scholarly journals Using the variance of pairwise differences to estimate the recombination rate

1997 ◽  
Vol 69 (1) ◽  
pp. 45-48 ◽  
Author(s):  
JOHN WAKELEY
Keyword(s):  
Population Size ◽  
Standard Error ◽  
Recombination Rate ◽  
Population Model ◽  
Finite Population ◽  
Pairwise Differences ◽  
Theoretical Developments

A new estimator is proposed for the parameter C=4Nc, where N is the population size and c is the recombination rate in a finite population model without selection. The estimator is an improved version of Hudson's (1987) estimator, which takes advantage of some recent theoretical developments. The improvement is slight, but the smaller bias and standard error of the new estimator support its use. The variance of the average number of pairwise differences is also derived, and is important in the formulation of the new estimator.

scholarly journals The Ancestry of a Sample of Sequences Subject to Recombination

Genetics ◽  
1999 ◽  
Vol 151 (3) ◽  
pp. 1217-1228 ◽  
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.

scholarly journals A note on the diffusion approximation for the variance of the number of generations until fixation of a neutral mutant gene

1970 ◽  
Vol 15 (2) ◽  
pp. 251-255 ◽  
Author(s):  
P. Narain
Keyword(s):  
Population Size ◽  
General Expression ◽  
Diffusion Approximation ◽  
Finite Population ◽  
Mutant Gene ◽  
Matrix Methods ◽  
Neutral Gene

SUMMARYA general expression is derived for the variance of time to fixation of a neutral gene in a finite population using a diffusion approximation. The results are compared with exact values derived by matrix methods for a population size of 8.

POPULATION DYNAMICS OF SEX-DETERMINING ALLELES IN HONEY BEES AND SELF-INCOMPATIBILITY ALLELES IN PLANTS

Genetics ◽  
1979 ◽  
Vol 91 (3) ◽  
pp. 609-626 ◽  
Author(s):  
Shozo Yokoyama ◽  
Masatoshi Nei
Keyword(s):  
Population Dynamics ◽  
Population Size ◽  
Honey Bee ◽  
Honey Bees ◽  
Finite Population ◽  
Large Population ◽  
Allele Frequencies ◽  
Self Incompatibility ◽  
Overdominant Selection ◽  
Incompatibility Alleles

ABSTRACT Mathematical theories of the population dynamics of sex-determining alleles in honey bees are developed. It is shown that in an infinitely large population the equilibrium frequency of a sex allele is l/n, where n is the number of alleles in the population, and the asymptotic rate of approach to this equilibrium is 2/(3n) per generation. Formulae for the distribution of allele frequencies and the effective and actual numbers of alleles that can be maintained in a finite population are derived by taking into account the population size and mutation rate. It is shown that the allele frequencies in a finite population may deviate considerably from l/n. Using these results, available data on the number of sex alleles in honey bee populations are discussed. It is also shown that the number of self-incompatibility alleles in plants can be studied in a much simpler way by the method used in this paper. A brief discussion about general overdominant selection is presented.

scholarly journals Simplified large African carnivore density estimators from track indices

PeerJ ◽  
2016 ◽  
Vol 4 ◽  
pp. e2662 ◽  
Author(s):  
Christiaan W. Winterbach ◽  
Sam M. Ferreira ◽  
Paul J. Funston ◽  
Michael J. Somers
Keyword(s):  
Linear Regression ◽  
Confidence Interval ◽  
Population Size ◽  
Linear Model ◽  
Standard Error ◽  
Linear Models ◽  
Information Criteria ◽  
Large Carnivores ◽  
Simple Linear Regression ◽  
Akaike Information Criteria

BackgroundThe range, population size and trend of large carnivores are important parameters to assess their status globally and to plan conservation strategies. One can use linear models to assess population size and trends of large carnivores from track-based surveys on suitable substrates. The conventional approach of a linear model with intercept may not intercept at zero, but may fit the data better than linear model through the origin. We assess whether a linear regression through the origin is more appropriate than a linear regression with intercept to model large African carnivore densities and track indices.MethodsWe did simple linear regression with intercept analysis and simple linear regression through the origin and used the confidence interval for ß in the linear modely = αx + ß, Standard Error of Estimate, Mean Squares Residual and Akaike Information Criteria to evaluate the models.ResultsThe Lion on Clay and Low Density on Sand models with intercept were not significant (P > 0.05). The other four models with intercept and the six models thorough origin were all significant (P < 0.05). The models using linear regression with intercept all included zero in the confidence interval for ß and the null hypothesis that ß = 0 could not be rejected. All models showed that the linear model through the origin provided a better fit than the linear model with intercept, as indicated by the Standard Error of Estimate and Mean Square Residuals. Akaike Information Criteria showed that linear models through the origin were better and that none of the linear models with intercept had substantial support.DiscussionOur results showed that linear regression through the origin is justified over the more typical linear regression with intercept for all models we tested. A general model can be used to estimate large carnivore densities from track densities across species and study areas. The formulaobserved track density = 3.26 × carnivore densitycan be used to estimate densities of large African carnivores using track counts on sandy substrates in areas where carnivore densities are 0.27 carnivores/100 km2or higher. To improve the current models, we need independent data to validate the models and data to test for non-linear relationship between track indices and true density at low densities.

scholarly journals Two-Locus Likelihoods Under Variable Population Size and Fine-Scale Recombination Rate Estimation

Genetics ◽  
2016 ◽  
Vol 203 (3) ◽  
pp. 1381-1399 ◽  
Author(s):  
John A. Kamm ◽  
Jeffrey P. Spence ◽  
Jeffrey Chan ◽  
Yun S. Song
Keyword(s):  
Population Size ◽  
Recombination Rate ◽  
Fine Scale ◽  
Rate Estimation ◽  
Variable Population ◽  
Variable Population Size

DIFFUSION OF A POPULATION OF INTERACTING REPLICATORS IN SEQUENCE SPACE

2002 ◽  
Vol 05 (04) ◽  
pp. 457-461 ◽  
Author(s):  
BÄRBEL M. R. STADLER
Keyword(s):  
Simple Model ◽  
Population Size ◽  
Computer Simulations ◽  
Mutation Rate ◽  
Sequence Space ◽  
Finite Population ◽  
Fitness Landscape ◽  
Diffusion Constant ◽  
Sequence Length

We consider a simple model for catalyzed replication. Computer simulations show that a finite population moves in sequence space by diffusion analogous to the behavior of a quasispecies on a flat fitness landscape. The diffusion constant depends linearly on the per position mutation rate and the ratio of sequence length and population size.

The supersession of one rumour by another

1977 ◽  
Vol 14 (1) ◽  
pp. 127-134 ◽  
Author(s):  
G. K. Osei ◽  
J. W. Thompson
Keyword(s):  
Population Size ◽  
Finite Population ◽  
Closed Population ◽  
Asymptotic Case ◽  
Distribution Of The Maximum ◽  
Maximum Value

A model is considered for a situation in which one rumour suppresses another in a closed population. The distribution of the maximum value attained by the proportion spreading the weaker rumour is obtained in the asymptotic case, and this is compared with some actual distributions for finite population size. Closer approximations to the latter distributions are obtained.

scholarly journals Looking Forwards and Backwards in the Multi-Allelic Neutral Cannings Population Model

2010 ◽  
Vol 47 (03) ◽  
pp. 713-731 ◽  
Author(s):  
M. Möhle
Keyword(s):  
Markov Chain ◽  
Population Size ◽  
Side Effect ◽  
Population Model ◽  
Inversion Formula ◽  
Transition Matrix ◽  
Duality Relation ◽  
Moran Model ◽  
Fisher Model ◽  
Fixed Population

We look forwards and backwards in the multi-allelic neutral exchangeable Cannings model with fixed population size and nonoverlapping generations. The Markov chain X is studied which describes the allelic composition of the population forward in time. A duality relation (inversion formula) between the transition matrix of X and an appropriate backward matrix is discussed. The probabilities of the backward matrix are explicitly expressed in terms of the offspring distribution, complementing the work of Gladstien (1978). The results are applied to fundamental multi-allelic Cannings models, among them the Moran model, the Wright-Fisher model, the Kimura model, and the Karlin and McGregor model. As a side effect, number theoretical sieve formulae occur in these examples.

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