On the use of correlated beta random variables with animal population modelling

We give reasons why demographic parameters such as survival and reproduction rates are often modelled well in stochastic population simulation using beta distributions. In practice, it is frequently expected that these parameters will be correlated, for example with survival rates for all age classes tending to be high or low in the same year. We therefore discuss a method for producing correlated beta random variables by transforming correlated normal random variables, and show how it can be applied in practice by means of a simple example. We also note how the same approach can be used to produce correlated uniform triangular, and exponential random variables. (C) 2008 Elsevier B.V. All rights reserved.

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.

Frequency and genotypic distribution of GB virus C (GBV-C) among Colombian population with Hepatitis B (HBV) or Hepatitis C (HCV) infection

Background: GB virus C (GBV-C) is an enveloped positive-sense ssRNA virus belonging to the Flaviviridae family. Studies on the genetic variability of the GBV-C reveals the existence of six genotypes: genotype 1 predominates in West Africa, genotype 2 in Europe and America, genotype 3 in Asia, genotype 4 in Southwest Asia, genotype 5 in South Africa and genotype 6 in Indonesia. The aim of this study was to determine the frequency and genotypic distribution of GBV-C in the Colombian population. Methods: Two groups were analyzed: i) 408 Colombian blood donors infected with HCV (n = 250) and HBV (n = 158) from Bogota and ii) 99 indigenous people with HBV infection from Leticia, Amazonas. A fragment of 344 bp from the 5' untranslated region (5' UTR) was amplified by nested RT PCR. Viral sequences were genotyped by phylogenetic analysis using reference sequences from each genotype obtained from GenBank (n = 160). Bayesian phylogenetic analyses were conducted using Markov chain Monte Carlo (MCMC) approach to obtain the MCC tree using BEAST v. 1.5.3. Results: Among blood donors, from 158 HBsAg positive samples, eight 5.06% (n = 8) were positive for GBV-C and from 250 anti-HCV positive samples, 3.2%(n = 8) were positive for GBV-C. Also, 7.7% (n = 7) GBV-C positive samples were found among indigenous people from Leticia. A phylogenetic analysis revealed the presence of the following GBV-C genotypes among blood donors: 2a (41.6%), 1 (33.3%), 3 (16.6%) and 2b (8.3%). All genotype 1 sequences were found in co-infection with HBV and 4/5 sequences genotype 2a were found in co-infection with HCV. All sequences from indigenous people from Leticia were classified as genotype 3. The presence of GBV-C infection was not correlated with the sex (p = 0.43), age (p = 0.38) or origin (p = 0.17). Conclusions: It was found a high frequency of GBV-C genotype 1 and 2 in blood donors. The presence of genotype 3 in indigenous population was previously reported from Santa Marta region in Colombia and in native people from Venezuela and Bolivia. This fact may be correlated to the ancient movements of Asian people to South America a long time ago.

Prevalence of fibromyalgia in a low socioeconomic status population

Background: The aim of this study was to estimate the prevalence of fibromyalgia, as well as to assess the major symptoms of this syndrome in an adult, low socioeconomic status population assisted by the primary health care system in a city in Brazil. Methods: We cross-sectionally sampled individuals assisted by the public primary health care system (n = 768, 35-60 years old). Participants were interviewed by phone and screened about pain. They were then invited to be clinically assessed (304 accepted). Pain was estimated using a Visual Analogue Scale (VAS). Fibromyalgia was assessed using the Fibromyalgia Impact Questionnaire (FIQ), as well as screening for tender points using dolorimetry. Statistical analyses included Bayesian Statistics and the Kruskal-Wallis Anova test (significance level = 5%). Results: From the phone-interview screening, we divided participants (n = 768) in three groups: No Pain (NP) (n = 185); Regional Pain (RP) (n = 388) and Widespread Pain (WP) (n = 106). Among those participating in the clinical assessments, (304 subjects), the prevalence of fibromyalgia was 4.4% (95% confidence interval [2.6%; 6.3%]). Symptoms of pain (VAS and FIQ), feeling well, job ability, fatigue, morning tiredness, stiffness, anxiety and depression were statically different among the groups. In multivariate analyses we found that individuals with FM and WP had significantly higher impairment than those with RP and NP. FM and WP were similarly disabling. Similarly, RP was no significantly different than NP. Conclusion: Fibromyalgia is prevalent in the low socioeconomic status population assisted by the public primary health care system. Prevalence was similar to other studies (4.4%) in a more diverse socioeconomic population. Individuals with FM and WP have significant impact in their well being.

Haplotype distribution of five nuclear genes based on network genealogies and Bayesian inference indicates that Trypanosoma cruzi hybrid strains are polyphyletic

Chagas disease is still a major public health problem in Latin America. Its causative agent, Trypanosoma cruzi, can be typed into three major groups, T. cruzi I, T. cruzi II and hybrids. These groups each have specific genetic characteristics and epidemiological distributions. Several highly virulent strains are found in the hybrid group; their origin is still a matter of debate. The null hypothesis is that the hybrids are of polyphyletic origin, evolving independently from various hybridization events. The alternative hypothesis is that all extant hybrid strains originated from a single hybridization event. We sequenced both alleles of genes encoding EF-1 alpha, actin and SSU rDNA of 26 T. cruzi strains and DHFR-TS and TR of 12 strains. This information was used for network genealogy analysis and Bayesian phylogenies. We found T. cruzi I and T. cruzi II to be monophyletic and that all hybrids had different combinations of T. cruzi I and T. cruzi II haplotypes plus hybrid-specific haplotypes. Bootstrap values (networks) and posterior probabilities (Bayesian phylogenies) of clades supporting the monophyly of hybrids were far below the 95% confidence interval, indicating that the hybrid group is polyphyletic. We hypothesize that T. cruzi I and T. cruzi II are two different species and that the hybrids are extant representatives of independent events of genome hybridization, which sporadically have sufficient fitness to impact on the epidemiology of Chagas disease.

Modeling associations between genetic markers using Bayesian networks

Motivation: Understanding the patterns of association between polymorphisms at different loci in a population ( linkage disequilibrium, LD) is of fundamental importance in various genetic studies. Many coefficients were proposed for measuring the degree of LD, but they provide only a static view of the current LD structure. Generative models (GMs) were proposed to go beyond these measures, giving not only a description of the actual LD structure but also a tool to help understanding the process that generated such structure. GMs based in coalescent theory have been the most appealing because they link LD to evolutionary factors. Nevertheless, the inference and parameter estimation of such models is still computationally challenging. Results: We present a more practical method to build GM that describe LD. The method is based on learning weighted Bayesian network structures from haplotype data, extracting equivalence structure classes and using them to model LD. The results obtained in public data from the HapMap database showed that the method is a promising tool for modeling LD. The associations represented by the learned models are correlated with the traditional measure of LD D`. The method was able to represent LD blocks found by standard tools. The granularity of the association blocks and the readability of the models can be controlled in the method. The results suggest that the causality information gained by our method can be useful to tell about the conservability of the genetic markers and to guide the selection of subset of representative markers.

Modelling the potential distribution of the invasive tomato red spider mite, Tetranychus evansi (Acari: Tetranychidae)

Predicting the potential geographical distribution of a species is particularly important for pests with strong invasive abilities. Tetranychus evansi Baker & Pritchard, possibly native to South America, is a spider mite pest of solanaceous crops. This mite is considered an invasive species in Africa and Europe. A CLIMEX model was developed to predict its global distribution. The model results fitted the known records of T. evansi except for some records in dry locations. Dryness as well as excess moisture stresses play important roles in limiting the spread of the mite in the tropics. In North America and Eurasia its potential distribution appears to be essentially limited by cold stress. Detailed potential distribution maps are provided for T. evansi in the Mediterranean Basin and in Japan. These two regions correspond to climatic borders for the species. Mite establishment in these areas can be explained by their relatively mild winters. The Mediterranean region is also the main area where tomato is grown in open fields in Europe and where the pest represents a threat. According to the model, the whole Mediterranean region has the potential to be extensively colonized by the mite. Wide expansion of the mite to new areas in Africa is also predicted. Agricultural issues highlighted by the modelled distribution of the pest are discussed.

Influence of Plasma Protein Binding on Pharmacodynamics: Estimation of In Vivo Receptor Affinities of beta Blockers Using a New Mechanism-Based PK-PD Modelling Approach

The objective of this investigation was to examine in a systematic manner the influence of plasma protein binding on in vivo pharmacodynamics. Comparative pharmacokinetic-pharmacodynamic studies with four beta blockers were performed in conscious rats, using heart rate under isoprenaline-induced tachycardia as a pharmacodynamic endpoint. A recently proposed mechanism-based agonist-antagonist interaction model was used to obtain in vivo estimates of receptor affinities (K(B),(vivo)). These values were compared with in vitro affinities (K(B),(vitro)) on the basis of both total and free drug concentrations. For the total drug concentrations, the K(B),(vivo) estimates were 26, 13, 6.5 and 0.89 nM for S(-)-atenolol, S(-)-propranolol, S(-)-metoprolol and timolol. The K(B),(vivo) estimates on the basis of the free concentrations were 25, 2.0, 5.2 and 0.56 nM, respectively. The K(B),(vivo)-K(B),(vitro) correlation for total drug concentrations clearly deviated from the line of identity, especially for the most highly bound drug S(-)-propranolol (ratio K(B),(vivo)/K(B),(vitro) similar to 6.8). For the free drug, the correlation approximated the line of identity. Using this model, for beta-blockers the free plasma concentration appears to be the best predictor of in vivo pharmacodynamics. (C) 2008 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 98:3816-3828, 2009

Molecular characterization of the Hepatitis B virus genotypes in Colombia: A Bayesian inference on the genotype F

Hepatitis B is a worldwide health problem affecting about 2 billion people and more than 350 million are chronic carriers of the virus. Nine HBV genotypes (A to I) have been described. The geographical distribution of HBV genotypes is not completely understood due to the limited number of samples from some parts of the world. One such example is Colombia, in which few studies have described the HBV genotypes. In this study, we characterized HBV genotypes in 143 HBsAg-positive volunteer blood donors from Colombia. A fragment of 1306 bp partially comprising HBsAg and the DNA polymerase coding regions (S/POL) was amplified and sequenced. Bayesian phylogenetic analyses were conducted using the Markov Chain Monte Carlo (MCMC) approach to obtain the maximum clade credibility (MCC) tree using BEAST v.1.5.3. Of all samples, 68 were positive and 52 were successfully sequenced. Genotype F was the most prevalent in this population (77%) - subgenotypes F3 (75%) and Fib (2%). Genotype G (7.7%) and subgenotype A2 (15.3%) were also found. Genotype G sequence analysis suggests distinct introductions of this genotype in the country. Furthermore, we estimated the time of the most recent common ancestor (TMRCA) for each HBV/F subgenotype and also for Colombian F3 sequences using two different datasets: (i) 77 sequences comprising 1306 bp of S/POL region and (ii) 283 sequences comprising 681 bp of S/POL region. We also used two other previously estimated evolutionary rates: (i) 2.60 x 10(-4) s/s/y and (ii) 1.5 x 10(-5) s/s/y. Here we report the HBV genotypes circulating in Colombia and estimated the TMRCA for the four different subgenotypes of genotype F. (C) 2010 Elsevier B.V. All rights reserved.

Modelling the control strategies against dengue in Singapore

Notified cases of dengue infections in Singapore reached historical highs in 2004 (9459 cases) and 2005 (13 817 cases) and the reason for such all increase is still to be established. We apply a mathematical model for dengue infection that takes into account the seasonal variation in incidence, characteristic of dengue fever, and which mimics the 2004-2005 epidemics in Singapore. We simulated a set of possible control strategies and confirmed the intuitive belief that killing adult mosquitoes is the most effective strategy to control an ongoing epidemic. On the other hand, the control of immature forms was very efficient ill preventing the resurgence of dengue epidemics. Since the control of immature forms allows the reduction of adulticide, it seems that the best strategy is to combine both adulticide and larvicide control measures during an outbreak, followed by the maintenance of larvicide methods after the epidemic has subsided. In addition, the model showed that the mixed strategy of adulticide and larvicide methods introduced by the government seems to be very effective in reducing the number of cases in the first weeks after the start of control.

Mitochondrial population genomics supports a single pre-Clovis origin with a coastal route for the peopling of the Americas

It is well accepted that the Americas were the last continents reached by modern humans, most likely through Beringia. However, the precise time and mode of the colonization of the New World remain hotly disputed issues. Native American populations exhibit almost exclusively five mitochondrial DNA (mtDNA) haplogroups (A-D and X). Haplogroups A-D are also frequent in Asia, suggesting a northeastern Asian origin of these lineages. However, the differential pattern of distribution and frequency of haplogroup X led some to suggest that it may represent an independent migration to the Americas. Here we show, by using 86 complete mitochondrial genomes, that all Native American haplogroups, including haplogroup X, were part of a single founding population, thereby refuting multiple-migration models. A detailed demographic history of the mtDNA sequences estimated with a Bayesian coalescent method indicates a complex model for the peopling of the Americas, in which the initial differentiation from Asian populations ended with a moderate bottleneck in Beringia during the last glacial maximum (LGM), around similar to 23,000 to similar to 19,000 years ago. Toward the end of the LGM, a strong population expansion started similar to 18,000 and finished similar to 15,000 years ago. These results support a pre-Clovis occupation of the New World, suggesting a rapid settlement of the continent along a Pacific coastal route.

Population genetic structure and dispersal in white-lipped peccaries (Tayassu pecari) from the Brazilian Pantanal

In many mammals social organization promotes genetic structuring, which can be influenced by the dispersal pattern of the species. We analyzed the population genetic structure and dispersal of white-lipped peccaries (Tayassu pecan) from the Pantanal, Brazil. We genotyped 100 individuals at 7 microsatellite loci from 2 adjacent locations with no obvious geographic barrier between them. We found a significant but low F(ST) value, and the Bayesian analysis indicated a unique cluster. No significant differences were observed between mean assignment indices of resident males and females from both locations, and the probability of being born at the location sampled of > 30% of the individuals analyzed was lower than average. Mean relatedness between resident female, male, and opposite-sex pairs was not statistically different in both locations. These results suggest a low degree of genetic differentiation between the locations analyzed, and dispersal by both sexes (contrary to the predicted male-biased dispersal of most mammalian species).

Using ecological niche modelling to infer past, present and future environmental suitability for Leiopelma hochstetteri, an endangered New Zealand native frog

Leiopelma hochstetteri is an endangered New Zealand frog now confined to isolated populations scattered across the North Island. A better understanding of its past, current and predicted future environmental suitability will contribute to its conservation which is in jeopardy due to human activities, feral predators, disease and climate change. Here we use ecological niche modelling with all known occurrence data (N = 1708) and six determinant environmental variables to elucidate current, pre-human and future environmental suitability of this species. Comparison among independent runs, subfossil records and a clamping method allow validation of models. Many areas identified as currently suitable do not host any known populations. This apparent discrepancy could be explained by several non exclusive hypotheses: the areas have not been adequately surveyed and undiscovered populations still remain, the model is over simplistic; the species` sensitivity to fragmentation and small population size; biotic interactions; historical events. An additional outcome is that apparently suitable, but frog-less areas could be targeted for future translocations. Surprisingly, pre-human conditions do not differ markedly highlighting the possibility that the range of the species was broadly fragmented before human arrival. Nevertheless, some populations, particularly on the west of the North Island may have disappeared as a result of human mediated habitat modification. Future conditions are marked with higher temperatures, which are predicted to be favourable to the species. However, such virtual gain in suitable range will probably not benefit the species given the highly fragmented nature of existing habitat and the low dispersal ability of this species. (C) 2010 Elsevier Ltd. All rights reserved.

A Bayesian model for estimating the malaria transition probabilities considering individuals lost to follow-up

It is known that patients may cease participating in a longitudinal study and become lost to follow-up. The objective of this article is to present a Bayesian model to estimate the malaria transition probabilities considering individuals lost to follow-up. We consider a homogeneous population, and it is assumed that the considered period of time is small enough to avoid two or more transitions from one state of health to another. The proposed model is based on a Gibbs sampling algorithm that uses information of lost to follow-up at the end of the longitudinal study. To simulate the unknown number of individuals with positive and negative states of malaria at the end of the study and lost to follow-up, two latent variables were introduced in the model. We used a real data set and a simulated data to illustrate the application of the methodology. The proposed model showed a good fit to these data sets, and the algorithm did not show problems of convergence or lack of identifiability. We conclude that the proposed model is a good alternative to estimate probabilities of transitions from one state of health to the other in studies with low adherence to follow-up.

Regression Models with Heteroscedasticity using Bayesian Approach

In this paper, we compare the performance of two statistical approaches for the analysis of data obtained from the social research area. In the first approach, we use normal models with joint regression modelling for the mean and for the variance heterogeneity. In the second approach, we use hierarchical models. In the first case, individual and social variables are included in the regression modelling for the mean and for the variance, as explanatory variables, while in the second case, the variance at level 1 of the hierarchical model depends on the individuals (age of the individuals), and in the level 2 of the hierarchical model, the variance is assumed to change according to socioeconomic stratum. Applying these methodologies, we analyze a Colombian tallness data set to find differences that can be explained by socioeconomic conditions. We also present some theoretical and empirical results concerning the two models. From this comparative study, we conclude that it is better to jointly modelling the mean and variance heterogeneity in all cases. We also observe that the convergence of the Gibbs sampling chain used in the Markov Chain Monte Carlo method for the jointly modeling the mean and variance heterogeneity is quickly achieved.