STATISTICAL PROPERTIES OF THE NUMBER OF RECOMBINATION EVENTS IN THE HISTORY OF A SAMPLE OF DNA SEQUENCES

ABSTRACT Some statistical properties of samples of DNA sequences are studied under an infinite-site neutral model with recombination. The two quantities of interest are R, the number of recombination events in the history of a sample of sequences, and RM, the number of recombination events that can be parsimoniously inferred from a sample of sequences. Formulas are derived for the mean and variance of R. In contrast to R, RM can be determined from the sample. Since no formulas are known for the mean and variance of RM, they are estimated with Monte Carlo simulations. It is found that RM is often much less than R, therefore, the number of recombination events may be greatly under-estimated in a parsimonious reconstruction of the history of a sample. The statistic RM can be used to estimate the product of the recombination rate and the population size or, if the recombination rate is known, to estimate the population size. To illustrate this, DNA sequences from the Adh region of Drosophila melanogaster are used to estimate the effective population size of this species.

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Effective population size: the effects of sex, genotype, and density on the mean and variance of offspring numbers in the flour beetle, Tribolium castaneum

Genetics Research ◽

10.1017/s0016672300019613 ◽

1980 ◽

Vol 36 (1) ◽

pp. 1-10 ◽

Cited By ~ 28

Author(s):

Michael J. Wade

Keyword(s):

Population Size ◽

Effective Population Size ◽

Tribolium Castaneum ◽

Black Body ◽

Body Colour ◽

Effective Population ◽

Flour Beetle ◽

Colour Mutant ◽

Mean And Variance ◽

The Mean

SUMMARYIn this paper I present the results of an experimental study of the effects of genotype and density on the mean and variance of offspring numbers in both sexes of the flour beetle, Tribolium castaneum. From the observed variance in offspring numbers the effective population size at several different densities is estimated using the methods of Crow & Morton (1955).I found that both the mean and variance of offspring numbers varied with genotype and density. In general, males were more variable in offspring numbers than females and this variability increased with density. Individuals homozygous for the black body colour mutant, b/b, were less variable in offspring numbers than + / + individuals, but the latter produced more offspring at most densities. As density increased, + / + individuals became more variable in offspring numbers whereas b/b individuals were less sensitive in this regard. These findings are discussed in relation to the ecology of selection at the black and closely linked loci.

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Models of long-term artificial selection in finite population with recurrent mutation

Genetics Research ◽

10.1017/s001667230002485x ◽

1986 ◽

Vol 48 (2) ◽

pp. 125-131 ◽

Cited By ~ 27

Author(s):

William G. Hill ◽

Jonathan Rasbash

Keyword(s):

Population Size ◽

First Generation ◽

Finite Population ◽

Effective Population ◽

Term Selection ◽

Cumulative Response ◽

Mean And Variance ◽

The Mean ◽

Selection For

SummaryThe effects of mutation on mean and variance of response to selection for quantitative traits are investigated. The mutants are assumed to be unlinked, to be additive, and to have their effects symmetrically distributed about zero, with absolute values of effects having a gamma distribution. It is shown that the ratio of expected cumulative response to generation t from mutants, , and expected response over one generation from one generation of mutants, , is a function of t/N, where t is generations and N is effective population size. Similarly, , is a function of t/N, where is the increment in genetic variance from one generation of mutants. The mean and standard deviation of response from mutations relative to that from initial variation in the population, in the first generation, are functions of . Evaluation of these formulae for a range of parameters quantifies the important role that population size can play in response to long-term selection.

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A Coalescent Estimator of the Population Recombination Rate

Genetics ◽

10.1093/genetics/145.3.833 ◽

1997 ◽

Vol 145 (3) ◽

pp. 833-846 ◽

Cited By ~ 6

Author(s):

Jody Hey ◽

John Wakeley

Keyword(s):

Population Size ◽

Effective Population Size ◽

Mutation Rate ◽

Dna Sequences ◽

Recombination Rate ◽

Population Sample ◽

Population Level ◽

Effective Population ◽

Genome Level ◽

Population Recombination

Population genetic models often use a population recombination parameter 4Nc, where N is the effective population size and c is the recombination rate per generation. In many ways 4Nc is comparable to 4Nu, the population mutation rate. Both combine genome level and population level processes, and together they describe the rate of production of genetic variation in a population. However, 4Nc is more difficult to estimate. For a population sample of DNA sequences, historical recombination can only be detected if polymorphisms exist, and even then most recombination events are not detectable. This paper describes an estimator of 4Nc, hereafter designated γ (gamma), that was developed using a coalescent model for a sample of four DNA sequences with recombination. The reliability of γ was assessed using multiple coalescent simulations. In general γ has low to moderate bias, and the reliability of γ is comparable, though less, than that for a widely used estimator of 4Nu. If there exists an independent estimate of the recombination rate (per generation, per base pair), γ can be used to estimate the effective population size or the neutral mutation rate.

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DNA Sequence Variation at the Period Locus Reveals the History of Species and Speciation Events in the Drosophila virilis Group

Genetics ◽

10.1093/genetics/144.3.1015 ◽

1996 ◽

Vol 144 (3) ◽

pp. 1015-1025 ◽

Cited By ~ 1

Author(s):

Holly Hilton ◽

Jody Hey

Keyword(s):

Population Size ◽

Dna Sequences ◽

Sequence Variation ◽

Drosophila Virilis ◽

Geographic Pattern ◽

Effective Population ◽

Dna Sequence Variation ◽

Virilis Group ◽

History Of ◽

Drosophila Virilis Group

Abstract The virilis phylad of the Drosophila virilis group consists of five closely related taxa: D. virilis, D. lummei, D. novamexicana, D. americana americana and D. americana texana. DNA sequences from a 2.1-kb pair portion of the period locus were generated in four to eight individuals from each of the five taxa. We found evidence of recombination and high levels of variation within species. We found no evidence of recent natural selection. Surprisingly there was no evidence of divergence between D. a. americana and D. a. texana, and they collectively appear to have had a large historical effective population size. The ranges of these two taxa overlap in a large hybrid zone that has been delineated in the eastern U.S. on the basis of the geographic pattern of a chromosomal fusion. Also surprisingly, D. novamexicana appears to consist of two distinct groups each with low population size and no gene flow between them.

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A phylogenetic estimator of effective population size or mutation rate.

Genetics ◽

10.1093/genetics/136.2.685 ◽

1994 ◽

Vol 136 (2) ◽

pp. 685-692 ◽

Cited By ~ 1

Author(s):

Y X Fu

Keyword(s):

Population Size ◽

Effective Population Size ◽

Mutation Rate ◽

Dna Sequences ◽

High Efficiency ◽

Minimum Variance ◽

Population Subdivision ◽

Effective Population ◽

Fisher Model ◽

Mitochondrial Sequences

Abstract A new estimator of the essential parameter theta = 4Ne mu from DNA polymorphism data is developed under the neutral Wright-Fisher model without recombination and population subdivision, where Ne is the effective population size and mu is the mutation rate per locus per generation. The new estimator has a variance only slightly larger than the minimum variance of all possible unbiased estimators of the parameter and is substantially smaller than that of any existing estimator. The high efficiency of the new estimator is achieved by making full use of phylogenetic information in a sample of DNA sequences from a population. An example of estimating theta by the new method is presented using the mitochondrial sequences from an American Indian population.

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The Ancestry of a Sample of Sequences Subject to Recombination

Genetics ◽

10.1093/genetics/151.3.1217 ◽

1999 ◽

Vol 151 (3) ◽

pp. 1217-1228 ◽

Cited By ~ 1

Author(s):

Carsten Wiuf ◽

Jotun Hein

Keyword(s):

Genetic Distance ◽

Population Size ◽

Upper Bound ◽

Recombination Rate ◽

Common Ancestor ◽

Recent Common Ancestor ◽

Sequence Length ◽

Most Recent Common Ancestor ◽

The Mean ◽

Mean Time

Abstract In this article we discuss the ancestry of sequences sampled from the coalescent with recombination with constant population size 2N. We have studied a number of variables based on simulations of sample histories, and some analytical results are derived. Consider the leftmost nucleotide in the sequences. We show that the number of nucleotides sharing a most recent common ancestor (MRCA) with the leftmost nucleotide is ≈log(1 + 4N Lr)/4Nr when two sequences are compared, where L denotes sequence length in nucleotides, and r the recombination rate between any two neighboring nucleotides per generation. For larger samples, the number of nucleotides sharing MRCA with the leftmost nucleotide decreases and becomes almost independent of 4N Lr. Further, we show that a segment of the sequences sharing a MRCA consists in mean of 3/8Nr nucleotides, when two sequences are compared, and that this decreases toward 1/4Nr nucleotides when the whole population is sampled. A measure of the correlation between the genealogies of two nucleotides on two sequences is introduced. We show analytically that even when the nucleotides are separated by a large genetic distance, but share MRCA, the genealogies will show only little correlation. This is surprising, because the time until the two nucleotides shared MRCA is reciprocal to the genetic distance. Using simulations, the mean time until all positions in the sample have found a MRCA increases logarithmically with increasing sequence length and is considerably lower than a theoretically predicted upper bound. On the basis of simulations, it turns out that important properties of the coalescent with recombinations of the whole population are reflected in the properties of a sample of low size.

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The history of genetic diversity and effective population size of an isolated Microtus oeconomus population on Kis Balaton

Mammalian Biology ◽

10.1007/s42991-021-00199-y ◽

2021 ◽

Author(s):

Veronika Sládkovičová ◽

Dávid Žiak ◽

Peter Miklós ◽

András Gubányi ◽

Győző Horváth

Keyword(s):

Genetic Diversity ◽

Population Size ◽

Effective Population Size ◽

Effective Population ◽

Microtus Oeconomus ◽

History Of

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GENETIC VARIABILITY MAINTAINED BY MUTATION AND OVERDOMINANT SELECTION IN FINITE POPULATIONS

Genetics ◽

10.1093/genetics/98.2.441 ◽

1981 ◽

Vol 98 (2) ◽

pp. 441-459 ◽

Cited By ~ 2

Author(s):

Takeo Maruyama ◽

Masatoshi Nei

Keyword(s):

Mutation Rate ◽

Allozyme Polymorphism ◽

Random Genetic Drift ◽

Effective Population ◽

Mathematical Properties ◽

Overdominant Selection ◽

Mean And Variance ◽

The Mean ◽

Neutral Mutations ◽

The Relationship

ABSTRACT Mathematical properties of the overdominance model with mutation and random genetic drift are studied by using the method of stochastic differential equations (Itô and McKean 1974). It is shown that overdominant selection is very powerful in increasing the mean heterozygosity as compared with neutral mutations, and if 2Ns (N = effective population size; s = selective disadvantage for homozygotes) is larger than 10, a very low mutation rate is sufficient to explain the observed level of allozyme polymorphism. The distribution of heterozygosity for overdominant genes is considerably different from that of neutral mutations, and if the ratio of selection coefficient (s) to mutation rate (ν) is large and the mean heterozygosity (h) is lower than 0.2, single-locus heterozygosity is either approximately 0 or 0.5. If h increases further, however, heterozygosity shows a multiple-peak distribution. Reflecting this type of distribution, the relationship between the mean and variance of heterozygosity is considerably different from that for neutral genes. When s/v is large, the proportion of polymorphic loci increases approximately linearly with mean heterozygosity. The distribution of allele frequencies is also drastically different from that of neutral genes, and generally shows a peak at the intermediate gene frequency. Implications of these results on the maintenance of allozyme polymorphism are discussed.

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IDENTITY COEFFICIENTS IN FINITE POPULATIONS. I. EVOLUTION OF IDENTITY COEFFICIENTS IN A RANDOM MATING DIPLOID DIOECIOUS POPULATION

Genetics ◽

10.1093/genetics/86.3.697 ◽

1977 ◽

Vol 86 (3) ◽

pp. 697-713

Author(s):

C Chevalet ◽

M Gillois ◽

R F Nassar

Keyword(s):

Genetic Variability ◽

Population Size ◽

Effective Population Size ◽

Random Mating ◽

Matrix Multiplication ◽

Inbred Lines ◽

Inbreeding Coefficient ◽

Effective Population ◽

The Mean ◽

Over Time

ABSTRACT Properties of identity relation between genes are discussed, and a derivation of recurrent equations of identity coefficients in a random mating, diploid dioecious population is presented. Computations are run by repeated matrix multiplication. Results show that for effective population size (Ne) larger than 16 and no mutation, a given identity coefficient at any time t can be expressed approximately as a function of (1—f), (1—f)3 and (1—f)6, where f is the mean inbreeding coefficient at time t. Tables are presented, for small Ne values and extreme sex ratios, showing the pattern of change in the identity coefficients over time. The pattern of evolution of identity coefficients is also presented and discussed with respect to N eu, where u is the mutation rate. Applications of these results to the evolution of genetic variability within and between inbred lines are discussed.

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