scholarly journals The Validity of the Coalescent Approximation for Large Samples

2017 ◽  
Author(s):  
Andrew Melfi ◽  
Divakar Viswanath
Keyword(s):  
Sample Size ◽  
Population Size ◽  
Exponential Growth ◽  
Asymptotic Theory ◽  
Triple Collision ◽  
Demographic Models ◽  
Large Samples ◽  
Population Sizes ◽  
Sample Frequency ◽  
Haploid Population

AbstractThe Kingman coalescent, widely used in genetics, is known to be a good approximation when the sample size is small relative to the population size. In this article, we investigate how large the sample size can get without violating the coalescent approximation. If the haploid population size is 2N, we prove that for samples of size N1/3−ϵ, ϵ > 0, coalescence under the Wright-Fisher (WF) model converges in probability to the Kingman coalescent in the limit of large N. For samples of size N2/5−ϵ or smaller, the WF coalescent converges to a mixture of the Kingman coalescent and what we call the mod-2 coalescent. For samples of size N1/2 or larger, triple collisions in the WF genealogy of the sample become important. The sample size for which the probability of conformance with the Kingman coalescent is 95% is found to be 1.47 × N0.31 for N ∈ [103, 105], showing the pertinence of the asymptotic theory. The probability of no triple collisions is found to be 95% for sample sizes equal to 0.92 × N0.49, which too is in accord with the asymptotic theory.Varying population sizes are handled using algorithms that calculate the probability of WF coalescence agreeing with the Kingman model or taking place without triple collisions. For a sample of size 100, the probabilities of coalescence according to the Kingman model are 2%, 0%, 1%, and 0% in four models of human population with constant N, constant N except for two bottlenecks, recent exponential growth, and increasing recent exponential growth, respectively. For the same four demographic models and the same sample size, the probabilities of coalescence with no triple collision are 92%, 73%, 88%, and 87%, respectively. Visualizations of the algorithm show that even distant bottlenecks can impede agreement between the coalescent and the WF model.Finally, we prove that the WF sample frequency spectrum for samples of size N1/3−ϵ or smaller converges to the classical answer for the coalescent.

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 Transition densities and sample frequency spectra of diffusion processes with selection and variable population size

2015 ◽  
Author(s):  
Daniel Zivkovic ◽  
Matthias Steinrücken ◽  
Yun S. Song ◽  
Wolfgang Stephan
Keyword(s):  
Population Size ◽  
Effective Population Size ◽  
Diffusion Processes ◽  
Transition Density ◽  
Effective Population ◽  
Frequency Spectra ◽  
Transition Densities ◽  
Population Sizes ◽  
Sample Frequency ◽  
The Impact

Advances in empirical population genetics have made apparent the need for models that simultaneously account for selection and demography. To address this need, we here study the Wright-Fisher diffusion under selection and variable effective population size. In the case of genic selection and piecewise-constant effective population sizes, we obtain the transition density function by extending a recently developed method for computing an accurate spectral representation for a constant population size. Utilizing this extension, we show how to compute the sample frequency spectrum (SFS) in the presence of genic selection and an arbitrary number of instantaneous changes in the effective population size. We also develop an alternate, efficient algorithm for computing the SFS using a method of moments. We apply these methods to answer the following questions: If neutrality is incorrectly assumed when there is selection, what effects does it have on demographic parameter estimation? Can the impact of negative selection be observed in populations that undergo strong exponential growth?

scholarly journals Gene genealogy in three related populations: consistency probability between gene and population trees.

Genetics ◽  
1989 ◽  
Vol 122 (4) ◽  
pp. 957-966 ◽  
Author(s):  
N Takahata
Keyword(s):  
Special Reference ◽  
Sample Size ◽  
Common Ancestor ◽  
Gene Tree ◽  
Divergence Time ◽  
Gene Genealogy ◽  
Large Samples ◽  
Genealogical Relationship ◽  
Population Sizes ◽  
Different Populations

Abstract A genealogical relationship among genes at a locus (gene tree) sampled from three related populations was examined with special reference to population relatedness (population tree). A phylogenetically informative event in a gene tree constructed from nucleotide differences consists of interspecific coalescences of genes in each of which two genes sampled from different populations are descended from a common ancestor. The consistency probability between gene and population trees in which they are topologically identical was formulated in terms of interspecific coalescences. It was found that the consistency probability thus derived substantially increases as the sample size of genes increases, unless the divergence time of populations is very long compared to population sizes. Hence, there are cases where large samples at a locus are very useful in inferring a population tree.

scholarly journals The Wright-Fisher Site Frequency Spectrum as a Perturbation of the Coalescent’s

2018 ◽  
Author(s):  
Andrew Melfi ◽  
Divakar Viswanath
Keyword(s):  
Sample Size ◽  
Population Size ◽  
Total Variation ◽  
Frequency Spectrum ◽  
Separate Analysis ◽  
Number Of Children ◽  
Large Samples ◽  
Variation Distance ◽  
Site Frequency Spectrum ◽  
The Difference

AbstractThe first terms of the Wright-Fisher (WF) site frequency spectrum that follow the coalescent approximation are determined precisely, with a view to understanding the accuracy of the coalescent approximation for large samples. The perturbing terms show that the probability of a single mutant in the sample (singleton probability) is elevated in WF but the rest of the frequency spectrum is lowered. A part of the perturbation can be attributed to a mismatch in rates of merger between WF and the coalescent. The rest of it can be attributed to the difference in the way WF and the coalescent partition children between parents. In particular, the number of children of a parent is approximately Poisson under WF and approximately geometric under the coalescent. Whereas the mismatch in rates raises the probability of singletons under WF, its offspring distribution being approximately Poisson lowers it. The two effects are of opposite sense everywhere except at the tail of the frequency spectrum. The WF frequency spectrum begins to depart from that of the coalescent only for sample sizes that are comparable to the population size. These conclusions are confirmed by a separate analysis that assumes the sample size n to be equal to the population size N. Partly thanks to the canceling effects, the total variation distance of WF minus coalescent is 0.12/ log N for a population sized sample with n = N, which is only 1% for N = 2 × 104.

scholarly journals Effect of Pheromone Blend Components, Sex Ratio, and Population Size on the Mating of Cadra cautella (Lepidoptera: Pyralidae)

2020 ◽  
Vol 20 (6) ◽  
Author(s):  
Abeysinghe Mudiyanselage Prabodha Sammani ◽  
Dissanayaka Mudiyanselage Saman Kumara Dissanayaka ◽  
Leanage Kanaka Wolly Wijayaratne ◽  
William Robert Morrison
Keyword(s):  
Sex Ratio ◽  
Population Size ◽  
Management Practices ◽  
Mating Disruption ◽  
Current Knowledge ◽  
Mating Status ◽  
Cadra Cautella ◽  
Synthetic Chemicals ◽  
Population Sizes ◽  
Lepidoptera Pyralidae

Abstract The almond moth Cadra cautella (Walker), a key pest of storage facilities, is difficult to manage using synthetic chemicals. Pheromone-based management methods remain a high priority due to advantages over conventional management practices, which typically use insecticides. Cadra cautella females release a blend of pheromone including (Z, E)-9,12-tetradecadienyl acetate (ZETA) and (Z)-9-tetradecadien-1-yl acetate (ZTA). The effect of these components on mating of C. cautella and how response varies with the population density and sex ratio remain unknown. In this study, the mating status of C. cautella was studied inside mating cages under different ratios of ZETA and ZTA diluted in hexane and at different population sizes either with equal or unequal sex ratio. The lowest percentage of mated females (highest mating disruption [MD] effects), corresponding to roughly 12.5%, was produced by a 5:1 and 3.3:1 ratio of ZETA:ZTA. Populations with equal sex ratio showed the lowest percentage of mated females, at 20% and 12.5% under lower and higher density, respectively. The next lowest percentage of mated females was produced when the sex ratio was set to 1: 2 and 2:1 male:female, with just 25% and 22.5% of moths mated, respectively. This study shows that mating status of C. cautella is influenced by ZETA:ZTA ratio, sex ratio, and population size. This current knowledge would have useful implications for mating disruption programs.

scholarly journals EFFECTS OF POPULATION SIZE AND SELECTION INTENSITY ON SHORT-TERM RESPONSE TO SELECTION FOR POSTWEANING GAIN IN MICE

Genetics ◽  
1973 ◽  
Vol 73 (3) ◽  
pp. 513-530
Author(s):  
J P Hanrahan ◽  
E J Eisen ◽  
J E Legates
Keyword(s):  
Population Size ◽  
Selection Response ◽  
Selection Intensity ◽  
Realized Heritability ◽  
Family Selection ◽  
Effective Population ◽  
Population Sizes ◽  
Selection For ◽  
Selection Intensities ◽  
Term Response

ABSTRACT The effects of population size and selection intensity on the mean response was examined after 14 generations of within full-sib family selection for postweaning gain in mice. Population sizes of 1, 2, 4, 8 and 16 pair matings were each evaluated at selection intensities of 100% (control), 50% and 25% in a replicated experiment. Selection response per generation increased as selection intensity increased. Selection response and realized heritability tended to increase with increasing population size. Replicate variability in realized heritability was large at population sizes of 1, 2 and 4 pairs. Genetic drift was implicated as the primary factor causing the reduced response and lowered repeatability at the smaller population sizes. Lines with intended effective population sizes of 62 yielded larger selection responses per unit selection differential than lines with effective population sizes of 30 or less.

Estimation of Catchabilities and Population Sizes of Lobsters

1963 ◽  
Vol 20 (1) ◽  
pp. 59-88 ◽  
Author(s):  
J. E. Paloheimo
Keyword(s):  
Environmental Factors ◽  
Population Size ◽  
Atlantic Coast ◽  
Temperature Data ◽  
New Method ◽  
Bottom Temperature ◽  
Population Size Estimates ◽  
Population Sizes ◽  
Estimate Population Size ◽  
Size Estimates

Techniques of estimating population size, level of fishing, and the degree of dependence of fishing success on environmental factors are examined on the basis of tagging, catch and effort data. A new method is developed to estimate population size from catch, effort, and temperature data when the catchability varies with temperature.The methods of estimation discussed are applied to data collected from a number of lobster fisheries on Canada's Atlantic coast. Analysis confirms a relationship between the catchability of lobsters and bottom temperature. Differences in this relationship are found between areas and between tagged and untagged lobsters within areas. It is suggested that these differences are attributable to the differences in densities as well as to aggregations of lobsters and fishing. The effect of these aggregations on population size estimates is considered.Calculated average catchabilities at comparable temperatures are different for different areas. These differences are correlated with the numbers of trap hauls per day per square miles fished. It is suggested that the differences in the catchabilities might be due to interactions between units of gear not predicted by the customary relationship between catch and effort.

scholarly journals DO LANGUAGE CHANGE RATES DEPEND ON POPULATION SIZE?

2008 ◽  
Vol 11 (03) ◽  
pp. 357-369 ◽  
Author(s):  
SØREN WICHMANN ◽  
DIETRICH STAUFFER ◽  
CHRISTIAN SCHULZE ◽  
ERIC W. HOLMAN
Keyword(s):  
Population Size ◽  
Computer Simulations ◽  
Empirical Data ◽  
Language Change ◽  
Strong Dependence ◽  
Language Model ◽  
Population Sizes

An earlier study [24] concluded, based on computer simulations and some inferences from empirical data, that languages will change the more slowly the larger the population gets. We replicate this study using a more complete language model for simulations (the Schulze model combined with a Barabási–Albert network) and a richer empirical dataset [12]. Our simulations show either a negligible or a strong dependence of language change on population sizes, depending on the parameter settings; while empirical data, like some of the simulations, show a negligible dependence.

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 Polygenic local adaptation in metapopulations: a stochastic eco-evolutionary model

2020 ◽  
Author(s):  
Enikő Szép ◽  
Himani Sachdeva ◽  
Nick Barton
Keyword(s):  
Population Size ◽  
Local Adaptation ◽  
Genetic Drift ◽  
Diffusion Approximation ◽  
Joint Distribution ◽  
Evolutionary Model ◽  
Ecological Niches ◽  
Demographic Stochasticity ◽  
Linkage Disequilibria ◽  
Population Sizes

AbstractThis paper analyses the conditions for local adaptation in a metapopulation with infinitely many islands under a model of hard selection, where population size depends on local fitness. Each island belongs to one of two distinct ecological niches or habitats. Fitness is influenced by an additive trait which is under habitat-dependent directional selection. Our analysis is based on the diffusion approximation and accounts for both genetic drift and demographic stochasticity. By neglecting linkage disequilibria, it yields the joint distribution of allele frequencies and population size on each island. We find that under hard selection, the conditions for local adaptation in a rare habitat are more restrictive for more polygenic traits: even moderate migration load per locus at very many loci is sufficient for population sizes to decline. This further reduces the efficacy of selection at individual loci due to increased drift and because smaller populations are more prone to swamping due to migration, causing a positive feedback between increasing maladaptation and declining population sizes. Our analysis also highlights the importance of demographic stochasticity, which exacerbates the decline in numbers of maladapted populations, leading to population collapse in the rare habitat at significantly lower migration than predicted by deterministic arguments.

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