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

Creativitat i subversió en les reescriptures de Joan Sales

Creativitat i subversió en les reescriptures de Joan Sales se centra en la figura de l’editor i novel•lista Joan Sales (1912-1983) i pretén ressituar l’autor d’Incerta glòria dins del panorama literari català a partir d’una diversificació dels punts de mira des dels quals esdevé possible realitzar-ne un estudi. Com a base, s’han utilitzat les teories traductològiques de finals del segle XX, elaborades per autors com André Lefevere i Susan Bassnett, que situen la traducció, l’edició, l’adaptació, la crítica literària i la historiografia dins del terreny de la reescriptura creativa i atorguen un poder subversiu a totes aquestes activitats. Així, doncs, s’ha intentat modificar la tendència que, històricament, havia dut a considerar de manera negativa les reescriptures de Sales. Sota el paraigua teòric de la reescriptura, les manipulacions, els canvis i les intervencions esdevenen una eina que contribueix a l’evolució literària d’una cultura.