scholarly journals Inferring past effective population size from distributions of coalescent-times

2015 ◽  
Author(s):  
Lucie Gattepaille ◽  
Mattias Jakobsson
Keyword(s):  
Sample Size ◽  
Population Size ◽  
Effective Population Size ◽  
Random Mating ◽  
Real Data ◽  
Effective Population ◽  
Modest Improvement ◽  
Inference Algorithms ◽  
Tree Inference ◽  
Over Time

Inferring and understanding changes in effective population size over time is a major challenge for population genetics. Here we investigate some theoretical properties of random mating populations with varying size over time. In particular, we present an exact method to compute the population size as a function of time using the distributions of coalescent-times of samples of any size. This result reduces the problem of population size inference to a problem of estimating coalescent-time distributions. Using tree inference algorithms and genetic data, we can investigate the effects of a range of conditions associated with real data, for instance finite number of loci, sample size, mutation rate and presence of cryptic recombination. We show that our method requires at least a modest number of loci (10,000 or more) and that increasing the sample size from 2 to 10 greatly improves the inference whereas further increase in sample size only results in a modest improvement, even under as scenario of exponential growth. We also show that small amounts of recombination can lead to biased population size reconstruction when unaccounted for. The approach can handle large sample sizes and the computations are fast. We apply our method on human genomes from 4 populations and reconstruct population size profiles that are coherent with previous knowledge, including the Out-of-Africa bottleneck. Additionally, a potential difference in population size between African and non-African populations as early as 400 thousand years ago is uncovered.

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

Genetics ◽  
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.

scholarly journals Estimating effective population size from samples of sequences: a bootstrap Monte Carlo integration method

1992 ◽  
Vol 60 (3) ◽  
pp. 209-220 ◽  
Author(s):  
Joseph Felsenstein
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Population Size ◽  
Effective Population Size ◽  
Random Mating ◽  
Computational Effort ◽  
Monte Carlo Integration ◽  
Bootstrap Sampling ◽  
Effective Population ◽  
Full Data

SummaryWe would like to use maximum likelihood to estimate parameters such as the effective population size Ne, or, if we do not know mutation rates, the product 4Neμof mutation rate per site and effective population size. To compute the likelihood for a sample of unrecombined nucleotide sequences taken from a random-mating population it is necessary to sum over all genealogies that could have led to the sequences, computing for each one the probability that it would have yielded the sequences, and weighting each one by its prior probability. The genealogies vary in tree topology and in branch lengths. Although the likelihood and the prior are straightforward to compute, the summation over all genealogies seems at first sight hopelessly difficult. This paper reports that it is possible to carry out a Monte Carlo integration to evaluate the likelihoods pproximately. The method uses bootstrap sampling of sites to create data sets for each of which a maximum likelihood tree is estimated. The resulting trees are assumed to be sampled from a distribution whose height is proportional to the likelihood surface for the full data. That it will be so is dependent on a theorem which is not proven, but seems likely to be true if the sequences are not short. One can use the resulting estimated likelihood curve to make a maximum likelihood estimate of the parameter of interest, Ne or of 4Neμ. The method requires at least 100 times the computational effort required for estimation of a phylogeny by maximum likelihood, but is practical on today's work stations. The method does not at present have any way of dealing with recombination.

scholarly journals The effect of sample size on estimates of genetic differentiation and effective population size for Schistosoma mansoni populations

2018 ◽  
Vol 48 (14) ◽  
pp. 1149-1154 ◽  
Author(s):  
Lúcio M. Barbosa ◽  
Bruna C. Barros ◽  
Moreno de Souza Rodrigues ◽  
Luciano K. Silva ◽  
Mitermayer G. Reis ◽  
...  
Keyword(s):  
Genetic Differentiation ◽  
Schistosoma Mansoni ◽  
Sample Size ◽  
Population Size ◽  
Effective Population Size ◽  
Effective Population

scholarly journals Nearly unbiased estimator of contemporary effective mother size using within-cohort maternal sibling pairs incorporating parental and nonparental reproductive variations

Heredity ◽  
2019 ◽  
Vol 124 (2) ◽  
pp. 299-312 ◽  
Author(s):  
Tetsuya Akita
Keyword(s):  
Sample Size ◽  
Population Size ◽  
Effective Population Size ◽  
Unbiased Estimator ◽  
Small Sample Size ◽  
Small Sample ◽  
Sibling Relationship ◽  
Effective Population ◽  
Sibling Pairs ◽  
Half Sibling

Abstract In this study, we developed a nearly unbiased estimator of contemporary effective mother size in a population, which is based on a known maternal half-sibling relationship found within the same cohort. Our method allows for variance of the average number of offspring per mother (i.e., parental variation, such as age-specific fecundity) and variance of the number of offspring among mothers with identical reproductive potential (i.e., nonparental variation, such as family-correlated survivorship). We also developed estimators of the variance and coefficient of variation of contemporary effective mother size and qualitatively evaluated the performance of the estimators by running an individual-based model. Our results provide guidance for (i) a sample size to ensure the required accuracy and precision when the order of effective mother size is available and (ii) a degree of uncertainty regarding the estimated effective mother size when information about the size is unavailable. To the best of our knowledge, this is the first report to demonstrate the derivation of a nearly unbiased estimator of effective population size; however, its current application is limited to effective mother size and situations, in which the sample size is not particularly small and maternal half-sibling relationships can be detected without error. The results of this study demonstrate the usefulness of a sibship assignment method for estimating effective population size; in addition, they have the potential to greatly widen the scope of genetic monitoring, especially in the situation of small sample size.

scholarly journals Breeding objectives, selection criteria and breeding system of indigenous goat types in bale zone, oromia, Ethiopia

2016 ◽  
Vol 5 (2) ◽  
pp. 7-15
Author(s):  
Belete Asefa ◽  
Kefelegn Kebede ◽  
Kefena Effa
Keyword(s):  
Population Size ◽  
Effective Population Size ◽  
Breeding System ◽  
Selection Criteria ◽  
Random Mating ◽  
Sampling Technique ◽  
Simple Random Sampling ◽  
Effective Population ◽  
Breeding Objectives ◽  
Bale Zone

The study was undertaken in bale zone to assess farmer’s selective breeding objectives, trait preferences, selection criteria and breeding system October 2012 to November 2013. A purposive and multistage sampling technique was applied for selection of 3 district and 9 kebeles. Then 360 households were selected by using simple random sampling techniques after the list of pastoralist having goats was identified. Statistical analysis system version 9.1 was used for analysis of data. Indices, effective population size and rate of inbreeding were calculated on average each respondent holds about 14 goats. Milk production is the main reason of goat keeping in the study area. Appearance is the first rank as selection criteria for male and female in all studies area. About 47.8% of the respondents have their own buck. The main use of breeding buck in the study area was for mating purpose (76.2%). Mean estimate of effective population size and mean rate of inbreeding was 2.43 and 0.21, respectively when a household flock is herded alone and under random mating. Therefore, any breed improvement strategies that are intended to be implemented in the study area and else- where should consider the traditional breeding practices and breeding objectives of the community.Int. J. Agril. Res. Innov. & Tech. 5 (2): 7-15, December, 2015

scholarly journals Effective population size of current human population

2011 ◽  
Vol 93 (2) ◽  
pp. 105-114 ◽  
Author(s):  
LEEYOUNG PARK
Keyword(s):  
Population Size ◽  
Effective Population Size ◽  
Human Population ◽  
Random Mating ◽  
Phase Iii ◽  
Human Populations ◽  
Effective Population ◽  
Hapmap Phase ◽  
Hardy Weinberg Equilibrium ◽  
Genetic Drifts

SummaryIn order to estimate the effective population size (Ne) of the current human population, two new approaches, which were derived from previous methods, were used in this study. One is based on the deviation from linkage equilibrium (LE) between completely unlinked loci in different chromosomes and another is based on the deviation from the Hardy–Weinberg Equilibrium (HWE). When random mating in a population is assumed, genetic drifts in population naturally induce linkage disequilibrium (LD) between chromosomes and the deviation from HWE. The latter provides information on the Ne of the current population, and the former provides the same when the Ne is constant. If Ne fluctuates, recent Ne changes are reflected in the estimates based on LE, and the comparison between two estimates can provide information regarding recent changes of Ne. Using HapMap Phase III data, the estimates were varied from 622 to 10 437, depending on populations and estimates. The Ne appeared to fluctuate as it provided different estimates for each of the two methods. These Ne estimates were found to agree approximately with the overall increment observed in recent human populations.

scholarly journals Coalescent models at small effective population sizes and population declines are positively misleading

2019 ◽  
Author(s):  
M. Elise Lauterbur
Keyword(s):  
Genetic Diversity ◽  
Sample Size ◽  
Population Size ◽  
Effective Population Size ◽  
Genetic Relationships ◽  
Population Decline ◽  
Population Declines ◽  
Effective Population ◽  
Analytical Approximations ◽  
Population Sizes

AbstractPopulation genetics employs two major models for conceptualizing genetic relationships among individuals – outcome-driven (coalescent) and process-driven (forward). These models are complementary, but the basic Kingman coalescent and its extensions make fundamental assumptions to allow analytical approximations: a constant effective population size much larger than the sample size. These make the probability of multiple coalescent events per generation negligible. Although these assumptions are often violated in species of conservation concern, conservation genetics often uses coalescent models of effective population sizes and trajectories in endangered species. Despite this, the effect of very small effective population sizes, and their interaction with bottlenecks and sample sizes, on such analyses of genetic diversity remains unexplored. Here, I use simulations to analyze the influence of small effective population size, population decline, and their relationship with sample size, on coalescent-based estimates of genetic diversity. Compared to forward process-based estimates, coalescent models significantly overestimate genetic diversity in oversampled populations with very small effective sizes. When sampled soon after a decline, coalescent models overestimate genetic diversity in small populations regardless of sample size. Such overestimates artificially inflate estimates of both bottleneck and population split times. For conservation applications with small effective population sizes, forward simulations that do not make population size assumptions are computationally tractable and should be considered instead of coalescent-based models. These findings underscore the importance of the theoretical basis of analytical techniques as applied to conservation questions.

scholarly journals Estimating effective population size using RADseq: Effects of SNP selection and sample size

2020 ◽  
Vol 10 (4) ◽  
pp. 1929-1937 ◽  
Author(s):  
Florianne Marandel ◽  
Grégory Charrier ◽  
Jean‐Baptiste Lamy ◽  
Sabrina Le Cam ◽  
Pascal Lorance ◽  
...  
Keyword(s):  
Sample Size ◽  
Population Size ◽  
Effective Population Size ◽  
Effective Population

scholarly journals An empirical examination of sample size effects on population demographic estimates in birds using single nucleotide polymorphism (SNP) data

PeerJ ◽  
2020 ◽  
Vol 8 ◽  
pp. e9939
Author(s):  
Jessica F. McLaughlin ◽  
Kevin Winker
Keyword(s):  
Single Nucleotide Polymorphism ◽  
Sample Size ◽  
Population Size ◽  
Effective Population Size ◽  
Population Level ◽  
Sample Sizes ◽  
Nucleotide Polymorphism ◽  
Effective Population ◽  
Single Nucleotide ◽  
Population Demographic

Sample size is a critical aspect of study design in population genomics research, yet few empirical studies have examined the impacts of small sample sizes. We used datasets from eight diverging bird lineages to make pairwise comparisons at different levels of taxonomic divergence (populations, subspecies, and species). Our data are from loci linked to ultraconserved elements and our analyses used one single nucleotide polymorphism per locus. All individuals were genotyped at all loci, effectively doubling sample size for coalescent analyses. We estimated population demographic parameters (effective population size, migration rate, and time since divergence) in a coalescent framework using Diffusion Approximation for Demographic Inference, an allele frequency spectrum method. Using divergence-with-gene-flow models optimized with full datasets, we subsampled at sequentially smaller sample sizes from full datasets of 6–8 diploid individuals per population (with both alleles called) down to 1:1, and then we compared estimates and their changes in accuracy. Accuracy was strongly affected by sample size, with considerable differences among estimated parameters and among lineages. Effective population size parameters (ν) tended to be underestimated at low sample sizes (fewer than three diploid individuals per population, or 6:6 haplotypes in coalescent terms). Migration (m) was fairly consistently estimated until <2 individuals per population, and no consistent trend of over-or underestimation was found in either time since divergence (T) or theta (Θ = 4Nrefμ). Lineages that were taxonomically recognized above the population level (subspecies and species pairs; that is, deeper divergences) tended to have lower variation in scaled root mean square error of parameter estimation at smaller sample sizes than population-level divergences, and many parameters were estimated accurately down to three diploid individuals per population. Shallower divergence levels (i.e., populations) often required at least five individuals per population for reliable demographic inferences using this approach. Although divergence levels might be unknown at the outset of study design, our results provide a framework for planning appropriate sampling and for interpreting results if smaller sample sizes must be used.

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