Discrete Gamma Distribution Research Articles

Molecular characterization, genetic divergence, expression of encapsidiation and synergism by a bipartite begomovirus; Tomato leaf curl Palampur virus (ToLCPMV) infecting bitter gourd (Momordica charantia)

The Tomato leaf curl Palampur virus (ToLCPMV) is a bipartite begomovirus that poses a substantial risk to agriculture by infecting a variety of crops, including cucurbitaceous group. This study examines the manifestation of encapsidation and synergism by ToLCPMV in bitter gourd (Momordica charantia) and focuses on its epidemiological approaches and implications of managing this virus in tomatoes growing areas. Through the utilization of molecular and biological techniques, we have successfully ascertained the epidemiology of this highly destructive virus, highlighting the vital roles played by its two genetic components. An analysis was conducted to identify the mechanism by which the virus clusters its DNA into virions, known as the encapsidation process. Additionally, the impact of synergism with other viral or environmental factors over the degree of infection was examined. The evolutionary rate differences among sites were modeled deploying a discrete Gamma distribution with 5 categories and a [+G] parameter. The results of this study provide important and unique information about synergism, encapsidiation and host-virus interactions. Sequencing study revealed that the bipartite ToLCPMV is linked to the occurrence of leaf curl disease in bitter gourd. The DNA-A and DNA-B of the ToLCPMV isolates infecting bitter gourd (SP1-4) showed 89 %, 93 %, 95 %, and 98 % similarity respectively. Mean evolutionary rates in these categories were 0.19, 0.47, 0.79, 1.24, 2.31 substitutions per site. Unexpectedly, the DNA-A sequences of ToLCPMV that infect this particular host seemed to be an amalgamation of sequences that are closely associated with tomato leaf curl New Delhi virus (ToLCNDV). Additionally, reiterate cropping of tomatoes with vegetables expanded the virus's host geographic region. This understanding will create some specific ways to regulate the dissemination of ToLCPMV and minimize its adverse impacts in tomato growing regions. Through the implementation of these strategies, the ability of crops to withstand and recover from adverse conditions can be enhanced, so encouraging the adoption of sustainable farming practices in affected regions.

Performance of tree-building methods using a morphological dataset and a well-supported Hexapoda phylogeny.

Recently, many studies have addressed the performance of phylogenetic tree-building methods (maximum parsimony, maximum likelihood, and Bayesian inference), focusing primarily on simulated data. However, for discrete morphological data, there is no consensus yet on which methods recover the phylogeny with better performance. To address this lack of consensus, we investigate the performance of different methods using an empirical dataset for hexapods as a model. As an empirical test of performance, we applied normalized indices to effectively measure accuracy (normalized Robinson-Foulds metric, nRF) and precision, which are measured via resolution, one minus Colless' consensus fork index (1-CFI). Additionally, to further explore phylogenetic accuracy and support measures, we calculated other statistics, such as the true positive rate (statistical power) and the false positive rate (type I error), and constructed receiver operating characteristic plots to visualize the relationship between these statistics. We applied the normalized indices to the reconstructed trees from the reanalyses of an empirical discrete morphological dataset from extant Hexapoda using a well-supported phylogenomic tree as a reference. Maximum likelihood and Bayesian inference applying the k-state Markov (Mk) model (without or with a discrete gamma distribution) performed better, showing higher precision (resolution). Additionally, our results suggest that most available tree topology tests are reliable estimators of the performance measures applied in this study. Thus, we suggest that likelihood-based methods and tree topology tests should be used more often in phylogenetic tree studies based on discrete morphological characters. Our study provides a fair indication that morphological datasets have robust phylogenetic signal.

Phylogenetic analysis of Prunus genus using nuclear and chloroplast gene markers as a bioorganic structure profiling

Prunus species are known as model species for the family Rosaceae and other woody plants with their small genome size and relatively small life cycle as woody plants. Also Prunus species are economically important plants in the subfamily Amygdaloideae of the Rosaceae have a controversial taxonomic history due to the lack of a phylogenetic framework. Therefore, mapping, classification, determination the genetic structure and characterization of genes as a spesific chemical and fuctional units of nucleic acids and making phylogenetic analysis in these species have important implications. The aim of this study to find any gene markers as a bioorganic – chemical structure profiling to determine genetic diversity of different Prunus species from Iraq by using nuclear and chloroplast DNA markers to evaluate the phylogeny of Prunus. A total of 12 species Prunus subgenus amygdalus were collected from Iraq. Ten gene region markers on both nuclear DNA and chloroplast DNA have been tested to evaluate the genetic variation at their molecular levels by using multiplex PCR with 10 gene region primers and sequence analysis for matK. The name of the gene regions using in this study are ITS (ITS1+ITS2+5.8S coding region), rbcL, matK, rpl16, trnL-trnF, atpB-rbcL, rp136-infA-rps8, trnK-rps16, pbsM-trnD, psbA-trnH. As a result, five different phylogenetic trees were obtained from the gene sequences of the samples and the base sequences were close to each other. The estimated value of the shape parameter for the discrete Gamma Distribution is 0.05. The nucleotide frequencies are A = 29.41%, T/U = 37.37%, C = 17.52%, and G = 15.67%. The nucleotide diversity of the sequence was low with the 0.004113 value. There were 14 different informative base site between the samples. The polymorphism observed was less in agreement with higher level of conservation of the gene regions. The Prunus species from Iraq region were grouped on two closed clusters on the phylogenetic trees.

Data-Supported Caching Policy Optimization for Wireless D2D Caching Networks

In this paper we study a data-supported caching policy design for wireless D2D caching networks, which is based on a dataset collected from a campus Wi-Fi network. After a well-designed preprocessing for the dataset, for the first time, we conduct a real dataset based performance evaluation for the caching policies designed based on the homogeneous Poisson Point Process (PPP) model and a clustered PPP model. We proceed to propose a novel approach for the design of the D2D caching policy. It directly models the number of D2D neighbours, instead of characterizing the locations of users as the PPP models. We show that the number of D2D neighbours can be well modeled by a discrete Gamma distribution. Given the model, we develop an iterative algorithm to optimize the D2D caching policy, and also provide a method to optimize the cache update time in order to balance the caching gain and overhead. Simulation results based on the dataset show that the proposed caching policy can achieve good performance with low cost of cache updating.

On the Discretization of Continuous Probability Distributions Using a Probabilistic Rounding Mechanism

Most existing flexible count distributions allow only approximate inference when used in a regression context. This work proposes a new framework to provide an exact and flexible alternative for modeling and simulating count data with various types of dispersion (equi-, under-, and over-dispersion). The new method, referred to as “balanced discretization”, consists of discretizing continuous probability distributions while preserving expectations. It is easy to generate pseudo random variates from the resulting balanced discrete distribution since it has a simple stochastic representation (probabilistic rounding) in terms of the continuous distribution. For illustrative purposes, we develop the family of balanced discrete gamma distributions that can model equi-, under-, and over-dispersed count data. This family of count distributions is appropriate for building flexible count regression models because the expectation of the distribution has a simple expression in terms of the parameters of the distribution. Using the Jensen–Shannon divergence measure, we show that under the equidispersion restriction, the family of balanced discrete gamma distributions is similar to the Poisson distribution. Based on this, we conjecture that while covering all types of dispersions, a count regression model based on the balanced discrete gamma distribution will allow recovering a near Poisson distribution model fit when the data are Poisson distributed.

A Phylogenetic Rate Parameter Indicates Different Sequence Divergence Patterns in Orthologs and Paralogs.

Heterotachy-the change in sequence evolutionary rate over time-is a common feature of protein molecular evolution. Decades of studies have shed light on the conditions under which heterotachy occurs, and there is evidence that site-specific evolutionary rate shifts are correlated with changes in protein function. Here, we present a large-scale, computational analysis using thousands of protein sequence alignments from animal and plant proteomes, representing genes related either by orthology (speciation events) or paralogy (gene duplication), to compare sequence divergence patterns in orthologous vs. paralogous sequence alignments. We use sequence-based phylogenetic analyses to infer overall sequence divergence (tree length/number of sequences) and to fit site-specific rates to a discrete gamma distribution with a shape parameter α. This inference method is applied to real protein sequence alignments, as well as alignments simulated under various models of protein sequence evolution. Our simulations indicate that sequence divergence and the α parameter are positively correlated when sequences evolve with heterotachy, meaning that inferred site rate distributions appear more uniform as sequences diverge. Divergence and α are also positively correlated in both orthologous and paralogous genes, but the average increase in α (as a function of divergence) is significantly higher in paralogous protein alignments than in orthologous alignments. This result is consistent with the widely held view that recently duplicated proteins initially evolve under relaxed selective pressure, promoting functional divergence by accumulation of amino acid replacements, and hence experience more evolutionary rate fluctuations than orthologous proteins. We discuss these findings in the context of the ortholog conjecture, a long-standing assumption in molecular evolution, which posits that protein sequences related by orthology tend to be more functionally conserved than paralogous proteins.

A26 Molecular epidemiology of hepatitis E virus in Ireland 2016

Foodborne viruses such as hepatitis E virus (HEV) pose an increasing risk to public health and to confidence in Irish food. Hepatitis E has been acknowledged as a significant pathogen of likely zoonotic transmission, with pork products and shellfish being implicated as potential sources. The European Food Safety Authority has recommended that systematic strain typing of viruses in humans, animals, and food commodities is needed to improve understanding of etiological agents and foodborne transmission pathways, in particular for HEV. The dominant autochthonous genotype of HEV in Europe is genotype 3, thought to be associated with consumption of contaminated food, specifically pork products. However, little is known about the epidemiology of HEV in Ireland. In 2016, HEV became a notifiable disease in Ireland. Following this, as part of the Department of Agriculture, Food and the Marine-funded FoVIRA study, the molecular epidemiology of HEV in Irish clinical samples has been characterized for the first time. HEV RNA-positive clinical specimens from 2016 were genetically characterized (n = 14). A 450 nucleotide fragment of the ORF2 region of the HEV genome was amplified, with contiguous sequence assembly performed using DNA Lasergene v14. Sequences were aligned with ClustalW implemented in Bioedit v7.1.9 and compared to reference strains from GenBank. A maximum likelihood phylogenetic tree was constructed using the Hasegawa–Kishino–Yano model and a discrete gamma distribution to model evolutionary rate distances between sites. Evolutionary analyses were conducted in MEGA7. Statistical support was provided by bootstrapping with 1,000 replicates. Fourteen strains belonged to genotype 3 and were classified as the following subtypes: 3c (n = 7), 3e (n = 4), 3f (n = 1), 3 untyped (n = 1), and 1 untyped. Phylogenetic analysis showed the formation of two distinct clusters of genotype 3:3abchij and 3efg, with strong bootstrap support. A genotype 1 was detected and found to be associated with travel. Data generated from this research will contribute to a risk exposure assessment and will be used to identify potential control points and risk mitigation measures for viral foodborne pathogens. This study will provide a unique opportunity to build national capability in the area of food testing within Irish public laboratories.

Identifiability of the unrooted species tree topology under the coalescent model with time-reversible substitution processes, site-specific rate variation, and invariable sites.

The inference of the evolutionary history of a collection of organisms is a problem of fundamental importance in evolutionary biology. The abundance of DNA sequence data arising from genome sequencing projects has led to significant challenges in the inference of these phylogenetic relationships. Among these challenges is the inference of the evolutionary history of a collection of species based on sequence information from several distinct genes sampled throughout the genome. It is widely accepted that each individual gene has its own phylogeny, which may not agree with the species tree. Many possible causes of this gene tree incongruence are known. The best studied is the incomplete lineage sorting, which is commonly modeled by the coalescent process. Numerous methods based on the coalescent process have been proposed for the estimation of the phylogenetic species tree given DNA sequence data. However, use of these methods assumes that the phylogenetic species tree can be identified from DNA sequence data at the leaves of the tree, although this has not been formally established. We prove that the unrooted topology of the n-leaf phylogenetic species tree is generically identifiable given observed data at the leaves of the tree that are assumed to have arisen from the coalescent process under a time-reversible substitution process with the possibility of site-specific rate variation modeled by the discrete gamma distribution and a proportion of invariable sites.

On Discrete Gamma Distribution

A new discrete counterpart of gamma distribution for modelling discrete life data is defined based on similar mathematical form and properties of the continuous version. The main statistical and reliability properties of this distribution are derived and it is shown that this model can deal with both over and under-dispersed data. Geometric variables and finite sum of geometric variables, i.e., negative binomial are shown to be special cases of the proposed discrete gamma. Also, the size-biased discrete gamma distribution is derived and discussed. Moreover, different estimation methods of the underlying parameters of this distribution are utilized and comparisons of their performance have been made. Finally, an application in real-life data is used to elucidate the earlier results of this article.

The impact of modelling rate heterogeneity among sites on phylogenetic estimates of intraspecific evolutionary rates and timescales.

Phylogenetic analyses of DNA sequence data can provide estimates of evolutionary rates and timescales. Nearly all phylogenetic methods rely on accurate models of nucleotide substitution. A key feature of molecular evolution is the heterogeneity of substitution rates among sites, which is often modelled using a discrete gamma distribution. A widely used derivative of this is the gamma-invariable mixture model, which assumes that a proportion of sites in the sequence are completely resistant to change, while substitution rates at the remaining sites are gamma-distributed. For data sampled at the intraspecific level, however, biological assumptions involved in the invariable-sites model are commonly violated. We examined the use of these models in analyses of five intraspecific data sets. We show that using 6–10 rate categories for the discrete gamma distribution of rates among sites is sufficient to provide a good approximation of the marginal likelihood. Increasing the number of gamma rate categories did not have a substantial effect on estimates of the substitution rate or coalescence time, unless rates varied strongly among sites in a non-gamma-distributed manner. The assumption of a proportion of invariable sites provided a better approximation of the asymptotic marginal likelihood when the number of gamma categories was small, but had minimal impact on estimates of rates and coalescence times. However, the estimated proportion of invariable sites was highly susceptible to changes in the number of gamma rate categories. The concurrent use of gamma and invariable-site models for intraspecific data is not biologically meaningful and has been challenged on statistical grounds; here we have found that the assumption of a proportion of invariable sites has no obvious impact on Bayesian estimates of rates and timescales from intraspecific data.

A New Discrete Distribution Related to Generalized Gamma Distribution and Its Properties

In this article, a new discrete distribution related to the generalized gamma distribution (Stacy, 1962) is derived from a statistical mechanical setup. This new distribution can be seen as generalization of two-parameter discrete gamma distribution (Chakraborty and Chakravarty, 2012) and encompasses discrete version of many important continuous distributions. Some basic distributional and reliability properties, parameter estimation by different methods, and their comparative performances using simulation are investigated. Two-real life data sets are considered for data modeling and likelihood ratio test for illustrating the advantages of the proposed distribution over two-parameter discrete gamma distribution.

Discrete Gamma Distributions: Properties and Parameter Estimations

A two-parameter discrete gamma distribution is derived corresponding to the continuous two parameters gamma distribution using the general approach for discretization of continuous probability distributions. One parameter discrete gamma distribution is obtained as a particular case. A few important distributional and reliability properties of the proposed distribution are examined. Parameter estimation by different methods is discussed. Performance of different estimation methods are compared through simulation. Data fitting is carried out to investigate the suitability of the proposed distribution in modeling discrete failure time data and other count data.

Composite Likelihood Modeling of Neighboring Site Correlations of DNA Sequence Substitution Rates

Sequence data from a series of homologous DNA segments from related organisms are typically polymorphic at many sites, and these polymorphisms are the result of evolutionary processes. Such data may be used to estimate the substitution rates as well as the variability of these rates. Careful characterization of the distribution of this variation is essential for accurate estimation of evolutionary distances and phylogeny reconstruction among these sequences. Many researchers have recognized the importance of the variability of substitution rates, which most have modeled using a discrete gamma distribution. Some have extended these methods to explicitly account for the correlation of substitution rates among sites using hidden Markov models; others have proposed context-dependent substitution rate schemes. We accommodate these correlations using a composite likelihood method based on a bivariate gamma distribution, which is more flexible than hidden Markov models in terms of correlation structure and more computationally tractable compared to the context-dependent schemes. We show that the estimates have good theoretical properties. We also use simulations to compare the maximum composite likelihood estimates to those obtained from maximum likelihood based on the independence assumption. We use data from the mitochondrial DNA of ten primates to obtain maximum composite likelihood estimates of the mean substitution rate, overdispersion, and correlation parameters, and use these estimates in a parametric phylogenetic bootstrap to assess the impact of serial correlation on the estimates of substitution rates and branch lengths.

Testing for Covarion-like Evolution in Protein Sequences

The covarion hypothesis of molecular evolution proposes that selective pressures on an amino acid or nucleotide site change through time, thus causing changes of evolutionary rate along the edges of a phylogenetic tree. Several kinds of Markov models for the covarion process have been proposed. One model, proposed by Huelsenbeck (2002), has 2 substitution rate classes: the substitution process at a site can switch between a single variable rate, drawn from a discrete gamma distribution, and a zero invariable rate. A second model, suggested by Galtier (2001), assumes rate switches among an arbitrary number of rate classes but switching to and from the invariable rate class is not allowed. The latter model allows for some sites that do not participate in the rate-switching process. Here we propose a general covarion model that combines features of both models, allowing evolutionary rates not only to switch between variable and invariable classes but also to switch among different rates when they are in a variable state. We have implemented all 3 covarion models in a maximum likelihood framework for amino acid sequences and tested them on 23 protein data sets. We found significant likelihood increases for all data sets for the 3 models, compared with a model that does not allow site-specific rate switches along the tree. Furthermore, we found that the general model fit the data better than the simpler covarion models in the majority of the cases, highlighting the complexity in modeling the covarion process. The general covarion model can be used for comparing tree topologies, molecular dating studies, and the investigation of protein adaptation.

On numbers, probability and dimensions

The exact expectation values 〈d〉 = 1 [〈d〉 − 4] and 〈n〉 = 1 [〈n〉 − 4] of the relevant space and fractal-Hausdorff dimensions n and d c ( n) of a Cantorian space & are derived using an exact discrete gamma distribution function. Possible number theoretical interpretation of our neurological perception of a 3 + 1-dimensional space time is discussed briefly.