952 resultados para Hardy-Weinberg Equilibrium


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The protein P29 is a potential serological marker for post-treatment monitoring of cystic echinococcosis (CE) especially in young patients. We now have demonstrated that P29 is encoded in the Echinococcus genus by a single gene consisting of 7 exons spanning 1.2 kb of DNA. Variability of the p29 gene at inter- and intra-species level was assessed with 50 cDNA and 280 genomic DNA clones isolated from different E. granulosus s.l. isolates (E. granulosus sensu stricto (G1), E. equinus (G4), E. ortleppi (G5), E. canadensis (G6), E. canadensis (G7) and E. canadensis (G10)) as well as four E. multilocularis isolates. Scarce interspecies polymorphism at the p29 locus was observed and affected predominantly E. granulosus s.s. (G1), where we identified two alleles (A1 and A2) coding for identical P29 proteins and yielding in three genotypes (A1/A1, A2/A2 and A1/A2). Genotypic frequencies expected under Hardy-Weinberg equilibrium revealed a high rate of heterozygosity (47%) that strongly supports the hypothesis that E. granulosus s.s. (G1) is predominantly outbreeding. Comparative sequence analyses of the complete p29 gene showed that phylogenetic relationships within the genus Echinococcus were in agreement with those of previous nuclear gene studies. At the protein level, the deduced P29 amino acid (AA) sequences exhibited a high level of conservation, ranging from 97.9% AA sequence identity among the whole E. granulosus s.l. group to 99.58% identity among E. multilocularis isolates. We showed that P29 proteins of these two species differ by three AA substitutions without implication for antigenicity. In Western-blot analyses, serum antibodies from a human CE patient infected with E. canadensis (G6) strongly reacted with recombinant P29 from E. granulosus s.s. (G1) (recEg(G1)P29). In the same line, human anti-Eg(G1)P29 antibodies bound to recEcnd(G6)P29. Thus, minor AA sequence variations appear not to impair the prognostic serological use of P29.

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Currently there is no general method to study the impact of population admixture within families on the assumptions of random mating and consequently, Hardy-Weinberg equilibrium (HWE) and linkage equilibrium (LE) and on the inference obtained from traditional linkage analysis. ^ First, through simulation, the effect of admixture of two populations on the log of the odds (LOD) score was assessed, using Prostate Cancer as the typical disease model. Comparisons between simulated mixed and homogeneous families were performed. LOD scores under both models of admixture (within families and within a data set of homogeneous families) were closest to the homogeneous family scores of the population having the highest mixing proportion. Random sampling of families or ascertainment of families with disease affection status did not affect this observation, nor did the mode of inheritance (dominant/recessive) or sample size. ^ Second, after establishing the effect of admixture on the LOD score and inference for linkage, the presence of induced disequilibria by population admixture within families was studied and an adjustment procedure was developed. The adjustment did not force all disequilibria to disappear but because the families were adjusted for the population admixture, those replicates where the disequilibria exist are no longer affected by the disequilibria in terms of maximization for linkage. Furthermore, the adjustment was able to exclude uninformative families or families that had such a high departure from HWE and/or LE that their LOD scores were not reliable. ^ Together these observations imply that the presence of families of mixed population ancestry impacts linkage analysis in terms of the LOD score and the estimate of the recombination fraction. ^

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My dissertation focuses on developing methods for gene-gene/environment interactions and imprinting effect detections for human complex diseases and quantitative traits. It includes three sections: (1) generalizing the Natural and Orthogonal interaction (NOIA) model for the coding technique originally developed for gene-gene (GxG) interaction and also to reduced models; (2) developing a novel statistical approach that allows for modeling gene-environment (GxE) interactions influencing disease risk, and (3) developing a statistical approach for modeling genetic variants displaying parent-of-origin effects (POEs), such as imprinting. In the past decade, genetic researchers have identified a large number of causal variants for human genetic diseases and traits by single-locus analysis, and interaction has now become a hot topic in the effort to search for the complex network between multiple genes or environmental exposures contributing to the outcome. Epistasis, also known as gene-gene interaction is the departure from additive genetic effects from several genes to a trait, which means that the same alleles of one gene could display different genetic effects under different genetic backgrounds. In this study, we propose to implement the NOIA model for association studies along with interaction for human complex traits and diseases. We compare the performance of the new statistical models we developed and the usual functional model by both simulation study and real data analysis. Both simulation and real data analysis revealed higher power of the NOIA GxG interaction model for detecting both main genetic effects and interaction effects. Through application on a melanoma dataset, we confirmed the previously identified significant regions for melanoma risk at 15q13.1, 16q24.3 and 9p21.3. We also identified potential interactions with these significant regions that contribute to melanoma risk. Based on the NOIA model, we developed a novel statistical approach that allows us to model effects from a genetic factor and binary environmental exposure that are jointly influencing disease risk. Both simulation and real data analyses revealed higher power of the NOIA model for detecting both main genetic effects and interaction effects for both quantitative and binary traits. We also found that estimates of the parameters from logistic regression for binary traits are no longer statistically uncorrelated under the alternative model when there is an association. Applying our novel approach to a lung cancer dataset, we confirmed four SNPs in 5p15 and 15q25 region to be significantly associated with lung cancer risk in Caucasians population: rs2736100, rs402710, rs16969968 and rs8034191. We also validated that rs16969968 and rs8034191 in 15q25 region are significantly interacting with smoking in Caucasian population. Our approach identified the potential interactions of SNP rs2256543 in 6p21 with smoking on contributing to lung cancer risk. Genetic imprinting is the most well-known cause for parent-of-origin effect (POE) whereby a gene is differentially expressed depending on the parental origin of the same alleles. Genetic imprinting affects several human disorders, including diabetes, breast cancer, alcoholism, and obesity. This phenomenon has been shown to be important for normal embryonic development in mammals. Traditional association approaches ignore this important genetic phenomenon. In this study, we propose a NOIA framework for a single locus association study that estimates both main allelic effects and POEs. We develop statistical (Stat-POE) and functional (Func-POE) models, and demonstrate conditions for orthogonality of the Stat-POE model. We conducted simulations for both quantitative and qualitative traits to evaluate the performance of the statistical and functional models with different levels of POEs. Our results showed that the newly proposed Stat-POE model, which ensures orthogonality of variance components if Hardy-Weinberg Equilibrium (HWE) or equal minor and major allele frequencies is satisfied, had greater power for detecting the main allelic additive effect than a Func-POE model, which codes according to allelic substitutions, for both quantitative and qualitative traits. The power for detecting the POE was the same for the Stat-POE and Func-POE models under HWE for quantitative traits.

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Complex diseases such as cancer result from multiple genetic changes and environmental exposures. Due to the rapid development of genotyping and sequencing technologies, we are now able to more accurately assess causal effects of many genetic and environmental factors. Genome-wide association studies have been able to localize many causal genetic variants predisposing to certain diseases. However, these studies only explain a small portion of variations in the heritability of diseases. More advanced statistical models are urgently needed to identify and characterize some additional genetic and environmental factors and their interactions, which will enable us to better understand the causes of complex diseases. In the past decade, thanks to the increasing computational capabilities and novel statistical developments, Bayesian methods have been widely applied in the genetics/genomics researches and demonstrating superiority over some regular approaches in certain research areas. Gene-environment and gene-gene interaction studies are among the areas where Bayesian methods may fully exert its functionalities and advantages. This dissertation focuses on developing new Bayesian statistical methods for data analysis with complex gene-environment and gene-gene interactions, as well as extending some existing methods for gene-environment interactions to other related areas. It includes three sections: (1) Deriving the Bayesian variable selection framework for the hierarchical gene-environment and gene-gene interactions; (2) Developing the Bayesian Natural and Orthogonal Interaction (NOIA) models for gene-environment interactions; and (3) extending the applications of two Bayesian statistical methods which were developed for gene-environment interaction studies, to other related types of studies such as adaptive borrowing historical data. We propose a Bayesian hierarchical mixture model framework that allows us to investigate the genetic and environmental effects, gene by gene interactions (epistasis) and gene by environment interactions in the same model. It is well known that, in many practical situations, there exists a natural hierarchical structure between the main effects and interactions in the linear model. Here we propose a model that incorporates this hierarchical structure into the Bayesian mixture model, such that the irrelevant interaction effects can be removed more efficiently, resulting in more robust, parsimonious and powerful models. We evaluate both of the 'strong hierarchical' and 'weak hierarchical' models, which specify that both or one of the main effects between interacting factors must be present for the interactions to be included in the model. The extensive simulation results show that the proposed strong and weak hierarchical mixture models control the proportion of false positive discoveries and yield a powerful approach to identify the predisposing main effects and interactions in the studies with complex gene-environment and gene-gene interactions. We also compare these two models with the 'independent' model that does not impose this hierarchical constraint and observe their superior performances in most of the considered situations. The proposed models are implemented in the real data analysis of gene and environment interactions in the cases of lung cancer and cutaneous melanoma case-control studies. The Bayesian statistical models enjoy the properties of being allowed to incorporate useful prior information in the modeling process. Moreover, the Bayesian mixture model outperforms the multivariate logistic model in terms of the performances on the parameter estimation and variable selection in most cases. Our proposed models hold the hierarchical constraints, that further improve the Bayesian mixture model by reducing the proportion of false positive findings among the identified interactions and successfully identifying the reported associations. This is practically appealing for the study of investigating the causal factors from a moderate number of candidate genetic and environmental factors along with a relatively large number of interactions. The natural and orthogonal interaction (NOIA) models of genetic effects have previously been developed to provide an analysis framework, by which the estimates of effects for a quantitative trait are statistically orthogonal regardless of the existence of Hardy-Weinberg Equilibrium (HWE) within loci. Ma et al. (2012) recently developed a NOIA model for the gene-environment interaction studies and have shown the advantages of using the model for detecting the true main effects and interactions, compared with the usual functional model. In this project, we propose a novel Bayesian statistical model that combines the Bayesian hierarchical mixture model with the NOIA statistical model and the usual functional model. The proposed Bayesian NOIA model demonstrates more power at detecting the non-null effects with higher marginal posterior probabilities. Also, we review two Bayesian statistical models (Bayesian empirical shrinkage-type estimator and Bayesian model averaging), which were developed for the gene-environment interaction studies. Inspired by these Bayesian models, we develop two novel statistical methods that are able to handle the related problems such as borrowing data from historical studies. The proposed methods are analogous to the methods for the gene-environment interactions on behalf of the success on balancing the statistical efficiency and bias in a unified model. By extensive simulation studies, we compare the operating characteristics of the proposed models with the existing models including the hierarchical meta-analysis model. The results show that the proposed approaches adaptively borrow the historical data in a data-driven way. These novel models may have a broad range of statistical applications in both of genetic/genomic and clinical studies.

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Phylogeographic analyses of the fauna of the Australian wet tropics rainforest have provided strong evidence for long-term isolation of populations among allopatric refugia, yet typically there is no corresponding divergence in morphology. This system provides an opportunity to examine the consequences of geographic isolation, independent of morphological divergence, and thus to assess the broader significance of historical subdivisions revealed through mitochondrial DNA phylogeography. We have located and characterized a zone of secondary contact between two long isolated (mtDNA divergence > 15%) lineages of the skink Carlia rubrigularis using one mitochondrial and eight nuclear (two intron, six microsatellite) markers. This revealed a remarkably narrow (width < 3 km) hybrid zone with substantial linkage disequilibrium and strong deficits of heterozygotes at two of three nuclear loci with diagnostic alleles. Cline centers were coincident across loci. Using a novel form of likelihood analysis, we were unable to distinguish between sigmoidal and stepped cline shapes except at one nuclear locus for which the latter was inferred. Given estimated dispersal rates of 90-133 m x gen(-1/2) and assuming equilibrium, the observed cline widths suggest effective selection against heterozygotes of at least 22-49% and possibly as high as 70%. These observations reveal substantial postmating isolation, although the absence of consistent deviations from Hardy-Weinberg equilibrium at diagnostic loci suggests that there is little accompanying premating isolation. The tight geographic correspondence between transitions in mtDNA and those for nuclear genes and corresponding evidence for selection against hybrids indicates that these morphologically cryptic phylogroups could be considered as incipient species. Nonetheless, we caution against the use of mtDNA phylogeography as a sole criterion for defining species boundaries.

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The term "pharmacogenetics" has been defined as the scientific study of inherited factors that affect the human drug response. Many pharmacogenetie studies have been published since 1995 and have focussed on the principal enzyme family involved in drug metabolism, the cytochrome P450 family, particularly cytochrome P4502C9 and 2C19. In order to investigate the pharmacogenetic aspect of pharmacotherapy, the relevant studies describing the association of pharmacogenetic factor(s) in drug responses must be retrieved from existing literature using a systematic review approach. In addition, the estimation of variant allele prevalence for the gene under study between different ethnic populations is important for pharmacogenetic studies. In this thesis, the prevalence of CYP2C9/2C19 alleles between different ethnicities has been estimated through meta-analysis and the population genetic principle. The clinical outcome of CYP2C9/2C19 allelic variation on the pharmacotherapy of epilepsy has been investigated; although many new antiepileptic drugs have been launched into the market, carbamazepine, phenobarbital and phenytoin are still the major agents in the pharmacotherapy of epilepsy. Therefore, phenytoin was chosen as a model AED and the effect of CYP2C9/2C19 genetic polymorphism on phenytoin metabolism was further examined.An estimation of the allele prevalence was undertaken for three CYP2C9/2C19 alleles respectively using a meta-analysis of studies that fit the Hardy-Weinberg equilibrium. The prevalence of CYP2C9*1 is approximately 81%, 96%, 97% and 94% in Caucasian, Chinese, Japanese, African populations respectively; the pooled prevalence of CYP2C19*1 is about 86%, 57%, 58% and 85% in these ethnic populations respectively. However, the studies of association between CYP2C9/2C19 polymorphism and phenytoin metabolism failed to achieve any qualitative or quantitative conclusion. Therefore, mephenytoin metabolism was examined as a probe drug for association between CYP2C19 polymorphism and mephenytoin metabolic ratio. Similarly, analysis of association between CYP2C9 polymorphism and warfarin dose requirement was undertaken.It was confirmed that subjects carrying two mutated CYP2C19 alleles have higher S/R mephenytoin ratio due to deficient CYP2C19 enzyme activity. The studies of warfarin and CYP2C9 polymorphism did not provide a conclusive result due to poor comparability between studies.The genetic polymorphism of drug metabolism enzymes has been studied extensively, however other genetic factors, such as multiple drug resistance genes (MDR) and genes encoding ion channels, which may contribute to variability in function of drug transporters and targets, require more attention in future pharmacogenetic studies of antiepileptic drugs.

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Dioon Lindl. (Zamiaceae) is a small genus restricted to Mexico (12 species) and Honduras (one species). Previous systematic studies have been unable to fully resolve species relationships within the genus. Phylogenetic analyses were conducted with data from several sources, including Restriction Fragment Length Polymorphisms from the chloroplast genome, morphology, two introns of the low copy nuclear gene S-adenosyl-L-homocysteine hydrolase (SAHH) and the 5.8S/ITS2 regions of the nuclear ribosomal DNA. The goals of the study were to construct a total evidence species level phylogeny and to explore current biogeographical hypotheses. None of the analyses performed produced a fully resolved topology. Dioon is comprised of two main lineages (the Edule and Spinulosum Clades), which represents an ancient divergence within the genus. The two introns of the nuclear gene SAHH offer additional evidence for the split into two lineages. Intron 2 contains a 18 bp deletion in the Spinulosum Clade, providing a synapomorphy for that group. The 5.8S/ITS2 regions were highly polymorphic and subsequently omitted from the combined analyses. In order to visualize congruence between morphology and molecular data, morphological characters were mapped onto the combined molecular tree. Current biogeographical hypotheses of a general northward pattern of migration and speciation are supported here. However, sister relationships within the Edule Clade are not fully resolved. Seven DNA microsatellite markers were developed to investigate patterns of genetic variation of seven populations of D. edule, a species restricted to Eastern Mexico. We found that most of the genetic variation lies within populations (Ho = 0.2166–0.3657) and that levels of population differentiation are low (Fst = 0.088); this finding is congruent with the breeding system of this species, dioicy. Four of the populations deviate from Hardy Weinberg Equilibrium and have a high number of identical genotypes, we suggest that this unexpected pattern is due to the life-history strategy of the species coupled with the few number of polymorphic loci detected in these populations. Our results are not congruent with earlier evidence from morphology and allozyme markers that suggest that the two northernmost populations represent a distinct entity that is recognized by some taxonomists as D. angustifolium.

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The highly polymorphic DlS80 locus has no known genetic function. This variable number of tandem repeat (VNTR) has been valuable in forensic identification. We have obtained allelic and genotypic frequencies for five African populations (Benin, Cameroon, Egypt, Kenya and Rwanda), which could be employed as databases to identify individuals. The polymerase chain reaction, followed by vertical polyacrylamide gel electrophoresis and silver staining was our method of analysis. Allele frequencies were used to infer genetic associations using Phylip 3.5, Principal Component and G-test statistical programs. Tests for Hardy-Weinberg equilibrium were employed. Fst estimates and power of discrimination values were also determined for each of our populations. Our analyses of 28 additional populations demonstrated that the D1 S80 locus alone provided for the discrimination of major racial groups. Genetic homogeneity between the African groups was observed. We have generated a database useful for human differentiation and phylogenetic studies.

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O cancro é um dos maiores causadores globais de mortalidade e morbilidade, ocorrendo cerca de 14 milhões de novos casos por ano e 8,2 milhões de mortes anuais com esta patologia, números que tendem a aumentar 70% nas próximas duas décadas. A característica tumoral mais nefasta é a sua capacidade de metastização para outros órgãos, um mecanismo que pode ser despoletado pela falha dos mecanismos normais de controlo de crescimento, proliferação e reparação celulares, que facilita o processo de transformação de células normais em células cancerígenas. A oncogénese processa-se em três etapas, a iniciação, a promoção e a progressão e pode ter origem em células estaminais cancerígenas, que regulam as capacidades de propagação e recidiva do tumor. As neoplasias hematológicas resultam de alterações genéticas e /ou epigenéticas que conduzem à desregulação da proliferação, ao bloqueio da diferenciação e/ou à resitência à apoptose. Para além dos fatores de risco exógenos, como agentes carcinogénicos físicos, químicos e biológicos, existem também fatores endógenos, incluindo características genéticas, que podem alterar a predisposição para o aparecimento de neoplasias, bem como influenciar a resposta à terapêutica. Uma das terapêuticas aplicadas no tratamento do cancro é a quimioterapia. Os fármacos administrados a doentes oncológicos seguem normalmente o percurso de absorção, distribuição, metabolização e eliminação. Este curso pode sofrer alterações caso as proteínas transportadoras e metabolizadoras necessárias não atuem corretamente. Para um melhor conhecimento da influência das alterações provocadas por variações nos genes que codificam proteínas transportadoras de efluxo (MDR1, MRP1), proteínas de influxo (OCTN2) e proteínas metabolizadoras (UCK2), o objetivo deste trabalho consistiu na avaliação de polimorfismos nos genes MDR1, MRP1, OCTN2 e UCK2 e da sua relação com a predisposição para o desenvolvimento de neoplasias hematológicas. Para isto, foram utilizadas amostras de 307 doentes com neoplasias hematológicas, 83 de Síndrome Mielodisplásica (SMD), 63 Leucemia Mieloide Aguda (LMA), 16 de Síndrome Mielodisplásica/Neoplasias Mieloproliferativas (SMD/NMP), 77 de Mieloma Múltiplo (MM) e 68 de Gamapatia Monoclonal de Significado Indeterminado (MGUS) e 164 de controlos não neoplásicos e/ou indivíduos saudáveis. As amostras de ADN foram extraídas do sangue periférico com protocolo adequado. De forma a determinar os genótipos correspondentes a cada amostra, realizaram-se técnicas de RFLP-PCR e ARMS-PCR. Posteriormente, calcularam-se estatisticamente as frequências alélicas e genotípicas relativas às variantes polimórficas dos genes MDR1, MRP1, OCTN2 e UCK2 e verificou-se se estavam em Equilíbrio de Hardy-Weinberg. De seguida, avaliou-se a força de associação entre as formas polimórficas e o risco de desenvolvimento de neoplasias hematológicas, através do cálculo do risco relativo por análise de regressão logística. Avaliaram-se ainda os perfis genéticos e a possível relação com o desenvolvimento e progressão da neoplasia com recurso a regressão logística e análise de Kaplan-Meier. De um modo geral as frequências alélicas e genotípicas não se revelaram alteradas comparativamente ao esperado. A análise do odds ratio associado ao polimorfismo rs1045642 do gene MDR1 revelou que o genótipo CT pode constituir um fator de risco aumentado de 1,84x para o desenvolvimento de Gamapatias Monoclonais e 2,27x para o desenvolvimento de Mieloma Múltiplo. Por outro lado, a presença de genótipos portadores do alelo T têm um efeito protetor no desenvolvimento de MM (OR=0,41). O cálculo do risco associado ao polimorfismo rs4148330 do gene MRP1 revela que o genótipo AG é um fator protetor (OR=0,50) para o desenvolvimento de LMA, assim como o alelo G (OR=0,50). Além disso, verificámos que existe uma associação de risco de desenvolver neoplasia com o polimorfismo rs2185268 do gene UCK2. De facto, a presença dos genótipos CC e AC representam um fator de risco 4,59x aumentado para o desenvolvimento de SMD/NMP. O polimorfismo rs274561 do gene OCTN2 não apresenta relação com o risco relativo de desenvolvimento neoplásico. Da avaliação da influência dos polimorfismos em estudo na sobrevivência global dos doentes, podemos assumir que a presença do genótipo GG relativo ao polimorfismo rs2185268 do gene UCK2 representa uma diminuição da sobrevivência em 11 meses. Os resultados obtidos a partir do nosso estudo permitem-nos concluir que os polimorfismos podem ser fatores relevantes na predisposição para o desenvolvimento de neoplasias hematológicas e na progressão destas doenças.

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The Aryl Hydrocarbon Receptor (AhR) is required for the toxicity of TCDD, and so the AhR of CRL:WI and CRL:WI(Han) rats was characterised. Western blot showed AhR proteins of ~110 and ~97 kDa in individual rats from both strains. The AhR cDNA from a CRL:WI(Han) rat with the ~110kDa protein revealed a sequence that was identical to that of the CRL:WI and SD rat. However, cloning of the AhR from a rat with the ~97kDa protein revealed a point mutation, and five variants encoding two C-terminally truncated variants of the AhR protein, arising from a point mutation in the intron/exon junction and consequent differential splicing. These C-terminally truncated variants were expressed and shown to give rise to a protein of ~97kDa; the recombinant AhR bound TCDD with an affinity that was not statistically different from the full-length protein. A single-nucleotide polymorphism (SNP) assay was developed, and showed that both alleles were represented in a Hardy-Weinberg equilibrium in samples of CRL:WI and CRL:WI(Han) populations; both alleles are abundant. Rats from two studies of TCDD developmental toxicity were genotyped, and the association with toxicity investigated using statistical analysis. There was no plausible evidence that the AhR allele had a significant effect on the toxic endpoints examined. These data show that the two AhR alleles are common in two strains of Wistar rat, and that the AhR alleles had no effect on TCDD-induced developmental toxicity in two independent studies.

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We describe the first microsatellite loci isolated from the giant otter (Pteronura brasiliensis), an endangered mustelid endemic to South America. Fourteen di- and trinucleotide polymorphic loci were characterised in fourteen individuals from the Pantanal wetlands, Central Brazil. Number of alleles per locus ranged from 2 to 5, and average observed heterozygosity was 0.577. Two loci were in linkage disequilibrium, and one further locus deviated from Hardy?Weinberg equilibrium, probably due to the presence of null alleles. The transferability of these markers to two other mustelids (Lontra longicaudis and Eira barbara) and to the mephitid Conepatus semistriatus was also evaluated. These loci are useful to study the ecology and evolution of these species.

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Background: Partially clonal organisms are very common in nature, yet the influence of partial asexuality on the temporal dynamics of genetic diversity remains poorly understood. Mathematical models accounting for clonality predict deviations only for extremely rare sex and only towards mean inbreeding coefficient (F-IS) over bar < 0. Yet in partially clonal species, both F-IS < 0 and F-IS > 0 are frequently observed also in populations where there is evidence for a significant amount of sexual reproduction. Here, we studied the joint effects of partial clonality, mutation and genetic drift with a state-and-time discrete Markov chain model to describe the dynamics of F-IS over time under increasing rates of clonality. Results: Results of the mathematical model and simulations show that partial clonality slows down the asymptotic convergence to F-IS = 0. Thus, although clonality alone does not lead to departures from Hardy-Weinberg expectations once reached the final equilibrium state, both negative and positive F-IS values can arise transiently even at intermediate rates of clonality. More importantly, such "transient" departures from Hardy Weinberg proportions may last long as clonality tunes up the temporal variation of F-IS and reduces its rate of change over time, leading to a hyperbolic increase of the maximal time needed to reach the final mean (F-IS,F-infinity) over bar value expected at equilibrium. Conclusion: Our results argue for a dynamical interpretation of F-IS in clonal populations. Negative values cannot be interpreted as unequivocal evidence for extremely scarce sex but also as intermediate rates of clonality in finite populations. Complementary observations (e.g. frequency distribution of multiloci genotypes, population history) or time series data may help to discriminate between different possible conclusions on the extent of clonality when mean (F-IS) over bar values deviating from zero and/or a large variation of F-IS over loci are observed.

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This paper deals with problems on population genetics in Hymenoptera and particularly in social Apidae. 1) The studies on populations of Hymenoptera were made according to the two basic types of reproduction: endogamy and panmixia. The populations of social Apinae have a mixed method of reproduction with higher percentage of panmixia and a lower of endogamy. This is shown by the following a) males can enter any hive in swarming time; b) males of Meliponini are expelled from hives which does not need them, and thus, are forced to look for some other place; c) Meliponini males were seen powdering themselves with pollen, thus becoming more acceptable in any other hive. The panmixia is not complete owing to the fact that the density of the breeding population as very low, even in the more frequent species as low as about 2 females and 160 males per reproductive area. We adopted as selection values (or survival indices) the expressions according to Brieger (1948,1950) which may be summarised as follows; a population: p2AA + ²pq Aa + q2aa became after selection: x p2AA + 2pq Aa + z q²aa. For alge-braics facilities Brieger divided the three selective values by y giving thus: x/y p2 AA + y/y 2 pq Aa + z/y q²aa. He called x/y of RA and z/y of Ra, that are survival or selective index, calculated in relation to the heterozygote. In our case all index were calculated in relation to the heterozygote, including the ones for haploid males; thus we have: RA surveval index of genotype AA Ra surveval index of genotype aa R'A surveval index of genotype A R'a surveval index of genotype a 1 surveval index of genotype Aa The index R'A ande R'a were equalized to RA and Ra, respectively, for facilities in the conclusions. 2) Panmitic populations of Hymenoptera, barring mutations, migrations and selection, should follow the Hardy-Weinberg law, thus all gens will be present in the population in the inicial frequency (see Graphifc 1). 3) Heterotic genes: If mutation for heterotic gene ( 1 > RA > Ra) occurs, an equilibrium will be reached in a population when: P = R A + Ra - 2R²a _____________ (9) 2(R A + Ra - R²A - R²a q = R A + Ra - 2R²A _____________ (10) 2(R A + Ra - R²A - R²a A heterotic gene in an hymenopteran population may be maintained without the aid of new mutation only if the survival index of the most viable mutant (RA) does not exced the limiting value given by the formula: R A = 1 + √1+Ra _________ 4 If RA has a value higher thah the one permitted by the formula, then only the more viable gene will remain present in the population (see Graphic 10). The only direct proof for heterotic genes in Hymenoptera was given by Mackensen and Roberts, who obtained offspring from Apis mellefera L. queens fertilized by their own sons. Such inbreeding resulted in a rapid loss of vigor the colony; inbred lines intercrossed gave a high hybrid vigor. Other fats correlated with the "heterosis" problem are; a) In a colony M. quadrifasciata Lep., which suffered severely from heat, the percentage of deths omong males was greater .than among females; b) Casteel and Phillips had shown that in their samples (Apis melifera L). the males had 7 times more abnormalities tian the workers (see Quadros IV to VIII); c) just after emerging the males have great variation, but the older ones show a variation equal to that of workers; d) The tongue lenght of males of Apis mellifera L., of Bombus rubicundus Smith (Quadro X), of Melipona marginata Lep. (Quadro XI), and of Melipona quadrifasciata Lep. Quadro IX, show greater variationthan that of workers of the respective species. If such variation were only caused by subviables genes a rapid increasse of homozigoty for the most viable alleles should be expected; then, these .wild populations, supposed to be in equilibrium, could .not show such variability among males. Thus we conclude that heterotic genes have a grat importance in these cases. 4) By means of mathematical models, we came to the conclusion tht isolating genes (Ra ^ Ra > 1), even in the case of mutations with more adaptability, have only the opor-tunity of survival when the population number is very low (thus the frequency of the gene in the breeding population will be large just after its appearence). A pair of such alleles can only remain present in a population when in border regions of two races or subspecies. For more details see Graphics 5 to 8. 5) Sex-limited genes affecting only females, are of great importance toHymenoptera, being subject to the same limits and formulas as diploid panmitic populations (see formulas 12 and 13). The following examples of these genes were given: a) caste-determining genes in the genus Melipona; b) genes permiting an easy response of females to differences in feeding in almost all social Hymenoptera; c) two genes, found in wild populations, one in Trigona (Plebéia) mosquito F. SMITH (quadro XII) and other in Melipona marginata marginata LEP. (Quadro XIII, colonies 76 and 56) showing sex-limited effects. Sex-limited genes affecting only males do not contribute to the plasticity or genie reserve in hymenopteran populations (see formula 14). 6) The factor time (life span) in Hymenoptera has a particular importance for heterotic genes. Supposing one year to be the time unit and a pair of heterotic genes with respective survival indice equal to RA = 0, 90 and Ra = 0,70 to be present; then if the life time of a population is either one or two years, only the more viable gene will remain present (see formula 11). If the species has a life time of three years, then both alleles will be maintained. Thus we conclude that in specis with long lif-time, the heterotic genes have more importance, and should be found more easily. 7) The colonies of social Hymenoptera behave as units in competition, thus in the studies of populations one must determine the survival index, of these units which may be subdivided in indice for egg-laying, for adaptive value of the queen, for working capacity of workers, etc. 8) A study of endogamic hymenopteran populations, reproduced by sister x brother mating (fig. 2), lead us to the following conclusions: a) without selection, a population, heterozygous for one pair of alleles, will consist after some generations (theoretically after an infinite number of generation) of females AA fecundated with males A and females aa fecundated with males a (see Quadro I). b) Even in endogamic population there is the theoretical possibility of the presence of heterotic genes, at equilibrium without the aid of new mutations (see Graphics 11 and 12), but the following! conditions must be satisfied: I - surveval index of both homozygotes (RA e Ra) should be below 0,75 (see Graphic 13); II - The most viable allele must riot exced the less viable one by more than is permited by the following formula (Pimentel Gomes 1950) (see Gra-fic 14) : 4 R5A + 8 Ra R4A - 4 Ra R³A (Ra - 1) R²A - - R²a (4 R²a + 4 Ra - 1) R A + 2 R³a < o Considering these two conditions, the existance of heterotic genes in endogamic populations of Hymenoptera \>ecames very improbable though not - impossible. 9) Genie mutation offects more hymenopteran than diploid populations. Thus we have for lethal genes in diploid populations: u = q2, and in Hymenoptera: u = s, being u the mutation ratio and s the frequency of the mutant in the male population. 10) Three factors, important to competition among species of Meliponini were analysed: flying capacity of workers, food gathering capacity of workers, egg-laying of the queen. In this connection we refer to the variability of the tongue lenght observed in colonies from several localites, to the method of transporting the pollen in the stomach, from some pots (Melliponi-ni storage alveolus) to others (e. g. in cases of pillage), and to the observation that the species with the most populous hives are almost always the most frequent ones also. 11) Several defensive ways used for Meliponini to avoid predation are cited, but special references are made upon the camouflage of both hive (fig. 5) and hive entrance (fig. 4) and on the mimetism (see list in page ). Also under the same heading we described the method of Lestrimelitta for pillage. 12) As mechanisms important for promoting genetic plasticity of hymenopteran species we cited: a) cytological variations and b) genie reserve. As to the former, duplications and numerical variations of chromosomes were studied. Diprion simile ATC was cited as example for polyploidy. Apis mellife-ra L. (n •= 16) also sugests polyploid origen since: a) The genus Melipona, which belongs to a" related tribe, presents in all species so far studied n = 9 chromosomes and b) there occurs formation of dyads in the firt spermatocyte division. It is su-gested that the origin of the sex-chromosome of Apis mellifera It. may be related to the possible origin of diplo-tetraploidy in this species. With regards to the genie reserve, several possible types of mutants were discussed. They were classified according to their survival indices; the heterotic and neutral mutants must be considered as more important for the genie reserve. 13) The mean radius from a mother to a daghter colony was estimated as 100 meters. Since the Meliponini hives swarm only once a year we may take 100 meters a year as the average dispersion of female Meliponini in ocordance to data obtained from Trigona (tetragonisca) jaty F. SMITH and Melipona marginata LEP., while other species may give different values. For males the flying distance was roughly estimated to be 10 times that for females. A review of the bibliography on Meliponini swarm was made (pg. 43 to 47) and new facts added. The population desity (breeding population) corresponds in may species of Meliponini to one male and one female per 10.000 square meters. Apparently the males are more frequent than the females, because there are sometimes many thousands, of males in a swarm; but for the genie frequency the individuals which have descendants are the ones computed. In the case of Apini and Meliponini, only one queen per hive and the males represented by. the spermatozoos in its spermateca are computed. In Meliponini only one male mate with the queen, while queens of Apis mellijera L. are fecundated by an average of about 1, 5 males. (Roberts, 1944). From the date cited, one clearly sees that, on the whole, populations of wild social bees (Meliponini) are so small that the Sewall Wright effect may become of great importance. In fact applying the Wright's formula: f = ( 1/aN♂ + 1/aN♀) (1 - 1/aN♂ + 1/aN♀) which measures the fixation and loss of genes per generation, we see that the fixation or loss of genes is of about 7% in the more frequent species, and rarer species about 11%. The variation in size, tergite color, background color, etc, of Melipona marginata Lep. is atributed to this genetic drift. A detail, important to the survival of Meliponini species, is the Constance of their breeding population. This Constance is due to the social organization, i. e., to the care given to the reproductive individuals (the queen with its sperm pack), to the way of swarming, to the food storage intended to control variations of feeding supply, etc. 14) Some species of the Meliponini are adapted to various ecological conditions and inhabit large geographical areas (e. g. T. (Tetragonisca jaty F. SMITH), and Trigona (Nanno-trigona testaceicornis LEP.) while others are limited to narrow regions with special ecological conditions (e. g. M. fuscata me-lanoventer SCHWARZ). Other species still, within the same geographical region, profit different ecological conditions, as do M. marginata LEP. and M. quadrifasciata LEP. The geographical distribution of Melipona quadrifasciata LEP. is different according to the subspecies: a) subsp anthidio-des LEP. (represented in Fig. 7 by black squares) inhabits a region fron the North of the S. Paulo State to Northeastern Brazil, ,b) subspecies quadrifasciata LEP., (marked in Fig. 7 with black triangles) accurs from the South of S. Paulo State to the middle of the State of Rio Grande do Sul (South Brazil). In the margined region between these two areas of distribution, hi-brid colonies were found (Fig. 7, white circles); they are shown with more details in fig. 8, while the zone of hybridization is roughly indicated in fig. 9 (gray zone). The subspecies quadrifasciata LEP., has 4 complete yellow bands on the abdominal tergites while anthidioides LEP. has interrupted ones. This character is determined by one or two genes and gives different adaptative properties to the subspecies. Figs. 10 shows certains meteorological isoclines which have aproximately the same configuration as the limits of the hybrid zone, suggesting different climatic adaptabilities for both genotypes. The exis-tance of a border zone between the areas of both subspecies, where were found a high frequency of hybrids, is explained as follows: being each subspecies adapted to a special climatic zone, we may suppose a poor adaptation of either one in the border region, which is also a region of intermediate climatic conditions. Thus, the hybrids, having a combination of the parent qualities, will be best adapted to the transition zone. Thus, the hybrids will become heterotic and an equilibrium will be reached with all genotypes present in the population in the border region.

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We report 22 new polymorphic microsatellites for the Ivory gull (Pagophila eburnea), and we describe how they can be efficiently co-amplified using multiplexed polymerase chain reactions. In addition, we report DNA concentration, amplification success, rates of genotyping errors and the number of genotyping repetitions required to obtain reliable data with three types of noninvasive or nondestructive samples: shed feathers collected in colonies, feathers plucked from living individuals and buccal swabs. In two populations from Greenland (n=21) and Russia (Severnaya Zemlya Archipelago, n=21), the number of alleles per locus varied between 2 and 17, and expected heterozygosity per population ranged from 0.18 to 0.92. Twenty of the markers conformed to Hardy-Weinberg and linkage equilibrium expectations. Most markers were easily amplified and highly reliable when analysed from buccal swabs and plucked feathers, showing that buccal swabbing is a very efficient approach allowing good quality DNA retrieval. Although DNA amplification success using single shed feathers was generally high, the genotypes obtained from this type of samples were prone to error and thus need to be amplified several times. The set of microsatellite markers described here together with multiplex amplification conditions and genotyping error rates will be useful for population genetic studies of the Ivory gull.