scholarly journals ESTIMATES OF INBREEDING IN A NATURAL POPULATION: A COMPARISON OF SAMPLING PROPERTIES

Genetics ◽  
1982 ◽  
Vol 100 (2) ◽  
pp. 339-358 ◽  
Author(s):  
Martin Curie-Cohen
Keyword(s):  
Maximum Likelihood ◽  
Natural Population ◽  
Inbreeding Coefficient ◽  
Single Locus ◽  
Maximum Likelihood Estimates ◽  
Gene Frequencies ◽  
Chi Square ◽  
Inbreeding Coefficients ◽  
Good For ◽  
Biased Estimates

ABSTRACT The average inbreeding coefficient f of a population can be estimated in several different ways based solely on the genotypic frequencies at a single locus. The means and variances of four different estimates have been compared. While the four estimates are equivalent when there are two alleles, the best estimates when there are three or more alleles are based upon total heterozygosity (see PDF) where x and y are the expected and observed number of heterozygotes) and the proportion of alleles that are homozygous (see PDF) where k = the number of alleles, aii = the number of AiAi homozygotes, and 2aij = the number of AiAj heterozygotes). Both are minimally biased estimates of f and have identical sampling variances when all alleles are equally frequent. However, when alleles have different frequencies, the choice between these two estimates depends on the gene frequencies and the true inbreeding coefficient of a population; f  2 is the best estimate when the true average inbreeding coefficient is suspected to be low or f = 0, while f  1 is best in populations with large average inbreeding coefficients. Approximate sampling variances of these two estimates are given for any f and any number of alleles with arbitrary gene frequencies; these approximations are accurate for samples as small as n = 100. The chi-square and maximum likelihood estimates of f are not as good for realistic sample sizes.

scholarly journals Revised Calculation of Kalinowski’s Ancestral and New Inbreeding Coefficients

Diversity ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 155 ◽  
Author(s):  
Harmen P. Doekes ◽  
Ino Curik ◽  
István Nagy ◽  
János Farkas ◽  
György Kövér ◽  
...  
Keyword(s):  
Software Package ◽  
Stochastic Approach ◽  
Inbreeding Coefficient ◽  
Data Sets ◽  
Inbreeding Coefficients ◽  
Holstein Friesian ◽  
Unbiased Estimates ◽  
Biased Estimates ◽  
Friesian Cattle

To test for the presence of purging in populations, the classical pedigree-based inbreeding coefficient (F) can be decomposed into Kalinowski’s ancestral (FANC) and new (FNEW) inbreeding coefficients. The FANC and FNEW can be calculated by a stochastic approach known as gene dropping. However, the only publicly available algorithm for the calculation of FANC and FNEW, implemented in GRain v 2.1 (and also incorporated in the PEDIG software package), has produced biased estimates. The FANC was systematically underestimated and consequently, FNEW was overestimated. To illustrate this bias, we calculated FANC and FNEW by hand for simple example pedigrees. We revised the GRain program so that it now provides unbiased estimates. Correlations between the biased and unbiased estimates of FANC and FNEW, obtained for example data sets of Hungarian Pannon White rabbits (22,781 individuals) and Dutch Holstein Friesian cattle (37,061 individuals), were high, i.e., >0.96. Although the magnitude of bias appeared to be small, results from studies based on biased estimates should be interpreted with caution. The revised GRain program (v 2.2) is now available online and can be used to calculate unbiased estimates of FANC and FNEW.

scholarly journals Maximum likelihood estimation of individual inbreeding coefficients and null allele frequencies

2012 ◽  
Vol 94 (3) ◽  
pp. 151-161 ◽  
Author(s):  
NATHAN HALL ◽  
LAINA MERCER ◽  
DAISY PHILLIPS ◽  
JONATHAN SHAW ◽  
AMY D. ANDERSON
Keyword(s):  
Maximum Likelihood ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
Allele Frequencies ◽  
Maximum Likelihood Estimates ◽  
Null Alleles ◽  
Single Individual ◽  
Em Algorithms ◽  
Inbreeding Coefficients ◽  
Missing Genotypes

SummaryIn this paper, we developed and compared several expectation–maximization (EM) algorithms to find maximum likelihood estimates of individual inbreeding coefficients using molecular marker information. The first method estimates the inbreeding coefficient for a single individual and assumes that allele frequencies are known without error. The second method jointly estimates inbreeding coefficients and allele frequencies for a set of individuals that have been genotyped at several loci. The third method generalizes the second method to include the case in which null alleles may be present. In particular, it is able to jointly estimate individual inbreeding coefficients and allele frequencies, including the frequencies of null alleles, and accounts for missing data. We compared our methods with several other estimation procedures using simulated data and found that our methods perform well. The maximum likelihood estimators consistently gave among the lowest root-mean-square-error (RMSE) of all the estimators that were compared. Our estimator that accounts for null alleles performed particularly well and was able to tease apart the effects of null alleles, randomly missing genotypes and differing degrees of inbreeding among members of the datasets we analysed. To illustrate the performance of our estimators, we analysed previously published datasets on mice (Mus musculus) and white-tailed deer (Odocoileus virginianus).

Evaluation of a Mark–Recapture Method for Estimating Mortality and Migration Rates of Stratified Populations

1991 ◽  
Vol 48 (2) ◽  
pp. 254-260 ◽  
Author(s):  
Robert M. Dorazio ◽  
Paul J. Rago
Keyword(s):  
Maximum Likelihood ◽  
Sockeye Salmon ◽  
Maximum Likelihood Estimates ◽  
Fishing Mortality ◽  
Mark Recapture ◽  
Sampling Variability ◽  
Migration Rates ◽  
Tag Loss ◽  
And Migration ◽  
Biased Estimates

We simulated mark–recapture experiments to evaluate a method for estimating fishing mortality and migration rates of populations stratified at release and recovery. When fish released in two or more strata were recovered from different recapture strata in nearly the same proportions, conditional recapture probabilities were estimated outside the [0, 1] interval. The maximum likelihood estimates tended to be biased and imprecise when the patterns of recaptures produced extremely "flat" likelihood surfaces. Absence of bias was not guaranteed, however, in experiments where recapture rates could be estimated within the [0, 1] interval. Inadequate numbers of tag releases and recoveries also produced biased estimates, although the bias was easily detected by the high sampling variability of the estimates. A stratified tag–recapture experiment with sockeye salmon (Oncorhynchus nerka) was used to demonstrate procedures for analyzing data that produce biased estimates of recapture probabilities. An estimator was derived to examine the sensitivity of recapture rate estimates to assumed differences in natural and tagging mortality, tag loss, and incomplete reporting of tag recoveries.

Statistical Justification of Pearson's Criterion for Testing a Complex Hypothesis on the Uniform Distribution

2018 ◽  
pp. 45-53
Author(s):  
T. V. Oblakova
Keyword(s):  
Uniform Distribution ◽  
Degrees Of Freedom ◽  
Likelihood Function ◽  
Random Number Generator ◽  
Maximum Likelihood Estimates ◽  
Chi Square ◽  
Main Hypothesis ◽  
Pearson Criterion ◽  
Complex Hypothesis ◽  
Uniform Law

The paper is studying the justification of the Pearson criterion for checking the hypothesis on the uniform distribution of the general totality. If the distribution parameters are unknown, then estimates of the theoretical frequencies are used [1, 2, 3]. In this case the quantile of the chi-square distribution with the number of degrees of freedom, reduced by the number of parameters evaluated, is used to determine the upper threshold of the main hypothesis acceptance [7]. However, in the case of a uniform law, the application of Pearson's criterion does not extend to complex hypotheses, since the likelihood function does not allow differentiation with respect to parameters, which is used in the proof of the theorem mentioned [7, 10, 11].A statistical experiment is proposed in order to study the distribution of Pearson statistics for samples from a uniform law. The essence of the experiment is that at first a statistically significant number of one-type samples from a given uniform distribution is modeled, then for each sample Pearson statistics are calculated, and then the law of distribution of the totality of these statistics is studied. Modeling and processing of samples were performed in the Mathcad 15 package using the built-in random number generator and array processing facilities.In all the experiments carried out, the hypothesis that the Pearson statistics conform to the chi-square law was unambiguously accepted (confidence level 0.95). It is also statistically proved that the number of degrees of freedom in the case of a complex hypothesis need not be corrected. That is, the maximum likelihood estimates of the uniform law parameters implicitly used in calculating Pearson statistics do not affect the number of degrees of freedom, which is thus determined by the number of grouping intervals only.

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