Population stratification has long been recognized as a confounding factor in genetic association studies. Estimated ancestries, derived from multi-locus genotype data, can be used to perform a statistical correction for population stratification. One popular technique for estimation of ancestry is the model-based approach embodied by the widely applied program structure. Another approach, implemented in the program EIGENSTRAT, relies on Principal Component Analysis rather than model-based estimation and does not directly deliver admixture fractions. EIGENSTRAT has gained in popularity in part owing to its remarkable speed in comparison to structure. We present a new algorithm and a program, ADMIXTURE, for model-based estimation of ancestry in unrelated individuals. ADMIXTURE adopts the likelihood model embedded in structure. However, ADMIXTURE runs considerably faster, solving problems in minutes that take structure hours. In many of our experiments, we have found that ADMIXTURE is almost as fast as EIGENSTRAT. The runtime improvements of ADMIXTURE rely on a fast block relaxation scheme using sequential quadratic programming for block updates, coupled with a novel quasi-Newton acceleration of convergence. Our algorithm also runs faster and with greater accuracy than the implementation of an Expectation-Maximization (EM) algorithm incorporated in the program FRAPPE. Our simulations show that ADMIXTURE's maximum likelihood estimates of the underlying admixture coefficients and ancestral allele frequencies are as accurate as structure's Bayesian estimates. On real-world data sets, ADMIXTURE's estimates are directly comparable to those from structure and EIGENSTRAT. Taken together, our results show that ADMIXTURE's computational speed opens up the possibility of using a much larger set of markers in model-based ancestry estimation and that its estimates are suitable for use in correcting for population stratification in association studies.

/pdf/fast-model-based-estimation-of-ancestry-in-unrelated-1hvb7yh3n1.pdf

Fast model-based estimation of ancestry in unrelated individuals

SUMMARY The Hardy-Weinberg law plays an important role in the field of population genetics and often serves as a basis for genetic inference. Because of its importance, much attention has been devoted to tests of Hardy-Weinberg proportions (HWP) over the decades. It has long been recognized that largesample goodness-of-fit tests can sometimes lead to spurious results when the sample size and/or some genotypic frequencies are small. Although a complete enumeration algorithm for the exact test has been proposed, it is not of practical use for loci with more than a few alleles due to the amount of computation required. We propose two algorithms to estimate the significance level for a test of HWP. The algorithms are easily applicable to loci with multiple alleles. Both are remarkably simple and computationally fast. Relative efficiency and merits of the two algorithms are compared. Guidelines regarding their usage are given. Numerical examples are given to illustrate the practicality of the algorithms.

Performing the exact test of Hardy-Weinberg proportion for multiple alleles.

Paternity inference using highly polymorphic codominant markers is becoming common in the study of natural populations. However, multiple males are often found to be genetically compatible with each offspring tested, even when the probability of excluding an unrelated male is high. While various methods exist for evaluating the likelihood of paternity of each nonexcluded male, interpreting these likelihoods has hitherto been difficult, and no method takes account of the incomplete sampling and error-prone genetic data typical of large-scale studies of natural systems. We derive likelihood ratios for paternity inference with codominant markers taking account of typing error, and define a statistic delta for resolving paternity. Using allele frequencies from the study population in question, a simulation program generates criteria for delta that permit assignment of paternity to the most likely male with a known level of statistical confidence. The simulation takes account of the number of candidate males, the proportion of males that are sampled and gaps and errors in genetic data. We explore the potentially confounding effect of relatives and show that the method is robust to their presence under commonly encountered conditions. The method is demonstrated using genetic data from the intensively studied red deer (Cervus elaphus) population on the island of Rum, Scotland. The Windows-based computer program, CERVUS, described in this study is available from the authors. CERVUS can be used to calculate allele frequencies, run simulations and perform parentage analysis using data from all types of codominant markers.

Statistical confidence for likelihood-based paternity inference in natural populations

Preface. List of Figures. List of Tables. 1. The Scope of Genetic Analyses. 2. Data Summary. 3. Biometrical Genetics. 4. Matrix Algebra. 5. Path Analysis and Structural Equations. 6. LISREL Models and Methods. 7. Model Fitting Functions and Optimization. 8. Univariate Analysis. 9. Power and Sample Size. 10. Social Interaction. 11. Sex Limitation and GE Interaction. 12. Multivariate Analysis. 13. Direction of Causation. 14. Repeated Measures. 15. Longitudinal Mean Trends. 16. Observer Ratings. 17. Assortment and Cultural Transmission. 18. Future Directions. Appendices: A. List of Participants. B. The Greek Alphabet. C. LISREL Scripts for Univariate Models. D. LISREL Script for Power Calculation. E. LISREL Scripts for Multivariate Models. F. LISREL Script for Sibling Interaction Model. G. LISREL Scripts for Sex and GE Interaction. H. LISREL Script for Rater Bias Model. I. LISREL Scripts for Direction of Causation. J. LISREL Script and Data for Simplex Model. K. LISREL Scripts for Assortment Models. Bibliography. Index.

Methodology for Genetic Studies of Twins and Families

Medical genetics was revolutionized during the 1980s by the application of genetic mapping to locate the genes responsible for simple Mendelian diseases. Most diseases and traits, however, do not follow simple inheritance patterns. Genetics have thus begun taking up the even greater challenge of the genetic dissection of complex traits. Four major approaches have been developed: linkage analysis, allele-sharing methods, association studies, and polygenic analysis of experimental crosses. This article synthesizes the current state of the genetic dissection of complex traits--describing the methods, limitations, and recent applications to biological problems.

https://focus.psychiatryonline.org/doi/pdf/10.1176/foc.4.3.442

Genetic dissection of complex traits

Path Analysis--A Primer.

Path analysis - a primer.

First Course in Population Genetics

Given the DNA fingerprints of two individuals with some bands being shared by both individuals, we define a new measure of the degree of similarity between the DNA profiles of two individuals. We use

C. C. Li

Papers

Path Analysis--A Primer.

Path analysis - a primer.

First Course in Population Genetics

Similarity of DNA Fingerprints Due to Chance and Relatedness

Introduction to Experimental Statistics