Utility of Genetic Markers in the Study of Human Resemblance

1980 ◽  
Vol 29 (4) ◽  
pp. 255-262 ◽  
Author(s):  
W. J. Kimberling ◽  
D. E. Goldgar
Keyword(s):  
Likelihood Function ◽  
Genetic Correlations ◽  
Marker Locus ◽  
Maximum Likelihood Estimates ◽  
Dizygotic Twin ◽  
Gene Frequencies ◽  
Nonrandom Mating ◽  
Marker Loci ◽  
Twin Families ◽  
Sib Pairs

A method for the estimation of genetic correlations based upon analysis of genetic marker phenotypes is presented. At a given marker locus, the probability of observing a pair of individuals with a specific combination of phenotypes can be expressed as a function of the gene frequencies at that locus and the genetic correlation (R) between that pair. The likelihood of obtaining a sample of n such pairs with their phenotypes at m marker loci can be expressed as a product of nm such functions. From the likelihood function, maximum likelihood estimates of R can be obtained, and hypotheses about R may be tested. A sample of Swedish twin families (61 dizygotic twin pairs, 268 husband-wife pairs, and 164 sib pairs) were analyzed by this method using information from 21 markers. It was found that for the twin pairs, R = 0.458, which was significantly different from the R calculated for sib pairs (R = 0.5 58) but not significantly different from the expected 0.5. For the husband-wife pairs, it was found that R = 0.086, which did differ significantly from the expected value of 0, indicating the presence of nonrandom mating in this population.

scholarly journals Linkage Analysis and Map Construction in Genetic Populations of Clonal F1 and Double Cross

2015 ◽  
Vol 5 (3) ◽  
pp. 427-439 ◽  
Author(s):  
Luyan Zhang ◽  
Huihui Li ◽  
Jiankang Wang
Keyword(s):  
Analytic Solution ◽  
Frequency Estimation ◽  
Female Parent ◽  
Marker Locus ◽  
Maximum Likelihood Estimates ◽  
F1 Hybrids ◽  
Map Construction ◽  
Marker Loci ◽  
Raphson Method ◽  
Double Cross

Abstract In this study, we considered four categories of molecular markers based on the number of distinguishable alleles at the marker locus and the number of distinguishable genotypes in clonal F1 progenies. For two marker loci, there are nine scenarios that allow the estimation of female, male, and/or combined recombination frequencies. In a double cross population derived from four inbred lines, five categories of markers are classified and another five scenarios are present for recombination frequency estimation. Theoretical frequencies of identifiable genotypes were given for each scenario, from which the maximum likelihood estimates of one or more of the three recombination frequencies could be estimated. If there was no analytic solution, then Newton-Raphson method was used to acquire a numerical solution. We then proposed to use an algorithm in Traveling Salesman Problem to determine the marker order. Finally, we proposed a procedure to build the two haploids of the female parent and the two haploids of the male parent in clonal F1. Once the four haploids were built, clonal F1 hybrids could be exactly regarded as a double cross population. Efficiency of the proposed methods was demonstrated in simulated clonal F1 populations and one actual maize double cross. Extensive comparisons with software JoinMap4.1, OneMap, and R/qtl show that the methodology proposed in this article can build more accurate linkage maps in less time.

scholarly journals NONRANDOM MATING IN AN OPEN-POLLINATED MAIZE POPULATION

Genetics ◽  
1986 ◽  
Vol 112 (3) ◽  
pp. 669-680
Author(s):  
R Bijlsma ◽  
R W Allard ◽  
A L Kahler
Keyword(s):  
Zea Mays L ◽  
Marker Locus ◽  
Mixed Mating ◽  
Nonrandom Mating ◽  
Gametophytic Selection ◽  
Maize Population ◽  
Marker Loci ◽  
Different Populations ◽  
Mixed Mating Model ◽  
Mating Model

ABSTRACT Randomness of fertilization was studied in an open-pollinated population of maize (Zea mays L.) through allozyme assays of seedlings from open-pollinated seeds produced on both tasseled and detasseled plants. Mixed-mating-model estimates of the amount of outcrossing (t) were not significantly different from t = 1.00 for four enzyme loci (Adh1, Idh2, Got1 and Acp1), indicating that fertilizations were at random in the population. However, for loci Prx1 and Est4, estimates of t were significantly smaller than unity-0.80 and 0.70 for tasseled plants and 0.81 and 0.80 for detasseled plants. The excesses of homogametic fertilizations detected on the detasseled plants could not have been due to selffertilization, s = 1 - t, because the detasseled plants shed no pollen. Analyses of allelic frequencies in the pollen that produced seed on the detasseled plants established that different maternal plants sampled genetically different populations of pollen from the outcross pollen pool. It was suggested that the causes of the differential sampling were temporal variation in the pollen pool, and/or gametophytic selection, correlated with marker-locus genotype. Two-, three- and four-locus interactions among the marker loci were often statistically significant, indicating that the factors responsible for the nonrandom gametic unions observed in the maize population studied were complexly interactive.

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.

Taste Thresholds in Twins and Siblings

1967 ◽  
Vol 16 (3) ◽  
pp. 229-243 ◽  
Author(s):  
A. R. Kaplan ◽  
R. Fischer ◽  
A. Karras ◽  
F. Griffin ◽  
W. Powell ◽  
...  
Keyword(s):  
Hydrochloric Acid ◽  
Monozygotic Twin ◽  
Quinine Sulfate ◽  
Dizygotic Twin ◽  
Same Sex ◽  
Significant Difference ◽  
The Difference ◽  
Taste Thresholds ◽  
Threshold Range ◽  
Sib Pairs

SummaryMonozygotic twin (MZ), dizygotic twin (DZ), and sibling (SIB) pairs were taste-tested for hydrochloric acid, 1-quinine sulfate, and 6-n-propylthiouracil (PROP). The numbers of pairs involved were 75 MZ, 70 DZ, and 78 SIB, for the latter two compounds; 26, 45, and 45, respectively, for the acid.There was a significant difference in intrapair variance, between the MZ and the same-sex DZ pairs, in thresholds for bitter-tasting 6-n-propylthiouracil (p < .001). The difference in intrapair threshold variance was not significant for bitter-tasting quinine (p > .05) or for sour-tasting hydrochloric acid (p > .10).The male MZ pairs had a significantly lower intrapair threshold variance than the male DZ or male SIB pairs for hydrochloric acid (p < .01), but the female pairs manifested no such difference. The intrapair variance in hydrochloric acid threshold was significantly less for the nine male MZ pairs than for the 17 female MZ pairs (p < .02).Repeated taste tests on the same subjects reproduced results similar within a single threshold range in a high proportion for each compound: for hydrochloric acid, 72.9% (N = 44); for quinine, 76.9% (N = 221); and for PROP, 76% (N = 225).Correlations between thresholds for the different substances were positive and significant (N = 308): between PROP and quinine, r = + 0.44 ± .05 (p < .01); between quinine and hydrochloric acid, r = + 0.35 ± .05 (p < .01); between PROP and hydrochloric acid, r = + 0.17 ± .06 (p < .05).

scholarly journals A quantile variant of the expectation–maximization algorithm and its application to parameter estimation with interval data

2018 ◽  
Vol 12 (3) ◽  
pp. 253-272 ◽  
Author(s):  
Chanseok Park
Keyword(s):  
Monte Carlo ◽  
Expectation Maximization ◽  
Likelihood Function ◽  
Expectation Maximization Algorithm ◽  
Parametric Models ◽  
Maximum Likelihood Estimates ◽  
Computational Technique ◽  
Stable Convergence ◽  
Explicit Integration ◽  
Monte Carlo Expectation Maximization

The expectation–maximization algorithm is a powerful computational technique for finding the maximum likelihood estimates for parametric models when the data are not fully observed. The expectation–maximization is best suited for situations where the expectation in each E-step and the maximization in each M-step are straightforward. A difficulty with the implementation of the expectation–maximization algorithm is that each E-step requires the integration of the log-likelihood function in closed form. The explicit integration can be avoided by using what is known as the Monte Carlo expectation–maximization algorithm. The Monte Carlo expectation–maximization uses a random sample to estimate the integral at each E-step. But the problem with the Monte Carlo expectation–maximization is that it often converges to the integral quite slowly and the convergence behavior can also be unstable, which causes computational burden. In this paper, we propose what we refer to as the quantile variant of the expectation–maximization algorithm. We prove that the proposed method has an accuracy of [Formula: see text], while the Monte Carlo expectation–maximization method has an accuracy of [Formula: see text]. Thus, the proposed method possesses faster and more stable convergence properties when compared with the Monte Carlo expectation–maximization algorithm. The improved performance is illustrated through the numerical studies. Several practical examples illustrating its use in interval-censored data problems are also provided.

scholarly journals The use of selection experiments for detecting quantitative trait loci

1997 ◽  
Vol 69 (3) ◽  
pp. 227-232 ◽  
Author(s):  
L. OLLIVIER ◽  
L. A. MESSER ◽  
M. F. ROTHSCHILD ◽  
C. LEGAULT
Keyword(s):  
Quantitative Trait ◽  
Marker Locus ◽  
Frequency Change ◽  
Gene Frequencies ◽  
Marker Allele ◽  
Gene Effects ◽  
Selection Experiments ◽  
Frequency Changes ◽  
Combined Selection ◽  
Number Of Individuals

Gene frequency changes following selection may reveal the existence of gene effects on the trait selected. Loci for the selected quantitative trait (SQTL) may thus be detected. Additionally, one can estimate the average effect (α) of a marker allele associated with an SQTL from the allele frequency change (Δq) due to selection of given intensity (i). In a sample of unrelated individuals, it is optimal to select the upper and lower 27% for generating Δq in order to estimate α. For a given number of individuals genotyped, this estimator is 0·25i2 times more efficient than the classical estimator of α, based on the regression of the trait on the genotype at the marker locus. The method is extended to selection criteria using information from relatives, showing that combined selection considerably increases the efficiency of estimation for traits of low heritability. The method has been applied to the detection of SQTL in a selection experiment in which the trait selected was pig litter size averaged over the first four parities, with i=3. Results for four genes are provided, one of which yielded a highly significant effect. The conditions required for valid application of the method are discussed, including selection experiments over several generations. Additional advantages of the method can be anticipated from determining gene frequencies on pooled samples of blood or DNA.

Maximum likelihood estimation in nonlinear structured fisheries models using survey and catch-at-age data

2011 ◽  
Vol 68 (10) ◽  
pp. 1717-1731 ◽  
Author(s):  
Christian N. Brinch ◽  
Anne Maria Eikeset ◽  
Nils Chr. Stenseth
Keyword(s):  
Maximum Likelihood ◽  
Gadus Morhua ◽  
Likelihood Function ◽  
Likelihood Estimation ◽  
Maximum Likelihood Estimates ◽  
Simulated Maximum Likelihood ◽  
True Parameter ◽  
Bayesian Techniques ◽  
Age Structured ◽  
Parameter Values

Age-structured population dynamics models play an important role in fisheries assessments. Such models have traditionally been estimated using crude likelihood approximations or more recently using Bayesian techniques. We contribute to this literature with three main messages. Firstly, we demonstrate how to estimate such models efficiently by simulated maximum likelihood using Laplace importance samplers for the likelihood function. Secondly, we demonstrate how simulated maximum likelihood estimates may be validated using different importance samplers known to approach the exact likelihood function in different regions of the parameter space. Thirdly, we show that our method works in practice by Monte Carlo simulations using parameter values as estimated from data on the Northeast Arctic cod ( Gadus morhua ) stock. The simulations suggest that we are able to recover the unknown true maximum likelihood estimates using moderate importance sample sizes and show that we are able to adequately recover the true parameter values.

AN ANALYSIS OF ACCELERATED PERFORMANCE DEGRADATION TESTS ASSUMING THE ARRHENIUS STRESS-RELATIONSHIP

2008 ◽  
Vol 25 (06) ◽  
pp. 847-864 ◽  
Author(s):  
TAE HYOUNG KANG ◽  
SANG WOOK CHUNG ◽  
WON YOUNG YUN
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Exposure Time ◽  
Failure Time ◽  
Likelihood Function ◽  
Likelihood Estimation ◽  
Location Parameter ◽  
Performance Degradation ◽  
Maximum Likelihood Estimates ◽  
Degradation Tests

An analytical model is developed for accelerated performance degradation tests. The performance degradations of products at a specified exposure time are assumed to follow a normal distribution. It is assumed that the relationship between the location parameter of normal distribution and the exposure time is a linear function of the exposure time that the slope coefficient of the linear relationship has an Arrhenius dependence on temperature, and that the scale parameter of the normal distribution is constant and independent of temperature or exposure time. The method of maximum likelihood estimation is used to estimate the parameters involved. The likelihood function for the accelerated performance degradation data is derived. The approximated variance-covariance matrix is also derived for calculating approximated confidence intervals of maximum likelihood estimates. Finally we use two real examples for estimating the failure-time distribution, technically defined as the time when performance degrades below a specified level.

The Estimated Probability of Dizygotic Twins: A Comparison of Two Methods

2009 ◽  
Vol 12 (1) ◽  
pp. 79-85 ◽  
Author(s):  
Jill Hardin ◽  
Steve Selvin ◽  
Suzan L. Carmichael ◽  
Gary M. Shaw
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Likelihood Estimation ◽  
Data Sources ◽  
Maximum Likelihood Estimates ◽  
Estimation Methods ◽  
Dizygotic Twin ◽  
Twin Data ◽  
Dizygotic Twins ◽  
The Relationship

AbstractThis study presents a general model of two binary variables and applies it to twin sex pairing data from 21 twin data sources to estimate the frequency of dizygotic twins. The purpose of this study is to clarify the relationship between maximum likelihood and Weinberg's differential rule zygosity estimation methods. We explore the accuracy of these zygosity estimation measures in relation to twin ascertainment methods and the probability of a male. Twin sex pairing data from 21 twin data sources representing 15 countries was collected for use in this study. Maximum likelihood estimation of the probability of dizygotic twins is applied to describe the variation in the frequency of dizygotic twin births. The differences between maximum likelihood and Weinberg's differential rule zygosity estimation methods are presented as a function of twin data ascertainment method and the probability of a male. Maximum likelihood estimation of the probability of dizygotic twins ranges from 0.083 (95% approximate CI: 0.082, 0.085) to 0.750 (95% approximate CI: 0.749, 0.752) for voluntary ascertainment data sources and from 0.374 (95% approximate CI: 0.373, 0.375) to 0.987 (95% approximate CI: 0.959, 1.016) for active ascertainment data sources. In 17 of the 21 twin data sources differences of 0.01 or less occur between maximum likelihood and Weinberg zygosity estimation methods. The Weinberg and maximum likelihood estimates are negligibly different in most applications. Using the above general maximum likelihood estimate, the probability of a dizygotic twin is subject to substantial variation that is largely a function of twin data ascertainment method.

scholarly journals Simple penalties on maximum likelihood estimates of genetic parameters to reduce sampling variation

2015 ◽  
Author(s):  
karin meyer
Keyword(s):  
Maximum Likelihood ◽  
Genetic Parameters ◽  
Likelihood Function ◽  
Maximum Likelihood Estimates ◽  
Data Sets ◽  
Simple Modification ◽  
Scale Free ◽  
Wide Range ◽  
Sampling Variation ◽  
The Difference

Multivariate estimates of genetic parameters are subject to substantial sampling variation, especially for smaller data sets and more than a few traits. A simple modification of standard, maximum likelihood procedures for multivariate analyses to estimate genetic covariances is described, which can improve estimates by substantially reducing their sampling variances. This is achieved maximizing the likelihood subject to a penalty. Borrowing from Bayesian principles, we propose a mild, default penalty -- derived assuming a Beta distribution of scale-free functions of the covariance components to be estimated -- rather than laboriously attempting to determine the stringency of penalization from the data. An extensive simulation study is presented demonstrating that such penalties can yield very worthwhile reductions in loss, i.e. the difference from population values, for a wide range of scenarios and without distorting estimates of phenotypic covariances. Moreover, mild default penalties tend not to increase loss in difficult cases and, on average, achieve reductions in loss of similar magnitude than computationally demanding schemes to optimize the degree of penalization. Pertinent details required for the adaptation of standard algorithms to locate the maximum of the likelihood function are outlined.

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