RUMOR PROCESSES ON N

We study four discrete-time stochastic systems on N, modeling processes of rumor spreading. The involved individuals can either have an active or a passive role, speaking up or asking for the rumor. The appetite for spreading or hearing the rumor is represented by a set of random variables whose distributions may depend on the individuals. Our goal is to understand-based on the distribution of the random variables-whether the probability of having an infinite set of individuals knowing the rumor is positive or not.

Derivation and external validation of a simple prediction model for the diagnosis of type 2 Diabetes Mellitus in the Brazilian urban population

A risk score model was developed based in a population of 1,224 individuals from the general population without known diabetes aging 35 years or more from an urban Brazilian population sample in order to select individuals who should be screened in subsequent testing and improve the efficacy of public health assurance. External validation was performed in a second, independent, population from a different city ascertained through a similar epidemiological protocol. The risk score was developed by multiple logistic regression and model performance and cutoff values were derived from a receiver operating characteristic curve. Model`s capacity of predicting fasting blood glucose levels was tested analyzing data from a 5-year follow-up protocol conducted in the general population. Items independently and significantly associated with diabetes were age, BMI and known hypertension. Sensitivity, specificity and proportion of further testing necessary for the best cutoff value were 75.9, 66.9 and 37.2%, respectively. External validation confirmed the model`s adequacy (AUC equal to 0.72). Finally, model score was also capable of predicting fasting blood glucose progression in non-diabetic individuals in a 5-year follow-up period. In conclusion, this simple diabetes risk score was able to identify individuals with an increased likelihood of having diabetes and it can be used to stratify subpopulations in which performing of subsequent tests is necessary and probably cost-effective.

Experimental evidence and model explanation for cell population characteristics modification when applying sequential photodynamic therapy

We present experimental evidence of the existence of cell variability in terms of threshold light dose for Hep G2 (liver cancer cells) cultured. Using a theoretical model to describe the effects caused by successive photodynamic therapy (PDT) sessions, and based on the consequences of a partial response we introduce the threshold dose distribution concept within a tumor. The experimental model consists in a stack of flasks, and simulates subsequent layers of a tissue exposed to PDT application. The result indicates that cells from the same culture could respond in different ways to similar PDT induced-damages. Moreover, the consequence is a partial killing of the cells submitted to PDT, and the death fraction decreased at each in vitro PDT session. To demonstrate the occurrence of cell population modification as a response to PDT, we constructed a simple theoretical model and assumed that the threshold dose distribution for a cell population of a tumor is represented by a modified Gaussian distribution.

Predicting random effects with an expanded finite population mixed model

Prediction of random effects is an important problem with expanding applications. In the simplest context, the problem corresponds to prediction of the latent value (the mean) of a realized cluster selected via two-stage sampling. Recently, Stanek and Singer [Predicting random effects from finite population clustered samples with response error. J. Amer. Statist. Assoc. 99, 119-130] developed best linear unbiased predictors (BLUP) under a finite population mixed model that outperform BLUPs from mixed models and superpopulation models. Their setup, however, does not allow for unequally sized clusters. To overcome this drawback, we consider an expanded finite population mixed model based on a larger set of random variables that span a higher dimensional space than those typically applied to such problems. We show that BLUPs for linear combinations of the realized cluster means derived under such a model have considerably smaller mean squared error (MSE) than those obtained from mixed models, superpopulation models, and finite population mixed models. We motivate our general approach by an example developed for two-stage cluster sampling and show that it faithfully captures the stochastic aspects of sampling in the problem. We also consider simulation studies to illustrate the increased accuracy of the BLUP obtained under the expanded finite population mixed model. (C) 2007 Elsevier B.V. All rights reserved.

Richards growth model and viability indicators for populations subject to interventions

In this work we study the problem of modeling identification of a population employing a discrete dynamic model based on the Richards growth model. The population is subjected to interventions due to consumption, such as hunting or farming animals. The model identification allows us to estimate the probability or the average time for a population number to reach a certain level. The parameter inference for these models are obtained with the use of the likelihood profile technique as developed in this paper. The identification method here developed can be applied to evaluate the productivity of animal husbandry or to evaluate the risk of extinction of autochthon populations. It is applied to data of the Brazilian beef cattle herd population, and the the population number to reach a certain goal level is investigated.

Population-based multicentric survey of hepatitis B infection and risk factor differences among three regions in Brazil

This multicentric population-based study in Brazil is the first national effort to estimate the prevalence of hepatitis B (HBV) and risk factors in the capital cities of the Northeast, Central-West, and Federal Districts (2004-2005). Random multistage cluster sampling was used to select persons 13-69 years of age. Markers for HBV were tested by enzyme-linked immunosorbent assay. The HBV genotypes were determined by sequencing hepatitis B surface antigen (HBsAg). Multivariate analyses and simple catalytic model were performed. Overall, 7,881 persons were included; < 70 per cent were not vaccinated. Positivity for HBsAg was less than 1 per cent among non-vaccinated persons and genotypes A, D, and F co-circulated. The incidence of infection increased with age with similar force of infection in all regions. Males and persons having initiated sexual activity were associated with HBV infection in the two settings; healthcare jobs and prior hospitalization were risk factors in the Federal District. Our survey classified these regions as areas with HBV endemicity and highlighted the risk factors differences among the settings

TCF7L2 variant genotypes and type 2 diabetes risk in Brazil: significant association, but not a significant tool for risk stratification in the general population

Background: Genetic polymorphisms of the TCF7L2 gene are strongly associated with large increments in type 2 diabetes risk in different populations worldwide. In this study, we aimed to confirm the effect of the TCF7L2 polymorphism rs7903146 on diabetes risk in a Brazilian population and to assess the use of this genetic marker in improving diabetes risk prediction in the general population. Methods: We genotyped the single nucleotide polymorphisms (SNP) rs7903146 of the TCF7L2 gene in 560 patients with known coronary disease enrolled in the MASS II (Medicine, Angioplasty, or Surgery Study) Trial and in 1,449 residents of Vitoria, in Southeast Brazil. The associations of this gene variant to diabetes risk and metabolic characteristics in these two different populations were analyzed. To access the potential benefit of using this marker for diabetes risk prediction in the general population we analyzed the impact of this genetic variant on a validated diabetes risk prediction tool based on clinical characteristics developed for the Brazilian general population. Results: SNP rs7903146 of the TCF7L2 gene was significantly associated with type 2 diabetes in the MASS-II population (OR = 1.57 per T allele, p = 0.0032), confirming, in the Brazilian population, previous reports of the literature. Addition of this polymorphism to an established clinical risk prediction score did not increased model accuracy (both area under ROC curve equal to 0.776). Conclusion: TCF7L2 rs7903146 T allele is associated with a 1.57 increased risk for type 2 diabetes in a Brazilian cohort of patients with known coronary heart disease. However, the inclusion of this polymorphism in a risk prediction tool developed for the general population resulted in no improvement of performance. This is the first study, to our knowledge, that has confirmed this recent association in a South American population and adds to the great consistency of this finding in studies around the world. Finally, confirming the biological association of a genetic marker does not guarantee improvement on already established screening tools based solely on demographic variables.

An assessment of population structure in eight breeds of cattle using a whole genome SNP panel

Background: Analyses of population structure and breed diversity have provided insight into the origin and evolution of cattle. Previously, these studies have used a low density of microsatellite markers, however, with the large number of single nucleotide polymorphism markers that are now available, it is possible to perform genome wide population genetic analyses in cattle. In this study, we used a high-density panel of SNP markers to examine population structure and diversity among eight cattle breeds sampled from Bos indicus and Bos taurus. Results: Two thousand six hundred and forty one single nucleotide polymorphisms ( SNPs) spanning all of the bovine autosomal genome were genotyped in Angus, Brahman, Charolais, Dutch Black and White Dairy, Holstein, Japanese Black, Limousin and Nelore cattle. Population structure was examined using the linkage model in the program STRUCTURE and Fst estimates were used to construct a neighbor-joining tree to represent the phylogenetic relationship among these breeds. Conclusion: The whole-genome SNP panel identified several levels of population substructure in the set of examined cattle breeds. The greatest level of genetic differentiation was detected between the Bos taurus and Bos indicus breeds. When the Bos indicus breeds were excluded from the analysis, genetic differences among beef versus dairy and European versus Asian breeds were detected among the Bos taurus breeds. Exploration of the number of SNP loci required to differentiate between breeds showed that for 100 SNP loci, individuals could only be correctly clustered into breeds 50% of the time, thus a large number of SNP markers are required to replace the 30 microsatellite markers that are currently commonly used in genetic diversity studies.

Relatedness and HLA-DRB1 typing may discriminate the magnitude of the genetic susceptibility to tuberculosis using a household contact model

Background Tuberculosis clusters in families may be due to increased household exposure, shared genetic factors, or both. Household contact studies are useful to control exposure because socioeconomic and environmental conditions are similar to all subjects, allowing the evaluation of the contribution of relatedness to disease development. Methods In this study, the familial aggregation of tuberculosis using relatedness and a specific inherited marker (HLA-DRB1) was evaluated. Fifty families, which had at least two cases of tuberculosis diagnosed within the past 5 years, were selected from a cohort of tuberculosis carried out in Recife, Brazil. The first case diagnosed was considered to be a primary case. The secondary attack rate of tuberculosis in household contacts was estimated according to the degree of relatedness. The relative risk of having tuberculosis based on the degree of relatedness household and the population attributable fraction to relatedness were also estimated. HLA-DRB1 typing and attributable etiologic/preventive fractions were calculated among sick and healthy household contacts. Results Compared to unrelated contacts, the relative risk for tuberculosis adjusted for age was 1.38 (95% CI 0.86 to 2.21). Relatedness contributed 23% to the development of tuberculosis at the population levels. The HLA-DRB1*04 allele group (OR = 2.44; p =0.0324; etiologic fraction =0.15) was overrepresented and the DRB1*15 allele group (OR=0.48; p=0.0488; protective fraction=0.19) was underrepresented among household contacts exhibiting tuberculosis. The presence of DRB1 shared alleles between primary cases and their contacts was a risk factor for tuberculosis (p=0.0281). Conclusion This household contact model together with the utilisation of two genetic variables permitted the evaluation of genetic factors contributing towards tuberculosis development.

Phylogeography of the common vampire bat (Desmodus rotundus): Marked population structure, Neotropical Pleistocene vicariance and incongruence between nuclear and mtDNA markers

Background: The common vampire bat Desmodus rotundus is an excellent model organism for studying ecological vicariance in the Neotropics due to its broad geographic range and its preference for forested areas as roosting sites. With the objective of testing for Pleistocene ecological vicariance, we sequenced a mitocondrial DNA (mtDNA) marker and two nuclear markers (RAG2 and DRB) to try to understand how Pleistocene glaciations affected the distribution of intraspecific lineages in this bat. Results: Five reciprocally monophyletic clades were evident in the mitochondrial gene tree, and in most cases with high bootstrap support: Central America (CA), Amazon and Cerrado (AMC), Pantanal (PAN), Northern Atlantic Forest (NAF) and Southern Atlantic Forest (SAF). The Atlantic forest clades formed a monophyletic clade with high bootstrap support, creating an east/west division for this species in South America. On the one hand, all coalescent and non-coalescent estimates point to a Pleistocene time of divergence between the clades. On the other hand, the nuclear markers showed extensive sharing of haplotypes between distant localities, a result compatible with male-biased gene flow. In order to test if the disparity between the mitochondrial and nuclear markers was due to the difference in mutation rate and effective size, we performed a coalescent simulation to examine the feasibility that, given the time of separation between the observed lineages, even with a gene flow rate close to zero, there would not be reciprocal monophyly for a neutral nuclear marker. We used the observed values of theta and an estimated mutation rate for the nuclear marker gene to perform 1000 iterations of the simulation. The results of this simulation were inconclusive: the number of iterations with and without reciprocal monophyly of one or more clades are similar. Conclusions: We therefore conclude that the pattern exhibited by the common vampire bat, with marked geographical structure for a mitochondrial marker and no phylogeographic structure for nuclear markers is compatible with a historical scenario of complete isolation of refuge-like populations during the Pleistocene. The results on demographic history on this species is compatible with the Carnaval-Moritz model of Pleistocene vicariance, with demographic expansions in the southern Atlantic forest.

Role of noise in population dynamics cycles

Noise is an intrinsic feature of population dynamics and plays a crucial role in oscillations called phase-forgetting quasicycles by converting damped into sustained oscillations. This function of noise becomes evident when considering Langevin equations whose deterministic part yields only damped oscillations. We formulate here a consistent and systematic approach to population dynamics, leading to a Fokker-Planck equation and the associate Langevin equations in accordance with this conceptual framework, founded on stochastic lattice-gas models that describe spatially structured predator-prey systems. Langevin equations in the population densities and predator-prey pair density are derived in two stages. First, a birth-and-death stochastic process in the space of prey and predator numbers and predator-prey pair number is obtained by a contraction method that reduces the degrees of freedom. Second, a van Kampen expansion in the inverse of system size is then performed to get the Fokker-Planck equation. We also study the time correlation function, the asymptotic behavior of which is used to characterize the transition from the cyclic coexistence of species to the ordinary coexistence.

An opinion dynamics model for the diffusion of innovations

We study the dynamics of the adoption of new products by agents with continuous opinions and discrete actions (CODA). The model is such that the refusal in adopting a new idea or product is increasingly weighted by neighbor agents as evidence against the product. Under these rules, we study the distribution of adoption times and the final proportion of adopters in the population. We compare the cases where initial adopters are clustered to the case where they are randomly scattered around the social network and investigate small world effects on the final proportion of adopters. The model predicts a fat tailed distribution for late adopters which is verified by empirical data. (C) 2009 Elsevier B.V. All rights reserved.

Successful maintenance of a stingless bee population despite a severe genetic bottleneck

Stingless bees play an important ecological role as pollinators of many wild plant species in the tropics and have significant potential for the pollination of agricultural crops. Nevertheless, conservation efforts as well as commercial breeding programmes require better guidelines on the amount of genetic variation that is needed to maintain viable populations. In this context, we carried out a long-term genetic study on the stingless bee Melipona scutellaris to evaluate the population viability consequences of prolonged breeding from a small number of founder colonies. In particular, it was artificially imposed a genetic bottleneck by setting up a population starting from only two founder colonies, and continued breeding from it for a period of over 10 years in a location outside its natural area of occurrence. We show that despite a great reduction in the number of alleles present at both neutral microsatellite loci and the sex-determining locus relative to its natural source population, and an increased frequency in the production of sterile diploid males, the genetically impoverished population could be successfully bred and maintained for at least 10 years. This shows that in stingless bees, breeding from a small stock of colonies may have less severe consequences than previously suspected. In addition, we provide a simulation model to determine the number of colonies that are needed to maintain a certain number of sex alleles in a population, thereby providing useful guidelines for stingless bee breeding and conservation efforts.

Land planarians (Platyhelminthes) as a model organism for fine-scale phylogeographic studies: understanding patterns of biodiversity in the Brazilian Atlantic Forest hotspot

The Brazilian Atlantic Forest is one of the richest biodiversity hotspots of the world. Paleoclimatic models have predicted two large stability regions in its northern and central parts, whereas southern regions might have suffered strong instability during Pleistocene glaciations. Molecular phylogeographic and endemism studies show, nevertheless, contradictory results: although some results validate these predictions, other data suggest that paleoclimatic models fail to predict stable rainforest areas in the south. Most studies, however, have surveyed species with relatively high dispersal rates whereas taxa with lower dispersion capabilities should be better predictors of habitat stability. Here, we have used two land planarian species as model organisms to analyse the patterns and levels of nucleotide diversity on a locality within the Southern Atlantic Forest. We find that both species harbour high levels of genetic variability without exhibiting the molecular footprint of recent colonization or population expansions, suggesting a long-term stability scenario. The results reflect, therefore, that paleoclimatic models may fail to detect refugia in the Southern Atlantic Forest, and that model organisms with low dispersal capability can improve the resolution of these models.

Distributed power control algorithm for multiple access systems based on Verhulst model

In this paper the continuous Verhulst dynamic model is used to synthesize a new distributed power control algorithm (DPCA) for use in direct sequence code division multiple access (DS-CDMA) systems. The Verhulst model was initially designed to describe the population growth of biological species under food and physical space restrictions. The discretization of the corresponding differential equation is accomplished via the Euler numeric integration (ENI) method. Analytical convergence conditions for the proposed DPCA are also established. Several properties of the proposed recursive algorithm, such as Euclidean distance from optimum vector after convergence, convergence speed, normalized mean squared error (NSE), average power consumption per user, performance under dynamics channels, and implementation complexity aspects, are analyzed through simulations. The simulation results are compared with two other DPCAs: the classic algorithm derived by Foschini and Miljanic and the sigmoidal of Uykan and Koivo. Under estimated errors conditions, the proposed DPCA exhibits smaller discrepancy from the optimum power vector solution and better convergence (under fixed and adaptive convergence factor) than the classic and sigmoidal DPCAs. (C) 2010 Elsevier GmbH. All rights reserved.