Recursive Test of Hardy-Weinberg Equilibrium in Tetraploids

Issues and Solutions in Psychiatric Clinical Trial with Case Studies

The coronavirus disease-2019 pandemic resulted in a major increase in depression and anxiety disorders worldwide, which increased the demand for mental health services. However, clinical interventions for treating mental disorders are currently insufficient to meet this growing demand. There is an urgent need to conduct scientific and standardized clinical research that are consistent with the features of mental disorders in order to deliver more effective and safer therapies in the clinic. Our study aimed to expose the challenges, complexities of study design, ethical issues, sample selection, and efficacy evaluation in clinical research for mental disorders. The reliance on subjective symptom presentation and rating scales for diagnosing mental diseases was discovered, emphasizing the lack of clear biological standards, which hampers the construction of rigorous research criteria. We underlined the possibility of psychotherapy in efficacy evaluation alongside medication treatment, proposing for a multidisciplinary approach comprising psychiatrists, neuroscientists, and statisticians. To comprehend mental disorders progression, we recommend the development of artificial intelligence integrated evaluation tools, the use of precise biomarkers, and the strengthening of longitudinal designs. In addition, we advocate for international collaboration to diversity samples and increase the dependability of findings, with the goal of improving clinical research quality in mental disorders through sample representativeness, accurate medical history gathering, and adherence to ethical principles.

Bayesian tests for random mating in polyploids

Hardy-Weinberg proportions (HWP) are often explored to evaluate the assumption of random mating. However, in autopolyploids, organisms with more than two sets of homologous chromosomes, HWP and random mating are different hypotheses that require different statistical testing approaches. Currently, the only available methods to test for random mating in autopolyploids (i) heavily rely on asymptotic approximations and (ii) assume genotypes are known, ignoring genotype uncertainty. Furthermore, these approaches are all frequentist, and so do not carry the benefits of Bayesian analysis, including ease of interpretability, incorporation of prior information, and consistency under the null. Here, we present Bayesian approaches to test for random mating, bringing the benefits of Bayesian analysis to this problem. Our Bayesian methods also (i) do not rely on asymptotic approximations, being appropriate for small sample sizes, and (ii) optionally account for genotype uncertainty via genotype likelihoods. We validate our methods in simulations and demonstrate on two real datasets how testing for random mating is more useful for detecting genotyping errors than testing for HWP (in a natural population) and testing for Mendelian segregation (in an experimental S1 population). Our methods are implemented in Version 2.0.2 of the hwep R package on the Comprehensive R Archive Network https://cran.r-project.org/package=hwep.

Asymptotic tests for Hardy-Weinberg equilibrium in hexaploids

Hexaploids, a group of organisms containing three complete sets of chromosomes in a single nucleus, are of utmost importance to evolutionary studies and breeding programs. Many studies have focused on hexaploid linkage analysis and QTL mapping in controlled crosses, but little methodology has been developed to reveal how hexaploids diversify and evolve in natural populations. We formulate a general framework for studying the pattern of genetic variation in autohexaploid populations through testing deviation from Hardy-Weinberg equilibrium (HWE) at individual molecular markers. We confirm that hexaploids cannot reach exact HWE but can approach asymptotic HWE at 8-9 generations of random mating. We derive a statistical algorithm for testing HWE and the occurrence of double reduction for autopolyploids, a phenomenon that affects population variation during long evolutionary processes. We perform computer simulation to validate the statistical behavior of our test procedure and demonstrate its usefulness by analyzing a real data set for autohexaploid chrysanthemum. When extended to allohexaploids, our test procedure will provide a generic tool for illustrating the genome structure of hexaploids in the quest to infer their evolutionary status and design association studies of complex traits.

The transitivity of the Hardy-Weinberg law

The Hardy-Weinberg law is shown to be transitive in the sense that a multi-allelic polymorphism that is in equilibrium will retain its equilibrium status if any allele together with its corresponding genotypes is deleted from the population. Similarly, the transitivity principle also applies if alleles are joined, which leads to the summation of allele frequencies and their corresponding genotype frequencies. These basic polymorphism properties are intuitive, but they have apparently not been formalized or investigated. This article provides a straightforward proof of the transitivity principle, and its usefulness in genetic data analysis is explored, using high-quality autosomal microsatellite databases from the US National Institute of Standards and Technology. We address the reduction of multi-allelic polymorphisms to variants with fewer alleles, two in the limit. Equilibrium test results obtained with the original and reduced polymorphisms are generally observed to be coherent, in particular when results obtained with length-based and sequence-based microsatellites are compared. We exploit the transitivity principle in order to identify disequilibrium-related alleles, and show its usefulness for detecting population substructure and genotyping problems that relate to null alleles and allele imbalance.

A Tracing Model for the Evolutionary Equilibrium of Octoploids

Testing Hardy-Weinberg equilibrium (HWE) is a fundamental approach for inferring population diversity and evolution, but its application to octoploids containing eight chromosome sets has not well been justified. We derive a mathematical model to trace how genotype frequencies transmit from parental to offspring generations in the natural populations of autooctoploids. We find that octoploids, including autooctolpoids undergoing double reduction, attach asymptotic HWE (aHWE) after 15 generations of random mating, in a contrast to diploids where one generation can assure exact equilibrium and, also, different from tetraploids that use 5 generations to reach aHWE. We develop a statistical procedure for testing aHWE in octoploids and apply it to analyze a real data set from octoploid switchgrass distributed in two ecologically different regions, demonstrating the usefulness of the test procedure. Our model provides a tool for studying the population genetic diversity of octoploids, inferring their evolutionary history, and identifying the ecological relationship of octoploid-genome structure with environmental adaptation.

Identification and QTL Analysis of Flavonoids and Carotenoids in Tetraploid Roses Based on an Ultra-High-Density Genetic Map

Roses are highly valuable within the flower industry. The metabolites of anthocyanins, flavonols, and carotenoids in rose petals are not only responsible for the various visible petal colors but also important bioactive compounds that are important for human health. In this study, we performed a QTL analysis on pigment contents to locate major loci that determine the flower color traits. An F1 population of tetraploid roses segregating for flower color was used to construct an ultra-high-density genetic linkage map using whole-genome resequencing technology to detect genome-wide SNPs. Previously developed SSR and SNP markers were also utilized to increase the marker density. Thus, a total of 9,259 markers were mapped onto seven linkage groups (LGs). The final length of the integrated map was 1285.11 cM, with an average distance of 0.14 cM between adjacent markers. The contents of anthocyanins, flavonols and carotenoids of the population were assayed to enable QTL analysis. Across the 33 components, 46 QTLs were detected, explaining 11.85-47.72% of the phenotypic variation. The mapped QTLs were physically clustered and primarily distributed on four linkage groups, namely LG2, LG4, LG6, and LG7. These results improve the basis for flower color marker-assisted breeding of tetraploid roses and guide the development of rose products.

Computational characterization of double reduction in autotetraploid natural populations

Population genetic theory has been well developed for diploid species, but its extension to study genetic diversity, variation and evolution in autopolyploids, a class of polyploids derived from the genome doubling of a single ancestral species, requires the incorporation of multisomic inheritance. Double reduction, which is characteristic of autopolyploidy, has long been believed to shape the evolutionary consequence of organisms in changing environments. Here, we develop a computational model for testing and estimating double reduction and its genomic distribution in autotetraploids. The model is implemented with the expectation-maximization (EM) algorithm to dissect unobservable allelic recombinations among multiple chromosomes, enabling the simultaneous estimation of allele frequencies and double reduction in natural populations. The framework fills an important gap in the population genetic theory of autopolyploids.