Hardy-Weinberg Equilibrium and the Ternary Plot

The Hardy-Weinberg law, formulated about 100 years ago, states that under certain assumptions, the three genotypes AA, AB and BB at a bi-allelic locus are expected to occur in the proportions p2, 2pq, and q2 respectively, where p is the allele frequency of A, and q = 1-p. There are many statistical tests being used to check whether empirical marker data obeys the Hardy-Weinberg principle. Among these are the classical xi-square test (with or without continuity correction), the likelihood ratio test, Fisher's Exact test, and exact tests in combination with Monte Carlo and Markov Chain algorithms. Tests for Hardy-Weinberg equilibrium (HWE) are numerical in nature, requiring the computation of a test statistic and a p-value. There is however, ample space for the use of graphics in HWE tests, in particular for the ternary plot. Nowadays, many genetical studies are using genetical markers known as Single Nucleotide Polymorphisms (SNPs). SNP data comes in the form of counts, but from the counts one typically computes genotype frequencies and allele frequencies. These frequencies satisfy the unit-sum constraint, and their analysis therefore falls within the realm of compositional data analysis (Aitchison, 1986). SNPs are usually bi-allelic, which implies that the genotype frequencies can be adequately represented in a ternary plot. Compositions that are in exact HWE describe a parabola in the ternary plot. Compositions for which HWE cannot be rejected in a statistical test are typically “close" to the parabola, whereas compositions that differ significantly from HWE are “far". By rewriting the statistics used to test for HWE in terms of heterozygote frequencies, acceptance regions for HWE can be obtained that can be depicted in the ternary plot. This way, compositions can be tested for HWE purely on the basis of their position in the ternary plot (Graffelman & Morales, 2008). This leads to nice graphical representations where large numbers of SNPs can be tested for HWE in a single graph. Several examples of graphical tests for HWE (implemented in R software), will be shown, using SNP data from different human populations

Tess of the d'Urbervilles. Thomas Hardy : AS-A level English literature resource pack.

Guía del profesor para el estudio de la obra 'Tess of the d'Urbervilles' (publicada a finales del siglo XIX) del autor británico Thomas Hardy, en el nivel AS-A (bachillerato) de la asignatura de Literatura Inglesa. Los materiales están divididos en cuatro secciones: contextos, actividades, evaluación y recursos. El objetivo es ayudar a los estudiantes a familiarizarse con el texto, a apreciar su importancia como obra literaria, y a responder de forma detallada y analítica en el desarrollo de un trabajo de curso o un examen. Para ello se trata ampliamente la caracterización de los personajes, los temas y el lenguaje, y se incluyen prácticas de examen de redacción y ensayo.

The serialization and publication of 'The return of the native': a new Thomas Hardy letter

This article presents and contextualises a newly-discovered letter by Thomas Hardy, housed in the Chatto & Windus archive at the University of Reading. The letter sheds new light on the publishing history of Hardy's novel 'The return of the native'

Measuring departures from Hardy-Weinberg: a Markov chain Monte Carlo method for estimating the inbreeding coefficient

Many well-established statistical methods in genetics were developed in a climate of severe constraints on computational power. Recent advances in simulation methodology now bring modern, flexible statistical methods within the reach of scientists having access to a desktop workstation. We illustrate the potential advantages now available by considering the problem of assessing departures from Hardy-Weinberg (HW) equilibrium. Several hypothesis tests of HW have been established, as well as a variety of point estimation methods for the parameter which measures departures from HW under the inbreeding model. We propose a computational, Bayesian method for assessing departures from HW, which has a number of important advantages over existing approaches. The method incorporates the effects-of uncertainty about the nuisance parameters--the allele frequencies--as well as the boundary constraints on f (which are functions of the nuisance parameters). Results are naturally presented visually, exploiting the graphics capabilities of modern computer environments to allow straightforward interpretation. Perhaps most importantly, the method is founded on a flexible, likelihood-based modelling framework, which can incorporate the inbreeding model if appropriate, but also allows the assumptions of the model to he investigated and, if necessary, relaxed. Under appropriate conditions, information can be shared across loci and, possibly, across populations, leading to more precise estimation. The advantages of the method are illustrated by application both to simulated data and to data analysed by alternative methods in the recent literature.

Short fiction of Thomas Hardy: an exploration and assessment

Hardy's novels and poetry have received extensive criticism, in due proportion to their merit. Hardy's short stories, however, have been virtually excluded from the annals of Hardy criticism, even though Hardy wrote over forty short stories, several of which are truly outstanding. In part, the reason for this neglect is because of the neglected state of the short story in Victorian England. Short fiction, published mainly only in periodicals and never collected in volume form, was obscured to a large extent by the highly popular serial novel. This thesis examines Thomas Hardy's short stories in the context of both the Victorian period and the Victorian short story genre, and explores the ways in which Thomas Hardy improved upon and deviated from some of the common types of short fiction being written in his day.