scholarly journals Distribution of linkage disequilibrium with selection and finite population size

1979 ◽  
Vol 33 (1) ◽  
pp. 29-48 ◽  
Author(s):  
P. J. Avery ◽  
W. G. Hill
Keyword(s):  
Linkage Disequilibrium ◽  
Population Size ◽  
Finite Population ◽  
Gene Frequencies ◽  
Infinite Population ◽  
Large Expansion ◽  
Large Populations ◽  
The Difference ◽  
Successive Generations ◽  
Stable Points

SUMMARYThe effects of finite population size, occurring either as a bottleneck in a single generation followed by a large expansion or in all generations, are considered for models of two linked heterotic loci. Linkage is assumed to be tight because it is required if there is to be stable linkage disequilibrium, D ǂ 0, in infinitely large populations. (D is the difference between gamete frequencies and the product of the gene frequencies.)If a substantial perturbation of frequencies occurs as a result of a bottleneck but the population is subsequently very large, D may take hundreds of generations to return to its stable point. In finite populations, the distribution of D can be ⋃-shaped, unimodal or bimodal. The correlation of D in successive generations is higher with tight linkage and is little affected by selection or the size of the population.The utility of infinite population studies of linkage disequilibrium and its stable points is questioned, and considerable pessimism is expressed about the possibilities of distinguishing selection and sampling effects at linked loci.

scholarly journals The effect of finite population size on models of linked overdominant loci

1978 ◽  
Vol 31 (3) ◽  
pp. 239-254 ◽  
Author(s):  
P. J. Avery
Keyword(s):  
Linkage Disequilibrium ◽  
Population Size ◽  
Genetic Drift ◽  
High Probability ◽  
Finite Population ◽  
Equilibrium Points ◽  
Gene Frequencies ◽  
Wide Range ◽  
Stable Equilibria ◽  
Range Of Values

SUMMARYModels of two linked overdominant loci in moderately large, but finite, populations are examined by looking at the variance-covariance matrix of the two gene frequencies and the linkage disequilibrium around stable deterministic equilibrium points. In particular, the effect of genetic drift is examined in cases where, in infinite populations, two stable equilibria with non-zero linkage disequilibrium, D, are maintained. Theoretical formulae are produced and checked by computer simulation. In general, the results show that unless the population size is very large indeed, genetic drift causes the values of D to vary considerably about the equilibrium values and that for many models, where stable equilibria exist at non-zero D values, a wide range of values of D have a high probability. Thus it is very difficult to draw conclusions about the selection regime by measuring Linkage disequilibrium in a finite population.

Linkage disequilibrium between neutral genes in finite populations

1974 ◽  
Vol 6 (01) ◽  
pp. 13-15
Author(s):  
William G. Hill
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Linkage Disequilibrium ◽  
Finite Populations ◽  
Gene Frequencies ◽  
Infinite Population ◽  
Asymptotic Values

There is now a large literature on linkage disequilibrium between pairs of loci, both for selection in infinite populations and for neutral genes in finite populations, but there have been few studies with more loci. Bennett (1954) showed how the frequencies of chromosomes with any number of neutral genes would change in an infinite population, and the author (unpublished) has extended Bennett's results to find expected changes in chromosome frequencies with up to six loci in finite populations. For two linked neutral genes in finite populations the expected disequilibrium is zero, but the variance of the disequilibrium or the correlation of gene frequencies in segregating populations has been found. This has been done by Monte Carlo simulation (Hill and Robertson (1968)), but an approximation can be obtained by diffusion methods (Ohta and Kimura (1969)) and the asymptotic values using inbreeding theory (Sved (1971)). In this note we discuss the case of disequilibrium between three neutral loci and show how it relates to that between two loci.

scholarly journals PROBABILITY OF FIXATION AND MEAN FIXATION TIME OF AN OVERDOMINANT MUTATION

Genetics ◽  
1973 ◽  
Vol 74 (2) ◽  
pp. 371-380
Author(s):  
Masatoshi Nei ◽  
A K Roychoudhury
Keyword(s):  
Population Size ◽  
Gene Frequency ◽  
Finite Population ◽  
Retardation Factor ◽  
Fixation Time ◽  
Selection Intensity ◽  
Infinite Population ◽  
Probability Of Fixation

ABSTRACT The probability of fixation of an overdominant mutation in a finite population depends on the equilibrium gene frequency in an infinite population (m) and the product (A) of population size and selection intensity. If m < 0.5 (disadvantageous overdominant genes), the probability is generally much lower than that of neutral genes; but if m is close to 0.5 and A is relatively small, it becomes higher. If m > 0.5 (advantageous overdominant genes), the probability is largely determined by the fitness of heterozygotes rather than that of mutant homozygotes. Thus, overdominance enhances the probability of fixation of advantageous mutations. The average number of generations until fixation of an overdominant mutation also depends on m and A. This average time is long when m is close to 0.5 but short when m is close to 0 or 1. This dependence on m and A is similar to that of Robertson's retardation factor.

scholarly journals LINKAGE DISEQUILIBRIUM IN A FINITE POPULATION THAT IS PARTIALLY SELFING

Genetics ◽  
1980 ◽  
Vol 94 (3) ◽  
pp. 777-789 ◽  
Author(s):  
G B Golding ◽  
C Strobeck
Keyword(s):  
Linkage Disequilibrium ◽  
Population Size ◽  
Finite Population ◽  
Random Mating ◽  
Effective Population ◽  
Infinite Allele Model ◽  
Inbreeding Coefficients ◽  
Linkage Disequilibria ◽  
Recombination Value ◽  
Allele Model

ABSTRACT The linkage disequilibrium expected in a finite, partially selfing population is analyzed, assuming the infinite allele model. Formulas for the expected sum of squares of the linkage disequilibria and the squared standard linkage disequilibrium are derived from the equilibrium values of sixteen inbreeding coefficients required to describe the behavior of the system. These formulas are identical to those obtained with random mating if the effective population size Ne = (l—½S)N and the effective recombination value re = (l-S)r/(l-½S), where S is the proportion of selfing, are substituted for the population size and the recombination value, Therefore, the effect of partial selfing at equilibrium is to reduce the population size by a factor 1 — ½S and the recombination value by a factor (l-S)/(l—½S).

scholarly journals Coevolution does not slow the rate of loss of heterozygosity in a stochastic host-parasite model with constant population size

2020 ◽  
Author(s):  
Ailene MacPherson ◽  
Matthew J. Keeling ◽  
Sarah P. Otto
Keyword(s):  
Genetic Variation ◽  
Natural Selection ◽  
Population Size ◽  
Finite Population ◽  
Extensive Literature ◽  
Stochastic Perturbations ◽  
Frequency Dependent Selection ◽  
Infinite Population ◽  
Negative Frequency Dependent Selection ◽  
Host Parasite

AbstractCoevolutionary negative frequency dependent selection has been hypothesized to maintain genetic variation in host and parasites. Despite the extensive literature pertaining to host-parasite coevolution, the effect of matching-alleles (MAM) coevolution on the maintenance of genetic variation has not been explicitly modelled in a finite population. The dynamics of the MAM in an infinite population, in fact, suggests that genetic variation in these coevolving populations behaves neutrally. We find that while this is largely true in finite populations two additional phenomena arise. The first of these effects is that of coevolutionary natural selection on stochastic perturbations in host and pathogen allele frequencies. While this may increase or decrease genetic variation, depending on the parameter conditions, the net effect is small relative to that of the second phenomena. Following fixation in the pathogen, the MAM becomes one of directional selection, which in turn rapidly erodes genetic variation in the host. Hence, rather than maintain it, we find that, on average, matching-alleles coevolution depletes genetic variation.

scholarly journals Selection may oppose invasion, yet favour fixation: consequences for evolutionary stability

2019 ◽  
Author(s):  
Chai Molina ◽  
David J. D. Earn
Keyword(s):  
Population Size ◽  
Selection Process ◽  
Sufficient Conditions ◽  
Finite Populations ◽  
Phenotypic Effect ◽  
Infinite Population ◽  
Rare Mutations ◽  
Large Populations ◽  
Evolution By Natural Selection ◽  
Limiting Case

AbstractModels of evolution by natural selection often make the simplifying assumption that populations are infinitely large. In this infinite population limit, rare mutations that are selected against always go extinct, whereas in finite populations they can persist and even reach fixation. Nevertheless, for mutations of small phenotypic effect, it is widely believed that in sufficiently large populations, if selection opposes the invasion of rare mutants, then it also opposes their fixation. Here, we identify circumstances under which infinite-population models do or do not accurately predict evolutionary outcomes in large, finite populations. We show that there is no population size above which considering only invasion generally suffices: for any finite population size, there are situations in which selection opposes the invasion of mutations of arbitrarily small effect, but favours their fixation. This is not an unlikely limiting case; it can occur when fitness is a smooth function of the evolving trait, and when the selection process is biologically sensible. Nevertheless, there are circumstances under which opposition of invasion does imply opposition of fixation: in fact, for the n-player snowdrift game (a common model of cooperation) we identify sufficient conditions under which selection against rare mutants of small effect precludes their fixation—in sufficiently large populations—for any selection process. We also find conditions under which—no matter how large the population—the trait that fixes depends on the selection process, which is important because any particular selection process is only an approximation of reality.

scholarly journals Variability in genetic parameters among small populations

1977 ◽  
Vol 29 (3) ◽  
pp. 193-213 ◽  
Author(s):  
P. J. Avery ◽  
W. G. Hill
Keyword(s):  
Linkage Disequilibrium ◽  
Genetic Parameters ◽  
Additive Genetic Variance ◽  
Genetic Correlations ◽  
Small Populations ◽  
Base Population ◽  
Gene Frequencies ◽  
Additive Variance ◽  
Successive Generations ◽  
Additive Genes

SUMMARYFor a model in which quantitative traits are assumed to be determined solely by additive genes at many loci, formulae are developed for the variance among replicated small populations of size N, maintained without selection, of the additive genetic variance, heritability, genetic correlations and similar parameters. The base population is assumed to be in linkage equilibrium, but it is argued that most of the variation in the within-line additive variance (VAt at generation t) is due to linkage disequilibrium caused by sampling. If is the squared correlation of gene frequencies averaged over all pairs of loci at time t, the coefficient of variation (CV) of VAt equals , with similar formulae for other parameters.The formulae are evaluated for models of loci distributed uniformly along the chromosome but much of the disequilibrium is due to loci on different chromosomes. For unlinked loci CV(VAt) reaches √4/(3(N)), and for mammalian models, this value is not greatly exceeded. The variance in successive generations has a correlation of at least one-half due to the maintenance of linkage disequilibrium. The magnitude of this variance in parameters and their autocorrelation with time shows that accurate predictions cannot be made about genetic parameters in the base population from single replicate results.

scholarly journals A population genetical model for sequence evolution under multiple types of mutation

1989 ◽  
Vol 54 (3) ◽  
pp. 231-237 ◽  
Author(s):  
Masaru Iizuka
Keyword(s):  
Population Size ◽  
Dna Sequence ◽  
Phylogenetic Relationships ◽  
Finite Population ◽  
Theoretical Study ◽  
Deleterious Mutation ◽  
Sequence Evolution ◽  
Infinite Population ◽  
Neutral Mutation ◽  
Dna Sequence Evolution

SummaryDNA sequencing and restriction mapping provide us with information on DNA sequence evolution within populations, from which the phylogenetic relationships among the sequences can be inferred. Mutations such as base substitutions, deletions, insertions and transposable element insertions can be identified in each sequence. Theoretical study of this type of sequence evolution has been initiated recently. In this paper, population genetical models for sequence evolution under multiple types of mutation are developed. Models of infinite population size with neutral mutation, infinite population size with deleterious mutation and finite population size with neutral mutation are considered.

Linkage disequilibrium between neutral genes in finite populations

1974 ◽  
Vol 6 (1) ◽  
pp. 13-15 ◽  
Author(s):  
William G. Hill
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Linkage Disequilibrium ◽  
Finite Populations ◽  
Gene Frequencies ◽  
Infinite Population ◽  
Asymptotic Values

There is now a large literature on linkage disequilibrium between pairs of loci, both for selection in infinite populations and for neutral genes in finite populations, but there have been few studies with more loci. Bennett (1954) showed how the frequencies of chromosomes with any number of neutral genes would change in an infinite population, and the author (unpublished) has extended Bennett's results to find expected changes in chromosome frequencies with up to six loci in finite populations. For two linked neutral genes in finite populations the expected disequilibrium is zero, but the variance of the disequilibrium or the correlation of gene frequencies in segregating populations has been found. This has been done by Monte Carlo simulation (Hill and Robertson (1968)), but an approximation can be obtained by diffusion methods (Ohta and Kimura (1969)) and the asymptotic values using inbreeding theory (Sved (1971)). In this note we discuss the case of disequilibrium between three neutral loci and show how it relates to that between two loci.

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