◽  
pp. 260-267 ◽  
Author(s):  
Peter L. Antonelli ◽  
Kenneth Morgan ◽  
G. Mark Lathrop
Keyword(s):  
Velocity Field ◽  
Markov Chains ◽  
Genetic Drift ◽  
Present Model ◽  
Random Mating ◽  
Recombination Fraction ◽  
Random Genetic Drift ◽  
Random Drift ◽  
Intrinsic Geometry ◽  
And Diffusion

A new diffusion model for random genetic drift of a two-locus di-allelic system is proposed. The Christoffel velocity field and the intrinsic geometry of the diffusion is computed for the equilibrium surface. It is seen to be radically non-spherical and to depend explicitly on the recombination fraction. The model has not been shown to be a limit of discrete Markov chains. For large values of the recombination, the present model is radically different from that of Ohta and Kimura, which is an approximation to the discrete process of random mating in the limit as the value of the recombination fraction goes to zero.

scholarly journals A White Noise Approach to Evolutionary Ecology

2020 ◽  
Author(s):  
Bob Week ◽  
Scott L. Nuismer ◽  
Luke J. Harmon ◽  
Stephen M. Krone
Keyword(s):  
White Noise ◽  
Genetic Drift ◽  
Evolutionary Ecology ◽  
Quantitative Character ◽  
Random Genetic Drift ◽  
Demographic Stochasticity ◽  
Selection Gradients ◽  
Evolutionary Response ◽  
Linear Selection ◽  
The Relationship

AbstractAlthough the evolutionary response to random genetic drift is classically modelled as a sampling process for populations with fixed abundance, the abundances of populations in the wild fluctuate over time. Furthermore, since wild populations exhibit demographic stochasticity, it is reasonable to consider the evolutionary response to demographic stochasticity and its relation to random genetic drift. Here we close this gap in the context of quantitative genetics by deriving the dynamics of the distribution of a quantitative character and the abundance of a biological population from a stochastic partial differential equation driven by space-time white noise. In the process we develop a useful set of heuristics to operationalize the powerful, but abstract theory of white noise and measure-valued stochastic processes. This approach allows us to compute the full implications of demographic stochasticity on phenotypic distributions and abundances of populations. We demonstrate the utility of our approach by deriving a quantitative genetic model of diffuse coevolution mediated by exploitative competition for a continuum of resources. In addition to trait and abundance distributions, this model predicts interaction networks defined by rates of interactions, competition coefficients, or selection gradients. Analyzing the relationship between selection gradients and competition coefficients reveals independence between linear selection gradients and competition coefficients. In contrast, absolute values of linear selection gradients and quadratic selection gradients tend to be positively correlated with competition coefficients. That is, competing species that strongly affect each other’s abundance tend to also impose selection on one another, but the directionality is not predicted. This approach contributes to the development of a synthetic theory of evolutionary ecology by formalizing first principle derivations of stochastic models that underlie rigorous investigations of the relationship between feedbacks of biological processes and the patterns of diversity they produce.

The geometry of random drift III. Recombination and diffusion

1977 ◽  
Vol 9 (2) ◽  
pp. 260-267 ◽  
Author(s):  
Peter L. Antonelli ◽  
Kenneth Morgan ◽  
G. Mark Lathrop
Keyword(s):  
Velocity Field ◽  
Markov Chains ◽  
Genetic Drift ◽  
Present Model ◽  
Random Mating ◽  
Recombination Fraction ◽  
Random Genetic Drift ◽  
Random Drift ◽  
Intrinsic Geometry ◽  
And Diffusion

A new diffusion model for random genetic drift of a two-locus di-allelic system is proposed. The Christoffel velocity field and the intrinsic geometry of the diffusion is computed for the equilibrium surface. It is seen to be radically non-spherical and to depend explicitly on the recombination fraction. The model has not been shown to be a limit of discrete Markov chains. For large values of the recombination, the present model is radically different from that of Ohta and Kimura, which is an approximation to the discrete process of random mating in the limit as the value of the recombination fraction goes to zero.

CYTO-NUCLEAR EPISTASIS: TWO-LOCUS RANDOM GENETIC DRIFT IN HERMAPHRODITIC AND DIOECIOUS SPECIES

Evolution ◽  
2006 ◽  
Vol 60 (4) ◽  
pp. 643 ◽  
Author(s):  
Michael J. Wade ◽  
Charles J. Goodnight
Keyword(s):  
Genetic Drift ◽  
Random Genetic Drift ◽  
Dioecious Species
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