Hardy-Weinberg Equilibrium and the Ternary Plot

The Hardy-Weinberg law, formulated about 100 years ago, states that under certainassumptions, the three genotypes AA, AB and BB at a bi-allelic locus are expected to occur inthe 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 theHardy-Weinberg principle. Among these are the classical xi-square test (with or withoutcontinuity correction), the likelihood ratio test, Fisher's Exact test, and exact tests in combinationwith 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 ternaryplot. Nowadays, many genetical studies are using genetical markers known as SingleNucleotide Polymorphisms (SNPs). SNP data comes in the form of counts, but from the countsone typically computes genotype frequencies and allele frequencies. These frequencies satisfythe unit-sum constraint, and their analysis therefore falls within the realm of compositional dataanalysis (Aitchison, 1986). SNPs are usually bi-allelic, which implies that the genotypefrequencies can be adequately represented in a ternary plot. Compositions that are in exactHWE describe a parabola in the ternary plot. Compositions for which HWE cannot be rejected ina statistical test are typically “close" to the parabola, whereas compositions that differsignificantly from HWE are “far". By rewriting the statistics used to test for HWE in terms ofheterozygote frequencies, acceptance regions for HWE can be obtained that can be depicted inthe ternary plot. This way, compositions can be tested for HWE purely on the basis of theirposition in the ternary plot (Graffelman & Morales, 2008). This leads to nice graphicalrepresentations where large numbers of SNPs can be tested for HWE in a single graph. Severalexamples of graphical tests for HWE (implemented in R software), will be shown, using SNPdata from different human populations

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

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.

Characterization Of Microsatellite Markers Developed From Prosopis Rubriflora And Prosopis Ruscifolia (leguminosae - Mimosoideae), Legume Species That Are Used As Models For Genetic Diversity Studies In Chaquenian Areas Under Anthropization In South America.

Prosopis rubriflora and Prosopis ruscifolia are important species in the Chaquenian regions of Brazil. Because of the restriction and frequency of their physiognomy, they are excellent models for conservation genetics studies. The use of microsatellite markers (Simple Sequence Repeats, SSRs) has become increasingly important in recent years and has proven to be a powerful tool for both ecological and molecular studies. In this study, we present the development and characterization of 10 new markers for P. rubriflora and 13 new markers for P. ruscifolia. The genotyping was performed using 40 P. rubriflora samples and 48 P. ruscifolia samples from the Chaquenian remnants in Brazil. The polymorphism information content (PIC) of the P. rubriflora markers ranged from 0.073 to 0.791, and no null alleles or deviation from Hardy-Weinberg equilibrium (HW) were detected. The PIC values for the P. ruscifolia markers ranged from 0.289 to 0.883, but a departure from HW and null alleles were detected for certain loci; however, this departure may have resulted from anthropic activities, such as the presence of livestock, which is very common in the remnant areas. In this study, we describe novel SSR polymorphic markers that may be helpful in future genetic studies of P. rubriflora and P. ruscifolia.

Microsatellite In Aeschynomene Falcata (leguminosae): Diversity, Cross-amplification, And Chromosome Localization.

Aeschynomene falcata is an important forage species; however, because of low seed production, it is underutilized as forage species. Aeschynomene is a polyphyletic genus with a challenging taxonomic position. Two subgenera have been proposed, and it is suggested that Aeschynomene can be split in 2 genera. Thus, new markers, such as microsatellite sequences, are desirable for improving breeding programs for A. falcata. Based on transferability and in situ localization, these microsatellite sequences can be applied as chromosome markers in the genus Aeschynomene and closely related genera. Here, we report the first microsatellite library developed for this genus; 11 microsatellites were characterized, with observed and expected heterozygosities ranging from 0.0000 to 0.7143 and from 0.1287 to 0.8360, respectively. Polymorphic information content varied from 0.1167 to 0.7786. The departure from Hardy-Weinberg equilibrium may have resulted from frequent autogamy, which is characteristic of A. falcata. Of the 11 microsatellites, 9 loci were cross-amplified in A. brevipes and A. paniculata and 7 in Dalbergia nigra and Machaerium vestitum. Five of these 7 cross-amplified microsatellites were applied as probes during the in situ hybridization assay and 2 showed clear signals on A. falcata chromosomes, ensuring their viability as chromosome markers.

The C242T polymorphism of the p22-phox gene (CYBA) is associated with higher left ventricular mass in Brazilian hypertensive patients

Background: Reactive oxygen species have been implicated in the physiopathogenesis of hypertensive end-organ damage. This study investigated the impact of the C242T polymorphism of the p22-phox gene (CYBA) on left ventricular structure in Brazilian hypertensive subjects. Methods: We cross-sectionally evaluated 561 patients from 2 independent centers [Campinas (n = 441) and Vitoria (n = 120)] by clinical history, physical examination, anthropometry, analysis of metabolic and echocardiography parameters as well as p22-phox C242T polymorphism genotyping. In addition, NADPH-oxidase activity was quantified in peripheral mononuclear cells from a subgroup of Campinas sample. Results: Genotype frequencies in both samples were consistent with the Hardy-Weinberg equilibrium. Subjects with the T allele presented higher left ventricular mass/height(2.7) than those carrying the CC genotype in Campinas (76.8 +/- 1.6 vs 70.9 +/- 1.4 g/m(2.7); p = 0.009), and in Vitoria (45.6 +/- 1.9 vs 39.9 +/- 1.4 g/m(2.7); p = 0.023) samples. These results were confirmed by stepwise regression analyses adjusted for age, gender, blood pressure, metabolic variables and use of anti-hypertensive medications. In addition, increased NADPH-oxidase activity was detected in peripheral mononuclear cells from T allele carriers compared with CC genotype carriers (p = 0.03). Conclusions: The T allele of the p22-phox C242T polymorphism is associated with higher left ventricular mass/height(2.7) and increased NADPH-oxidase activity in Brazilian hypertensive patients. These data suggest that genetic variation within NADPH-oxidase components may modulate left ventricular remodeling in subjects with systemic hypertension.

Disequilibrium Coefficient: A Bayesian Perspective

Hardy-Weinberg Equilibrium (HWE) is an important genetic property that populations should have whenever they are not observing adverse situations as complete lack of panmixia, excess of mutations, excess of selection pressure, etc. HWE for decades has been evaluated; both frequentist and Bayesian methods are in use today. While historically the HWE formula was developed to examine the transmission of alleles in a population from one generation to the next, use of HWE concepts has expanded in human diseases studies to detect genotyping error and disease susceptibility (association); Ryckman and Williams (2008). Most analyses focus on trying to answer the question of whether a population is in HWE. They do not try to quantify how far from the equilibrium the population is. In this paper, we propose the use of a simple disequilibrium coefficient to a locus with two alleles. Based on the posterior density of this disequilibrium coefficient, we show how one can conduct a Bayesian analysis to verify how far from HWE a population is. There are other coefficients introduced in the literature and the advantage of the one introduced in this paper is the fact that, just like the standard correlation coefficients, its range is bounded and it is symmetric around zero (equilibrium) when comparing the positive and the negative values. To test the hypothesis of equilibrium, we use a simple Bayesian significance test, the Full Bayesian Significance Test (FBST); see Pereira, Stern andWechsler (2008) for a complete review. The disequilibrium coefficient proposed provides an easy and efficient way to make the analyses, especially if one uses Bayesian statistics. A routine in R programs (R Development Core Team, 2009) that implements the calculations is provided for the readers.

Validation of dot blot hybridization and denaturing high performance liquid chromatography as reliable methods for TP53 codon 72 genotyping in molecular epidemiologic studies

Background: Mutations in TP53 are common events during carcinogenesis. In addition to gene mutations, several reports have focused on TP53 polymorphisms as risk factors for malignant disease. Many studies have highlighted that the status of the TP53 codon 72 polymorphism could influence cancer susceptibility. However, the results have been inconsistent and various methodological features can contribute to departures from Hardy-Weinberg equilibrium, a condition that may influence the disease risk estimates. The most widely accepted method of detecting genotyping error is to confirm genotypes by sequencing and/or via a separate method. Results: We developed two new genotyping methods for TP53 codon 72 polymorphism detection: Denaturing High Performance Liquid Chromatography (DHPLC) and Dot Blot hybridization. These methods were compared with Restriction Fragment Length Polymorphism (RFLP) using two different restriction enzymes. We observed high agreement among all methodologies assayed. Dot-blot hybridization and DHPLC results were more highly concordant with each other than when either of these methods was compared with RFLP. Conclusions: Although variations may occur, our results indicate that DHPLC and Dot Blot hybridization can be used as reliable screening methods for TP53 codon 72 polymorphism detection, especially in molecular epidemiologic studies, where high throughput methodologies are required.

Gene and genotypic diversity of Phytophthora cinnamomi in South Africa and Australia revealed by DNA polymorphisms

Phytophthora cinnamomi isolates from South Africa and Australia were compared to assess genetic differentiation between the two populations. These two populations were analysed for levels of phenotypic diversity using random amplified polymorphic DNAs (RAPDs) and gene and genotypic diversity using restriction fragment length polymorphisms (RFLPs). Sixteen RAPD markers from four decanucleotide Operon primers and 34 RFLP alleles from 15 putative loci were used. A few isolates from Papua New Guinea known to posses alleles different from Australian isolates were also included for comparative purposes. South African and Australian P. cinnamomi populations were almost identical with an extremely low level of genetic distance between them (D-m = 0.003). Common features for the two populations include shared alleles, low levels of phenotypic/genotypic diversity, high clonality, and low observed and expected levels of heterozygosity. Furthermore, relatively high levels of genetic differentiation between mating type populations (D-m South Africa = 0.020 and D-m Australia = 0.025 respectively), negative fixation indices, and significant deviations from Hardy-Weinberg equilibrium, all provided evidence for the lack of frequent sexual reproduction in both populations. The data strongly suggest that both the South African and Australian P. cinnamomi populations are introduced.

Population structure of Phytophthora cinnamomi in South Africa

Phytophthora cinnamomi isolates collected from 1977 to 1986 and 1991 to 1993 in two regions in South Africa were analyzed using isozymes. A total of 135 isolates was analyzed for 14 enzymes representing 20 putative loci, of which four were polymorphic. This led to the identification of nine different multilocus isozyme genotypes. Both mating types of P. cinnamomi occurred commonly in the Cape region, whereas, predominantly, the A2 mating type occurred in the Mpumalanga region of South Africa. A2 mating type isolates could be resolved into seven multilocus isozyme genotypes, compared with only two multilocus isozyme genotypes for the A1 mating type isolates. Low levels of gene (0.115) and genotypic (2.4%) diversity and a low number of alleles per locus (1.43) were observed for the South African P. cinnamomi population. The genetic distance between the Cape and Mpumalanga P. cinnamomi populations was relatively low (D-m = 0.165), and no specific pattern in regional distribution of multilocus isozyme genotypes could be observed. The genetic distance between the ''old'' (isolated between 1977 and 1986) and ''new'' (isolated between 1991 and 1993) P. cinnamomi populations from the Cape was low (D-m = 0.164), indicating a stable population over time. Three of the nine multilocus isozyme genotypes were specific to the ''old'' population, and only one multilocus isozyme genotype was specific to the ''new'' population. Significant differences in allele frequencies, a high genetic distance (D-m = 0.581) between the Cape A1 and A2 mating type isolates, significant deviations from Hardy-Weinberg equilibrium, a low overall level of heterozygosity, and a high fixation index (0.71) all indicate that sexual reproduction occurs rarely, if at all, in the South African P. cinnamomi population.

Frequency distribution of XbaIG > T and HaeIIIT > C GLUT1 polymorphisms among different Brazilian ethnic groups

GLUT is the major glucose transporter in mammalian cells. Single nucleotide polymorphisms (SNP) at GLUT1 promoter and regulatory regions have been associated to the risk of developing nephropathy in different type 1 and type 2 diabetic populations. It has been demonstrated that differences in allelic and genotypic frequencies of GLUT1 gene (SLC2A1) polymorphisms occur among different populations. Therefore, ethnic differences in distribution of GLUT1 gene polymorphisms may be an important factor in determining gene-disease association. In this study, we investigated the XbaIG > T and HaeIIIT > C polymorphisms in six different Brazilian populations: 102 individuals from Salvador population (Northern Brazil), 56 European descendants from Joinville (South Brazil), 85 Indians from Tiryi tribe (North Brazil) and 127 samples from Southern Brazil: 44 from European descendants, 42 from African descendants and 41 from Japanese descendants. Genotype frequencies from both sites did not differ significantly from those expected under the Hardy-Weinberg equilibrium. We verified that the allele frequencies of both polymorphisms were heterogeneous in these six Brazilian ethnic groups.

Polymorphisms in genes encoding drugs and xenobiotic metabolizing enzymes in a Brazilian population

Polymorphic variations of several genes associated with drugs and xenobiotic metabolism have been linked to the factors that predispose to the carcinogenesis process. As considerable interindividual and interethnic variation in metabolizing enzyme activity has been associated with polymorphic alleles, we evaluated the frequency of the polymorphisms of CYP2D6, EPHX1 and NQO1 genes in 361 Brazilian individuals separated by ethnicity (European and African ancestry), using the polymerase chain reaction-restriction fragment length (PCR-RFLP) method. The allele frequencies of the variants *3 and *4 for the gene CYP2D6 were 0.04 and 0.14 for white subjects and 0.03 and 0.10 for black individuals, respectively. For the both variants of the gene EPHX1, we found higher allele frequencies among white individuals compared with mulatto subjects (0.62 vs 0.54 and 0.18 vs 0.14, respectively); however, these differences were not statistically significant (p = 0.39 and 0.56, respectively). For the NQO1 gene we observed a higher frequency of the homozygous genotype among black individuals (7.9%) compared with white subjects (6.3%) (p = 0.003). The genotype frequencies were within the Hardy-Weinberg equilibrium. We concluded that the allele frequencies of CYP2D6, EPHX1 and NQO1 gene polymorphisms in this Brazilian population showed ethnic variability when compared with those observed in other populations.

Panmixia in Pocillopora verrucosa from South Africa

The genetic structure of six local collections of Pocillopora verrrucosa from six coral reefs in KwaZulu-Natal, South Africa, was examined using allozyme electrophoresis. The six separate reefs lie within two different reef complexes. Twenty-two enzymes were screened on five buffer systems, but only five polymorphic loci (Gpi-1, Gdh-1, Lgg-2, Lpp-1, Est-1) could be consistently resolved. No significant differences in allelic frequencies were detected among the six sites. All local collections were genotypically diverse, with evidence of only very limited clonal replication at each site. Indeed, the ratio of observed to expected genotypic diversity (mean Go:Ge=0.64 +/-0.05 SD), the ratio of observed number of genotypes to the number of individuals (mean Ng:N = 0.65 +/-0.04 SE), and deviations from the Hardy-Weinberg equilibrium indicate that sexual reproduction plays a major role in the maintenance of the populations. No genetic differentiation was found either within (FSR = 0.026 +/-0.003 SE) or between (FRT = 0.000 +/-0.001 SE) reef complexes. The homogeneity of the gene frequencies across the six reefs strongly supports the assumption that the KwaZulu-Natal reef complexes are highly connected by gene flow (Nem=44). The reefs in the southern and central reef complexes along the northern Maputaland coastline can therefore be considered part of a single population.

Influência de polimorfismos nos genes FcγRIIa, CD209, VDR, TNF-α, IL-4, IL-6 e INF-γ na persistência de sintomas clínicos da dengue na fase de covalescença

Diferenças na susceptibilidade do hospedeiro à infecção, na gravidade e na permanência do quadro clínico da doença podem ser atribuídas, em parte, às variações da resposta imune. Estas variações são associadas a polimorfismos de nucleotídeo único (do inglês: single nucleotide polymorphisms - SNPs). Como estudo prévio, foi realizada a caracterização da população geral do Espírito Santo (ES) - Brasil e de uma subpopulação do estado, de origem Pomerana, quanto aos SNPs -131 H/R, -336 A/G, TaqI, -308 A/G, -590 C/T, -174 G/C e +874 A/T nos genes FcγRIIa, CD209, VDR, TNFα, IL-4, IL-6 e INF-γ, respectivamente. Cem indivíduos da Grande Vitória representaram a população geral do ES e 59 indivíduos de Santa Maria de Jetibá representaram a população de origem Pomerana. Como a fase aguda da dengue é bem caracterizada, este estudo objetivou ampliar o conhecimento da fase de convalescença. Noventa e seis indivíduos diagnosticados com dengue sintomática no final de 2012 e início de 2013, no ES, foram acompanhados por 60 dias a partir do início dos sintomas por meio do preenchimento de um questionário clínico e epidemiológico em quatro entrevistas. A persistência de 37 sintomas clínicos da dengue foi avaliada. Para analisar a influência da genética do sistema imunológico do hospedeiro na persistência de sintomas clínicos da dengue na fase de convalescença, foi determinada a associação entre os sete SNPs, para os quais a população do ES foi caracterizada, e a persistência de sintomas. O DNA genômico dos participantes do estudo foi extraído do sangue periférico e a genotipagem dos SNPs foi realizada por reação em cadeia da polimerase - polimorfismo de comprimento de fragmento de restrição (do inglês: polymerase chain reaction - restriction fragment length polymorphism - PCR-RFLP) As frequências genotípicas de todos os SNPs encontraram-se em equilíbrio de Hardy-Weinberg (do inglês: Hardy-Weinberg equilibrium - HWE), com exceção do SNP no gene IL-6. Não houve diferença estatisticamente significante nas frequências genotípicas dos SNPs nos genes FcγRIIa, CD209, VDR, TNF-α e IL-4 entre as duas populações. Diferença estatisticamente significante foi encontrada entre as duas populações nas distribuições genotípicas dos SNPs nos genes IL-6 (p = 0,03) e INF-γ (p = 0,007). Trinta e sessenta dias após o início dos sintomas, 38,5% e 11,5% dos indivíduos com dengue sintomática reportaram ter pelo menos um sintoma clínico da dengue, respectivamente. Dos sintomas analisados, os mais persistentes foram os relacionados à síndrome da fadiga como mialgia, artralgia, astenia e mal-estar, sendo a mialgia o mais frequente. A persistência de sintomas em 30 dias foi associada ao gênero feminino (p = 0,044) e a persistência de sintomas constitucionais foi associada à dengue secundária (p = 0,041). O SNP no gene FcγRIIa, foi associado à persistência de sintomas em 30 dias, no subgrupo de indivíduos com dengue secundária (p = 0,046), sendo a presença do alelo H associada à não persistência de sintomas (p = 0,014). A presença do alelo A do SNP no gene TNF-α foi associada à não persistência de sintomas no subgrupo de indivíduos com dengue secundária (p = 0,025), sendo o genótipo GG associado à persistência de sintomas neurológicos, psicológicos e comportamentais em 30 dias (p = 0,038). A presença do alelo C do SNP no gene IL-6 foi associado à persistência de sintomas dermatológicos em 30 dias (p = 0,005). O perfil genético desses SNPs pode favorecer o estabelecimento de marcadores imunogenéticos associados à fase convalescente da infecção pelo vírus da dengue (do inglês: dengue virus - DENV).