PubTransformer

A site to transform Pubmed publications into these bibliographic reference formats: ADS, BibTeX, EndNote, ISI used by the Web of Knowledge, RIS, MEDLINE, Microsoft's Word 2007 XML.

Models, Statistical - Top 30 Publications

Poisson regression.

Nomograms predicting disease-specific regional recurrence and distant recurrence of papillary thyroid carcinoma following partial or total thyroidectomy.

The study aimed to establish effective nomograms for prediction of tumor regional recurrence and distant recurrence of papillary thyroid carcinoma (PTC) patients after partial or total thyroidectomy.These nomograms were based on a retrospective study on 1034 patients who underwent partial or total thyroidectomy for PTC. The predictive accuracy and discriminative ability of the nomograms were evaluated by the concordance index (C-index) and calibration curve. In addition, a validation cohort was included at the same institution.Multivariate analysis demonstrated that family history, maximal tumor diameter, capsular invasion, and lymph node staging were independent risk factors for regional recurrence-free survival; and family history, histological variants, capsular invasion, perineuronal invasion, and vascular invasion were independent risk factors for distant recurrence-free survival. They were selected into the 2 nomograms, respectively, and the C-index for regional recurrence-free survival and distant recurrence-free survival prediction were 0.72 and 0.83, respectively. In the validation cohort, the 2 nomograms displayed a C-index of 0.72 and 0.89, respectively.The nomograms developed in this study demonstrated their discrimination capability for predicting 3 and 5-year regional recurrence and distant recurrence after partial or total thyroidectomy, and can be used to identify high-risk patients.

The Prime Diabetes Model: Novel Methods for Estimating Long-Term Clinical and Cost Outcomes in Type 1 Diabetes Mellitus.

Recent publications describing long-term follow-up from landmark trials and diabetes registries represent an opportunity to revisit modeling options in type 1 diabetes mellitus (T1DM).

Less Is More: Cross-Validation Testing of Simplified Nonlinear Regression Model Specifications for EQ-5D-5L Health State Values.

The conventional method for modeling of the five-level EuroQol five-dimensional questionnaire (EQ-5D-5L) health state values in national valuation studies is an additive 20-parameter main-effects regression model. Statistical models with many parameters are at increased risk of overfitting-fitting to noise and measurement error, rather than the underlying relationship.

Modeling the risk of transmission of schistosomiasis in Akure North Local Government Area of Ondo State, Nigeria using satellite derived environmental data.

Schistosomiasis is a parasitic disease and its distribution, in space and time, can be influenced by environmental factors such as rivers, elevation, slope, land surface temperature, land use/cover and rainfall. The aim of this study is to identify the areas with suitable conditions for schistosomiasis transmission on the basis of physical and environmental factors derived from satellite imagery and spatial analysis for Akure North Local Government Area (LGA) of Ondo State. Nigeria. This was done through methodology multicriteria evaluation (MCE) using Saaty's analytical hierarchy process (AHP). AHP is a multi-criteria decision method that uses hierarchical structures to represent a problem and makes decisions based on priority scales. In this research AHP was used to obtain the mapping weight or importance of each individual schistosomiasis risk factor. For the purpose of identifying areas of schistosomiasis risk, this study focused on temperature, drainage, elevation, rainfall, slope and land use/land cover as the factors controlling schistosomiasis incidence in the study area. It is by reclassifying and overlaying these factors that areas vulnerable to schistosomiasis were identified. The weighted overlay analysis was done after each factor was given the appropriate weight derived through the analytical hierarchical process. The prevalence of urinary schistosomiasis in the study area was also determined by parasitological analysis of urine samples collected through random sampling. The results showed varying risk of schistosomiasis with a larger portion of the area (82%) falling under the high and very high risk category. The study also showed that one community (Oba Ile) had the lowest risk of schistosomiasis while the risk increased in the four remaining communities (Iju, Igoba, Ita Ogbolu and Ogbese). The predictions made by the model correlated strongly with observations from field study. The high risk zones corresponded to known endemic communities. This study revealed that environmental factors can be used in identifying and predicting the transmission of schistosomiasis as well as effective monitoring of disease risk in newly established rural and agricultural communities.

Parkinson Disease and Melanoma: Confirming and Reexamining an Association.

To examine an association between melanoma and Parkinson disease (PD).

A nomogram prediction of postoperative surgical site infections in patients with perihilar cholangiocarcinoma.

Surgical site infection (SSI) is one of the major morbidities after radical resection for perihilar cholangiocarcinoma (PHCC). This study aimed to clarify the risk factors and construct a nomogram to predict SSIs in patients with PHCC.A total of 335 consecutive patients who underwent hepatectomy combined with hepaticojejunostomy between January 2013 and December 2015 were analyzed retrospectively. SSIs, including incisional (superficial and deep) and space/organ infection, were defined according to the Centers for Disease Control and Prevention (CDC)'s National Nosocomial Infection Surveillance (NNIS) system. Risk factors associated with postoperative SSIs were analyzed by univariate and multivariate analyses. A nomogram was developed on the basis of results from the multivariate logistic model and the discriminatory ability of the model was analyzed.PHCC patients had higher organ/space SSI rate than incisional SSI rate after radical resection. Multivariate analysis showed that risk factors indicating postoperative overall SSIs (incisional and organ/space) included coexisting cholangiolithiasis [odds ratio (OR): 6.77; 95% confidence interval (95% CI): 2.40-19.11; P < .001], blood loss >1500 mL (OR: 4.77; 95% CI: 1.45-15.65; P  =  .010), having abdominal surgical history (OR: 5.85; 95% CI: 1.91-17.97; P  =  .002), and bile leakage (OR: 15.28; 95% CI: 5.90-39.62; P < .001). The β coefficients from the multivariate logistic model were used to construct the model for estimation of SSI risk. The scoring model was as follows: -4.12 +1.91 × (coexisting cholangiolithiasis  =  1) + 1.77 × (having previous abdominal surgical history  =  1) +1.56 × (blood loss >1500 mL  =  1) + 2.73 × (bile leakage  =  1). The discriminatory ability of the model was good and the area under the receiver operating characteristic (ROC) curve (AUC) was 0.851.In PHCC patients, there may be a relationship between postoperative SSIs and abdominal surgical history, coexisting cholangiolithiasis, bile leakage, and blood loss. The nomogram can be used to estimate the risk of postoperative SSIs in patients with PHCC.

Comparison of two on-line risk calculators versus the detection of circulating prostate cells for the detection of high risk prostate cancer at first biopsy.

The limitations of total serum PSA values remains problematic; nomograms may improve the prediction of a positive prostate biopsy (PB). We compare in a prospective study of Chilean men with suspicion of prostate cancer due to an elevated total serum PSA and/or abnormal digital rectal examination, the use of two on-line nomograms with the detection of primary malignant circulating prostate cells (CPCs) to predict a positive PB for high risk prostate cancer.

Assessing the accuracy and stability of variable selection methods for random forest modeling in ecology.

Random forest (RF) modeling has emerged as an important statistical learning method in ecology due to its exceptional predictive performance. However, for large and complex ecological data sets, there is limited guidance on variable selection methods for RF modeling. Typically, either a preselected set of predictor variables are used or stepwise procedures are employed which iteratively remove variables according to their importance measures. This paper investigates the application of variable selection methods to RF models for predicting probable biological stream condition. Our motivating data set consists of the good/poor condition of n = 1365 stream survey sites from the 2008/2009 National Rivers and Stream Assessment, and a large set (p = 212) of landscape features from the StreamCat data set as potential predictors. We compare two types of RF models: a full variable set model with all 212 predictors and a reduced variable set model selected using a backward elimination approach. We assess model accuracy using RF's internal out-of-bag estimate, and a cross-validation procedure with validation folds external to the variable selection process. We also assess the stability of the spatial predictions generated by the RF models to changes in the number of predictors and argue that model selection needs to consider both accuracy and stability. The results suggest that RF modeling is robust to the inclusion of many variables of moderate to low importance. We found no substantial improvement in cross-validated accuracy as a result of variable reduction. Moreover, the backward elimination procedure tended to select too few variables and exhibited numerous issues such as upwardly biased out-of-bag accuracy estimates and instabilities in the spatial predictions. We use simulations to further support and generalize results from the analysis of real data. A main purpose of this work is to elucidate issues of model selection bias and instability to ecologists interested in using RF to develop predictive models with large environmental data sets.

Dynamic decomposition of spatiotemporal neural signals.

Neural signals are characterized by rich temporal and spatiotemporal dynamics that reflect the organization of cortical networks. Theoretical research has shown how neural networks can operate at different dynamic ranges that correspond to specific types of information processing. Here we present a data analysis framework that uses a linearized model of these dynamic states in order to decompose the measured neural signal into a series of components that capture both rhythmic and non-rhythmic neural activity. The method is based on stochastic differential equations and Gaussian process regression. Through computer simulations and analysis of magnetoencephalographic data, we demonstrate the efficacy of the method in identifying meaningful modulations of oscillatory signals corrupted by structured temporal and spatiotemporal noise. These results suggest that the method is particularly suitable for the analysis and interpretation of complex temporal and spatiotemporal neural signals.

Conditional logistic regression.

ROTS: An R package for reproducibility-optimized statistical testing.

Differential expression analysis is one of the most common types of analyses performed on various biological data (e.g. RNA-seq or mass spectrometry proteomics). It is the process that detects features, such as genes or proteins, showing statistically significant differences between the sample groups under comparison. A major challenge in the analysis is the choice of an appropriate test statistic, as different statistics have been shown to perform well in different datasets. To this end, the reproducibility-optimized test statistic (ROTS) adjusts a modified t-statistic according to the inherent properties of the data and provides a ranking of the features based on their statistical evidence for differential expression between two groups. ROTS has already been successfully applied in a range of different studies from transcriptomics to proteomics, showing competitive performance against other state-of-the-art methods. To promote its widespread use, we introduce here a Bioconductor R package for performing ROTS analysis conveniently on different types of omics data. To illustrate the benefits of ROTS in various applications, we present three case studies, involving proteomics and RNA-seq data from public repositories, including both bulk and single cell data. The package is freely available from Bioconductor (https://www.bioconductor.org/packages/ROTS).

Quality of reporting of multivariable logistic regression models in Chinese clinical medical journals.

Multivariable logistic regression (MLR) has been increasingly used in Chinese clinical medical research during the past few years. However, few evaluations of the quality of the reporting strategies in these studies are available.To evaluate the reporting quality and model accuracy of MLR used in published work, and related advice for authors, readers, reviewers, and editors.A total of 316 articles published in 5 leading Chinese clinical medical journals with high impact factor from January 2010 to July 2015 were selected for evaluation. Articles were evaluated according 12 established criteria for proper use and reporting of MLR models.Among the articles, the highest quality score was 9, the lowest 1, and the median 5 (4-5). A total of 85.1% of the articles scored below 6. No significant differences were found among these journals with respect to quality score (χ = 6.706, P = .15). More than 50% of the articles met the following 5 criteria: complete identification of the statistical software application that was used (97.2%), calculation of the odds ratio and its confidence interval (86.4%), description of sufficient events (>10) per variable, selection of variables, and fitting procedure (78.2%, 69.3%, and 58.5%, respectively). Less than 35% of the articles reported the coding of variables (18.7%). The remaining 5 criteria were not satisfied by a sufficient number of articles: goodness-of-fit (10.1%), interactions (3.8%), checking for outliers (3.2%), collinearity (1.9%), and participation of statisticians and epidemiologists (0.3%). The criterion of conformity with linear gradients was applicable to 186 articles; however, only 7 (3.8%) mentioned or tested it.The reporting quality and model accuracy of MLR in selected articles were not satisfactory. In fact, severe deficiencies were noted. Only 1 article scored 9. We recommend authors, readers, reviewers, and editors to consider MLR models more carefully and cooperate more closely with statisticians and epidemiologists. Journals should develop statistical reporting guidelines concerning MLR.

Nomogram for Predicting Intradiscal Cement Leakage Following Percutaneous Vertebroplasty in Patients with Osteoporotic Related Vertebral Compression Fractures.

Intradiscal cement leakage (ICL) is a common complication following percutaneous vertebroplasty (PVP). However, the risk factors for such a complication are under debate and there is no accurate predictive nomogram to predict ICL.

Cost-Effectiveness of Dengue Vaccination Programs in Brazil.

AbstractThe first approved dengue vaccine, CYD-TDV, a chimeric, live-attenuated, tetravalent dengue virus vaccine, was recently licensed in 13 countries, including Brazil. In light of recent vaccine approval, we modeled the cost-effectiveness of potential vaccination policies mathematically based on data from recent vaccine efficacy trials that indicated that vaccine efficacy was lower in seronegative individuals than in seropositive individuals. In our analysis, we investigated several vaccination programs, including routine vaccination, with various vaccine coverage levels and those with and without large catch-up campaigns. As it is unclear whether the vaccine protects against infection or just against disease, our model incorporated both direct and indirect effects of vaccination. We found that in the presence of vaccine-induced indirect protection, the cost-effectiveness of dengue vaccination decreased with increasing vaccine coverage levels because the marginal returns of herd immunity decreases with vaccine coverage. All routine dengue vaccination programs that we considered were cost-effective, reducing dengue incidence significantly. Specifically, a routine dengue vaccination of 9-year-olds would be cost-effective when the cost of vaccination per individual is less than $262. Furthermore, the combination of routine vaccination and large catch-up campaigns resulted in a greater reduction of dengue burden (by up to 93%) than routine vaccination alone, making it a cost-effective intervention as long as the cost per course of vaccination is $255 or less. Our results show that dengue vaccination would be cost-effective in Brazil even with a relatively low vaccine efficacy in seronegative individuals.

Exact likelihood ratio calculations for pairwise cases.

Some practical and theoretical aspects of evaluation of evidence based on the likelihood ratio (LR) in kinship cases are discussed. If relationships are complex or if complicating factors like mutation, correction for population structure or silent alleles need to be accounted for, available software may fail. We present an explicit general formula for non-inbred pairwise cases. Equipped with this formula it is possible to evaluate, say, how strongly a shared rare allele, points towards a specific relationship. Moreover, a general expression as the one presented, adds to the understanding of models and the underlying biological mechanisms. It is also useful for checking software and defining the limitations of programs. Some ideas for improving software may also be generated by the derivation of exact expressions. We argue that a proportional mutation model is well suited from a pragmatic point of view and derive some theoretical properties of this model. Several examples based on the general pairwise formula and its implementation in the freely available R package mut are presented.

Spatial interpolation and radiological mapping of ambient gamma dose rate by using artificial neural networks and fuzzy logic methods.

The aim of this study was to determine spatial risk dispersion of ambient gamma dose rate (AGDR) by using both artificial neural network (ANN) and fuzzy logic (FL) methods, compare the performances of methods, make dose estimations for intermediate stations with no previous measurements and create dose rate risk maps of the study area. In order to determine the dose distribution by using artificial neural networks, two main networks and five different network structures were used; feed forward ANN; Multi-layer perceptron (MLP), Radial basis functional neural network (RBFNN), Quantile regression neural network (QRNN) and recurrent ANN; Jordan networks (JN), Elman networks (EN). In the evaluation of estimation performance obtained for the test data, all models appear to give similar results. According to the cross-validation results obtained for explaining AGDR distribution, Pearson's r coefficients were calculated as 0.94, 0.91, 0.89, 0.91, 0.91 and 0.92 and RMSE values were calculated as 34.78, 43.28, 63.92, 44.86, 46.77 and 37.92 for MLP, RBFNN, QRNN, JN, EN and FL, respectively. In addition, spatial risk maps showing distributions of AGDR of the study area were created by all models and results were compared with geological, topological and soil structure.

Logistic regression: Part 2.

Evaluating Model-Data Fit by Comparing Parametric and Nonparametric Item Response Functions: Application of a Tukey-Hann Procedure.

This study describes an approach for examining model-data fit for the dichotomous Rasch model using Tukey-Hann item response functions (TH-IRFs). The procedure proposed in this paper is based on an iterative version of a smoothing technique proposed by Tukey (1977) for estimating nonparametric item response functions (IRFs). A root integrated squared error (RISE) statistic (Douglas and Cohen, 2001) is used to compare the TH-IRFs to the Rasch IRFs. Data from undergraduate students at a large university are used to demonstrate this iterative smoothing technique. The RISE statistic is used for comparing the item response functions to assess model-data fit. A comparison between the residual based Infit and Outfit statistics and RISE statistics are also examined. The results suggest that the RISE statistic and TH-IRFs provide a useful analytical and graphical approach for evaluating item fit. Implications for research, theory and practice related to model-data fit are discussed.

Scale Anchoring with the Rasch Model.

Scale anchoring is a method to provide additional meaning to particular scores at different points along a score scale by identifying representative items associated with the particular scores. These items are then analyzed to write statements of what types of performance can be expected of a person with the particular scores to help test takers and other stakeholders better understand what it means to achieve the different scores. This article provides simple formulas that can be used to identify possible items to serve as scale anchors with the Rasch model. Specific attention is given to practical considerations and challenges that may be encountered when applying the formulas in different contexts. An illustrative example using data from a medical imaging certification program demonstrates how the formulas can be applied in practice.

Comparing Imputation Methods for Trait Estimation Using the Rating Scale Model.

This study examined the performance of four methods of handling missing data for discrete response options on a questionnaire: (1) ignoring the missingness (using only the observed items to estimate trait levels); (2) nearest-neighbor hot deck imputation; (3) multiple hot deck imputation; and (4) semi-parametric multiple imputation. A simulation study examining three questionnaire lengths (41-, 20-, and 10-item) crossed with three levels of missingness (10, 25, and 40 percent) was conducted to see which methods best recovered trait estimates when data were missing completely at random and the polytomous items were scored with Andrich's (1978) rating scale model. The results showed that ignoring the missingness and semi-parametric imputation best recovered known trait levels across all conditions, with the semi-parametric technique providing the most precise trait estimates. This study demonstrates the power of specific objectivity in Rasch measurement, as ignoring the missingness leads to generally unbiased trait estimates.

Constructing an Outcome Measure of Occupational Experience: An Application of Rasch Measurement Methods.

Rasch methods were used to evaluate and further develop the Daily Experiences of Pleasure, Productivity, and Restoration Profile (PPR Profile) into a health outcome measure of occupational experience. Analyses of 263 participant PPR Profiles focused on rating scale structure, dimensionality, and reliability. All rating scale categories increased with the intended meaning of the scales, but only 20 of the 21 category measures fit the Rasch rating scale model (RRSM). Several items also did not fit the RRSM and results of residual principal components analyses suggested possible second dimensions in each scale. More importantly, reliability coefficients were very low and participants could not be separated into more than one group as demonstrated by low person separation indices. The authors offer several recommendations for the next steps in the development of the PPR Profile as a health outcome measure of occupational experience.

Best (but oft-forgotten) practices: mediation analysis.

This contribution in the "Best (but Oft-Forgotten) Practices" series considers mediation analysis. A mediator (sometimes referred to as an intermediate variable, surrogate endpoint, or intermediate endpoint) is a third variable that explains how or why ≥2 other variables relate in a putative causal pathway. The current article discusses mediation analysis with the ultimate intention of helping nutrition researchers to clarify the rationale for examining mediation, avoid common pitfalls when using the model, and conduct well-informed analyses that can contribute to improving causal inference in evaluations of underlying mechanisms of effects on nutrition-related behavioral and health outcomes. We give specific attention to underevaluated limitations inherent in common approaches to mediation. In addition, we discuss how to conduct a power analysis for mediation models and offer an applied example to demonstrate mediation analysis. Finally, we provide an example write-up of mediation analysis results as a model for applied researchers.

Validation of SmartRank: A likelihood ratio software for searching national DNA databases with complex DNA profiles.

Searching a national DNA database with complex and incomplete profiles usually yields very large numbers of possible matches that can present many candidate suspects to be further investigated by the forensic scientist and/or police. Current practice in most forensic laboratories consists of ordering these 'hits' based on the number of matching alleles with the searched profile. Thus, candidate profiles that share the same number of matching alleles are not differentiated and due to the lack of other ranking criteria for the candidate list it may be difficult to discern a true match from the false positives or notice that all candidates are in fact false positives. SmartRank was developed to put forward only relevant candidates and rank them accordingly. The SmartRank software computes a likelihood ratio (LR) for the searched profile and each profile in the DNA database and ranks database entries above a defined LR threshold according to the calculated LR. In this study, we examined for mixed DNA profiles of variable complexity whether the true donors are retrieved, what the number of false positives above an LR threshold is and the ranking position of the true donors. Using 343 mixed DNA profiles over 750 SmartRank searches were performed. In addition, the performance of SmartRank and CODIS were compared regarding DNA database searches and SmartRank was found complementary to CODIS. We also describe the applicable domain of SmartRank and provide guidelines. The SmartRank software is open-source and freely available. Using the best practice guidelines, SmartRank enables obtaining investigative leads in criminal cases lacking a suspect.

Identifying and characterizing hepatitis C virus hotspots in Massachusetts: a spatial epidemiological approach.

Hepatitis C virus (HCV) infections have increased during the past decade but little is known about geographic clustering patterns.

High resolution microscopy reveals significant impacts of ocean acidification and warming on larval shell development in Laternula elliptica.

Environmental stressors impact marine larval growth rates, quality and sizes. Larvae of the Antarctic bivalve, Laternula elliptica, were raised to the D-larvae stage under temperature and pH conditions representing ambient and end of century projections (-1.6°C to +0.4°C and pH 7.98 to 7.65). Previous observations using light microscopy suggested pH had no influence on larval abnormalities in this species. Detailed analysis of the shell using SEM showed that reduced pH is in fact a major stressor during development for this species, producing D-larvae with abnormal shapes, deformed shell edges and irregular hinges, cracked shell surfaces and even uncalcified larvae. Additionally, reduced pH increased pitting and cracking on shell surfaces. Thus, apparently normal larvae may be compromised at the ultrastructural level and these larvae would be in poor condition at settlement, reducing juvenile recruitment and overall survival. Elevated temperatures increased prodissoconch II sizes. However, the overall impacts on larval shell quality and integrity with concurrent ocean acidification would likely overshadow any beneficial results from warmer temperatures, limiting populations of this prevalent Antarctic species.

InMAP: A model for air pollution interventions.

Mechanistic air pollution modeling is essential in air quality management, yet the extensive expertise and computational resources required to run most models prevent their use in many situations where their results would be useful. Here, we present InMAP (Intervention Model for Air Pollution), which offers an alternative to comprehensive air quality models for estimating the air pollution health impacts of emission reductions and other potential interventions. InMAP estimates annual-average changes in primary and secondary fine particle (PM2.5) concentrations-the air pollution outcome generally causing the largest monetized health damages-attributable to annual changes in precursor emissions. InMAP leverages pre-processed physical and chemical information from the output of a state-of-the-science chemical transport model and a variable spatial resolution computational grid to perform simulations that are several orders of magnitude less computationally intensive than comprehensive model simulations. In comparisons run here, InMAP recreates comprehensive model predictions of changes in total PM2.5 concentrations with population-weighted mean fractional bias (MFB) of -17% and population-weighted R2 = 0.90. Although InMAP is not specifically designed to reproduce total observed concentrations, it is able to do so within published air quality model performance criteria for total PM2.5. Potential uses of InMAP include studying exposure, health, and environmental justice impacts of potential shifts in emissions for annual-average PM2.5. InMAP can be trained to run for any spatial and temporal domain given the availability of appropriate simulation output from a comprehensive model. The InMAP model source code and input data are freely available online under an open-source license.

Electricity forecasting on the individual household level enhanced based on activity patterns.

Leveraging smart metering solutions to support energy efficiency on the individual household level poses novel research challenges in monitoring usage and providing accurate load forecasting. Forecasting electricity usage is an especially important component that can provide intelligence to smart meters. In this paper, we propose an enhanced approach for load forecasting at the household level. The impacts of residents' daily activities and appliance usages on the power consumption of the entire household are incorporated to improve the accuracy of the forecasting model. The contributions of this paper are threefold: (1) we addressed short-term electricity load forecasting for 24 hours ahead, not on the aggregate but on the individual household level, which fits into the Residential Power Load Forecasting (RPLF) methods; (2) for the forecasting, we utilized a household specific dataset of behaviors that influence power consumption, which was derived using segmentation and sequence mining algorithms; and (3) an extensive load forecasting study using different forecasting algorithms enhanced by the household activity patterns was undertaken.

Zooming in: From spatially extended traveling waves to localized structures: The case of the Sine-Gordon equation in (1+3) dimensions.

The Sine-Gordon equation in (1+3) dimensions has N-traveling front ("kink", "domain wall")- solutions for all N ≥ 1. A nonlinear functional of the solution, which vanishes on a single-front, maps multi-front solutions onto sets of infinitely long, but laterally bounded, rods, which move in space. Each rod is localized in the vicinity of the intersection of two Sine-Gordon fronts. The rod systems are solutions of the linear wave equation, driven by a term that is constructed out of Sine-Gordon fronts. An additional linear operation maps multi-rod systems onto sets of blobs. Each blob is localized in the vicinity of rod intersection, and moves in space. The blob systems are solutions of the linear wave equation, driven by a term that is also constructed out of Sine-Gordon fronts. The temporal evolution of multi-blob solutions mimics elastic collisions of systems of spatially extended particles.

Rainfall changes affect the algae dominance in tank bromeliad ecosystems.

Climate change and biodiversity loss have been reported as major disturbances in the biosphere which can trigger changes in the structure and functioning of natural ecosystems. Nonetheless, empirical studies demonstrating how both factors interact to affect shifts in aquatic ecosystems are still unexplored. Here, we experimentally test how changes in rainfall distribution and litter diversity affect the occurrence of the algae-dominated condition in tank bromeliad ecosystems. Tank bromeliads are miniature aquatic ecosystems shaped by the rainwater and allochthonous detritus accumulated in the bases of their leaves. Here, we demonstrated that changes in the rainfall distribution were able to reduce the chlorophyll-a concentration in the water of bromeliad tanks affecting significantly the occurrence of algae-dominated conditions. On the other hand, litter diversity did not affect the algae dominance irrespective to the rainfall scenario. We suggest that rainfall changes may compromise important self-reinforcing mechanisms responsible for maintaining high levels of algae on tank bromeliads ecosystems. We summarized these results into a theoretical model which suggests that tank bromeliads may show two different regimes, determined by the bromeliad ability in taking up nutrients from the water and by the total amount of light entering the tank. We concluded that predicted climate changes might promote regime shifts in tropical aquatic ecosystems by shaping their structure and the relative importance of other regulating factors.