scholarly journals Coalescent theory for a Monoecious Random Mating Population with a Varying Size

2010 ◽  
Vol 47 (1) ◽  
pp. 41-57 ◽  
Author(s):  
Edward Pollak
Keyword(s):  
Markov Chain ◽  
Population Size ◽  
Effective Population Size ◽  
Random Sample ◽  
Random Mating ◽  
Coalescent Theory ◽  
Effective Population ◽  
Diploid Population ◽  
Mating Population ◽  
Population Sizes

Consider a monoecious diploid population with nonoverlapping generations, whose size varies with time according to an irreducible, aperiodic Markov chain with states x1N,…,xKN, where K ≪ N. It is assumed that all matings except for selfing are possible and equally probable. At time 0 a random sample of n ≪ N genes is taken. Given two successive population sizes xjN and xiN, the numbers of gametes that individual parents contribute to offspring can be shown to be exchangeable random variables distributed as Gij. Under minimal conditions on the first three moments of Gij for all i and j, a suitable effective population size Ne is derived. Then if time is recorded in a backward direction in units of 2Ne generations, it can be shown that coalescent theory holds.

scholarly journals Coalescent theory for a Monoecious Random Mating Population with a Varying Size

2010 ◽  
Vol 47 (01) ◽  
pp. 41-57 ◽  
Author(s):  
Edward Pollak
Keyword(s):  
Markov Chain ◽  
Population Size ◽  
Effective Population Size ◽  
Random Sample ◽  
Random Mating ◽  
Coalescent Theory ◽  
Effective Population ◽  
Diploid Population ◽  
Mating Population ◽  
Population Sizes

Consider a monoecious diploid population with nonoverlapping generations, whose size varies with time according to an irreducible, aperiodic Markov chain with states x 1 N,…,x K N, where K ≪ N. It is assumed that all matings except for selfing are possible and equally probable. At time 0 a random sample of n ≪ N genes is taken. Given two successive population sizes x j N and x i N, the numbers of gametes that individual parents contribute to offspring can be shown to be exchangeable random variables distributed as G ij . Under minimal conditions on the first three moments of G ij for all i and j, a suitable effective population size N e is derived. Then if time is recorded in a backward direction in units of 2N e generations, it can be shown that coalescent theory holds.

scholarly journals Coalescent Theory for a Partially Selfing Population

Genetics ◽  
1997 ◽  
Vol 146 (4) ◽  
pp. 1489-1499 ◽  
Author(s):  
Yun-Xin Fu
Keyword(s):  
Population Size ◽  
Effective Population Size ◽  
Mutation Rate ◽  
Dna Sequences ◽  
Coalescent Theory ◽  
Selfing Rate ◽  
Effective Population ◽  
Diploid Population ◽  
Approximate Formulas ◽  
Segregating Sites

A coalescent theory for a sample of DNA sequences from a partially selfing diploid population and an algorithm for simulating such samples are developed in this article. Approximate formulas are given for the expectation and the variance of the number of segregating sites in a sample of k sequences from n individuals. Several new estimators of the important parameters θ = 4Nμ and the selfing rate s, where N and μ are, respectively, the effective population size and the mutation rate per sequence per generation, are proposed and their sampling properties are studied.

scholarly journals GENETIC DRIFT AND ESTIMATION OF EFFECTIVE POPULATION SIZE

Genetics ◽  
1981 ◽  
Vol 98 (3) ◽  
pp. 625-640
Author(s):  
Masatoshi Nei ◽  
Fumio Tajima
Keyword(s):  
Population Size ◽  
Effective Population Size ◽  
Random Mating ◽  
Effective Size ◽  
Isolated Population ◽  
Effective Population ◽  
Dacus Oleae ◽  
Census Size ◽  
Mating Population ◽  
Frequency Changes

ABSTRACT The statistical properties of the standardized variance of gene frequency changes (a quantity equivalent to Wright's inbreeding coefficient) in a random mating population are studied, and new formulae for estimating the effective population size are developed. The accuracy of the formulae depends on the ratio of sample size to effective size, the number of generations involved (t), and the number of loci or alleles used. It is shown that the standardized variance approximately follows the Χ2 distribution unless t is very large, and the confidence interval of the estimate of effective size can be obtained by using this property. Application of the formulae to data from an isolated population of Dacus oleae has shown that the effective size of this population is about one tenth of the minimum census size, though there was a possibility that the procedure of sampling genes was improper.

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 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 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 Mitochondrial DNA Sequence Diversity in Mammals: A Correlation between the Effective and Census Population Sizes

2020 ◽  
Vol 12 (12) ◽  
pp. 2441-2449
Author(s):  
Jennifer James ◽  
Adam Eyre-Walker
Keyword(s):  
Mitochondrial Dna ◽  
Metabolic Rate ◽  
Population Size ◽  
Effective Population Size ◽  
Dna Sequence ◽  
Range Size ◽  
Effective Population ◽  
Population Sizes ◽  
Census Population Size ◽  
The Relationship

Abstract What determines the level of genetic diversity of a species remains one of the enduring problems of population genetics. Because neutral diversity depends upon the product of the effective population size and mutation rate, there is an expectation that diversity should be correlated to measures of census population size. This correlation is often observed for nuclear but not for mitochondrial DNA. Here, we revisit the question of whether mitochondrial DNA sequence diversity is correlated to census population size by compiling the largest data set to date, using 639 mammalian species. In a multiple regression, we find that nucleotide diversity is significantly correlated to both range size and mass-specific metabolic rate, but not a variety of other factors. We also find that a measure of the effective population size, the ratio of nonsynonymous to synonymous diversity, is also significantly negatively correlated to both range size and mass-specific metabolic rate. These results together suggest that species with larger ranges have larger effective population sizes. The slope of the relationship between diversity and range is such that doubling the range increases diversity by 12–20%, providing one of the first quantifications of the relationship between diversity and the census population size.

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 Biodiversity Management Under Limiting Conditions: Estimating Effective Population Size Using the Molecular Mark and Recapture (MMR) Method

Sociobiology ◽  
2014 ◽  
Vol 59 (1) ◽  
pp. 165
Author(s):  
Kaori Murase ◽  
Masaharu Fukita
Keyword(s):  
Population Size ◽  
Effective Population Size ◽  
National Parks ◽  
Hot Spots ◽  
First Generation ◽  
Second Generation ◽  
Effective Population ◽  
Simple Method ◽  
Population Sizes ◽  
Virtual Species

Although many people have been paying attention to the decrease of biodiversity on earth in recent years, many local people, even staff of national parks, live under limiting conditions (such as a shortage of funds, specialists, literature, equipment for experiments and so on). To conserve biodiversity, it is important to be clear about which species decrease or increase. To find such information, it is quite important to know the dynamics of effective population size for each species. Although a large number of papers have been written about how to improve the precision of the estimated effective population size, little has been studied on how to estimate the dynamics of the effective population sizes for many species together under limiting situations, very similar to the management methods of national parks in countries which have biological hot spots. In this paper, we are not concerned with the improvement of the precision of the estimates. We do, however, propose a simple method for the estimation of the effective population size. We named it the “MMR method.” It is not difficult to understand and is easily applied to many species. To show the usefulness of the MMR method we made simple virtual species, which included the first generation and the second generation, on a computer, and then we conducted simulations to estimate the effective population size of the first generation. We calculated three statistics to estimate whether the MMR method is useful or not. The three statistics showed that the MMR method is useful.

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