Comparison of complex modeling strategies for prediction of a binary outcome based on a few,highly correlated predictors

Motivated by a clinical prediction problem, a simulation study was performed to compare different approaches for building risk prediction models. Robust prediction models for hospital survival in patients with acute heart failure were to be derived from three highly correlated blood parameters measured up to four times, with predictive ability having explicit priority over interpretability. Methods that relied only on the original predictors were compared with methods using an expanded predictor space including transformations and interactions. Predictors were simulated as transformations and combinations of multivariate normal variables which were fitted to the partly skewed and bimodally distributed original data in such a way that the simulated data mimicked the original covariate structure. Different penalized versions of logistic regression as well as random forests and generalized additive models were investigated using classical logistic regression as a benchmark. Their performance was assessed based on measures of predictive accuracy, model discrimination, and model calibration. Three different scenarios using different subsets of the original data with different numbers of observations and events per variable were investigated. In the investigated setting, where a risk prediction model should be based on a small set of highly correlated and interconnected predictors, Elastic Net and also Ridge logistic regression showed good performance compared to their competitors, while other methods did not lead to substantial improvements or even performed worse than standard logistic regression. Our work demonstrates how simulation studies that mimic relevant features of a specific data set can support the choice of a good modeling strategy.     

Cognitive predictors of balance in Parkinson’s disease

Postural instability is one of the most incapacitating symptoms of Parkinson’s disease (PD) and appears to be related to cognitive deficits. This study aims to determine the cognitive factors that can predict deficits in static and dynamic balance in individuals with PD. A sociodemographic questionnaire characterized 52 individuals with PD for this work. The Trail Making Test, Rule Shift Cards Test, and Digit Span Test assessed the executive functions. The static balance was assessed using a plantar pressure platform, and dynamic balance was based on the Timed Up and Go Test. The results were statistically analysed using SPSS Statistics software through linear regression analysis. The results show that a statistically significant model based on cognitive outcomes was able to explain the variance of motor variables. Also, the explanatory value of the model tended to increase with the addition of individual and clinical variables, although the resulting model was not statistically significant The model explained 25–29% of the variability of the Timed Up and Go Test, while for the anteroposterior displacement it was 23–34%, and for the mediolateral displacement it was 24–39%. From the findings, we conclude that the cognitive performance, especially the executive functions, is a predictor of balance deficit in individuals with PD.     

Multimodel inference in ecology and evolution: challenges and solutions

Information theoretic approaches and model averaging are increasing in popularity, but this approach can be difficult to apply to the realistic, complex models that typify many ecological and evolutionary analyses. This is especially true for those researchers without a formal background in information theory. Here, we highlight a number of practical obstacles to model averaging complex models. Although not meant to be an exhaustive review, we identify several important issues with tentative solutions where they exist (e.g. dealing with collinearity amongst predictors; how to compute model-averaged parameters) and highlight areas for future research where solutions are not clear (e.g. when to use random intercepts or slopes; which information criteria to use when random factors are involved). We also provide a worked example of a mixed model analysis of inbreeding depression in a wild population. By providing an overview of these issues, we hope that this approach will become more accessible to those investigating any process where multiple variables impact an evolutionary or ecological response.     

Testing Darwin's naturalization hypothesis in the Azores

Invasive species are a threat for ecosystems worldwide, especially oceanic islands. Predicting the invasive potential of introduced species remains difficult, and only a few studies have found traits correlated to invasiveness. We produced a molecular phylogenetic dataset and an ecological trait database for the entire Azorean flora and find that the phylogenetic nearest neighbour distance (PNND), a measure of evolutionary relatedness, is significantly correlated with invasiveness. We show that introduced plant species are more likely to become invasive in the absence of closely related species in the native flora of the Azores, verifying Darwin's 'naturalization hypothesis'. In addition, we find that some ecological traits (especially life form and seed size) also have predictive power on invasive success in the Azores. Therefore, we suggest a combination of PNND with ecological trait values as a universal predictor of invasiveness that takes into account characteristics of both introduced species and receiving ecosystem.     

Regarding paper: "robustness of shrunken predictors in stratified population"

Article http://dx.doi.org/10.1002/bimj.4710360113 Authors reply http://dx.doi.org/10.1002/bimj.200810432     

Correction of Eye-estimation by Using Shrunken Predictors

The eye-estimation method is widely used in practice. Several agronomic and biological measures are currently estimated by this method. If a simple linear regression is the kernel model a shrinkage technique can be used for correcting the bias associated with this method. Two predictors of the population total are proposed and the corresponding model-based errors are deduced. A simulation study fixes the behaviour of the predictors.     

Diversity of European habitat types is correlated with geography more than climate and human pressure

Habitat richness, that is, the diversity of ecosystem types, is a complex, spatially explicit aspect of biodiversity, which is affected by bioclimatic, geographic, and anthropogenic variables. The distribution of habitat types is a key component for understanding broad‐scale biodiversity and for developing conservation strategies. We used data on the distribution of European Union (EU) habitats to answer the following questions: (i) how do bioclimatic, geographic, and anthropogenic variables affect habitat richness? (ii) Which of those factors is the most important? (iii) How do interactions among these variables influence habitat richness and which combinations produce the strongest interactions? The distribution maps of 222 terrestrial habitat types as defined by the Natura 2000 network were used to calculate habitat richness for the 10 km × 10 km EU grid map. We then investigated how environmental variables affect habitat richness, using generalized linear models, generalized additive models, and boosted regression trees. The main factors associated with habitat richness were geographic variables, with negative relationships observed for both latitude and longitude, and a positive relationship for terrain ruggedness. Bioclimatic variables played a secondary role, with habitat richness increasing slightly with annual mean temperature and overall annual precipitation. We also found an interaction between anthropogenic variables, with the combination of increased landscape fragmentation and increased population density strongly decreasing habitat richness. This is the first attempt to disentangle spatial patterns of habitat richness at the continental scale, as a key tool for protecting biodiversity. The number of European habitats is related to geography more than climate and human pressure, reflecting a major component of biogeographical patterns similar to the drivers observed at the species level. The interaction between anthropogenic variables highlights the need for coordinated, continental‐scale management plans for biodiversity conservation.     

Likelihood of changes in forest species suitability,distribution, and diversity under future climate: The case of Southern Europe

Forest conservation strategies and plans can be unsuccessful if the new habitat conditions determined by climate change are not considered. Our work aims at investigating the likelihood of future suitability, distribution and diversity for some common European forest species under the projected changes in climate, focusing on Southern Europe. We combine an Ensemble Platform for Species Distribution Models (SDMs) to five Global Circulation Models (GCMs) driven by two Representative Concentration Pathways (RCPs), to produce maps of future climate‐driven habitat suitability for ten categories of forest species and two time horizons. For each forest category and time horizon, ten maps of future distribution (5 GCMs by 2 RCPs) are thus combined in a single suitability map supplied with information about the “likelihood” adopting the IPCC terminology based on consensus among projections. Then, the statistical significance of spatially aggregated changes in forest composition at local and regional level is analyzed. Finally, we discuss the importance, among SDMs, that environmental predictors seem to have in influencing forest distribution. Future impacts of climate change appear to be diversified across forest categories. A strong change in forest regional distribution and local diversity is projected to take place, as some forest categories will find more suitable conditions in previously unsuitable locations, while for other categories the same new conditions will become less suited. A decrease in species diversity is projected in most of the area, with Alpine region showing the potentiality to become a refuge for species migration.     

Truffle biogeography—A case study revealing ecological niche separation of different Tuber species

Ecology of hypogeic mycorrhizal fungi, such as truffles, remains largely unknown, both in terms of their geographical distribution and their environmental niches. Occurrence of true truffles (Tuber spp.) was therefore screened using specific polymerase chain reaction (PCR) assays and subsequent PCR amplicon sequencing in tree roots collected at 322 field sites across the Czech Republic. These sites spanned a wide range of climatic and soil conditions. The sampling was a priori restricted to areas thought to be suitable for Tuber spp. inasmuch as they were characterized by weakly acidic to alkaline soils, warmer climate, and with tree species previously known to host true truffles. Eight operational taxonomic units (OTUs) corresponding to Tuber aestivum, T. borchii, T. foetidum, T. rufum, T. indicum, T. huidongense, T. dryophilum, and T. oligospermum were detected. Among these, T. borchii was the OTU encountered most frequently. It was detected at nearly 19% of the sites. Soil pH was the most important predictor of Tuber spp. distribution. Tuber borchii preferred weakly acidic soils, T. foetidum and T. rufum were most abundant in neutral soils, and T. huidongense was restricted to alkaline soils. Distribution of T. aestivum was mainly dictated by climate, with its range restricted to the warmest sites. Host preferences of the individual Tuber spp. were weak compared to soil and climatic predictors, with the notable exception that T. foetidum appeared to avoid oak trees. Our results open the way to better understanding truffle ecology and, through this new knowledge, also to better‐informed trufficulture.     

Environmental predictors of the occurrence of exotic <Emphasis Type="Italic">Hydrilla verticillata</Emphasis> (L.f.) Royle and native <Emphasis Type="Italic">Egeria najas</Emphasis> Planch. in a sub-tropical river floodplain: the Upper River Paraná, Brazil

The Upper River Paraná Floodplain System comprises the rivers Ivinheima, Baía and Paraná, which with their associated waterbodies form three subsystems, each showing individual characteristics. Hydrilla verticillata recently invaded the Upper Paraná Floodplain, while Egeria najas is the native most abundant submersed macrophyte. A large flood-pulse, during January–March 2007, abruptly reduced macrophyte stands in many areas to near-zero and dispersed propagules over the entire floodplain. From April 2007 to April 2008, we conducted three surveys sampling for the presence–absence of H. verticillata and E. najas and environmental variables aiming to answer: (1) How rapid is the colonization–regeneration process for both species? (2) Which habitats seem to be more susceptible to their colonization? (3) Which environmental factors can best predict their occurrence? Neither H. verticillata nor E. najas colonized the Ivinheima subsystem. In the Baía subsystem, E. najas had only two occurrences while H. verticillata was not present. In the Paraná subsystem, E. najas predominantly occurred in river channels, but it was also common in floodplain lakes. In April 2007, it was found in 13% of the sites in the Paraná subsystem, increasing to 30% in November 2007 and reaching 34% in April 2008. H. verticillata did not successfully colonize floodplain lakes of the Paraná subsystem. In channels, it had 34% occurrence in April 2007, increasing to 62% in November 2007 and remaining at 62% in April 2008. The role of environmental variables in predicting species occurrence changed depending upon the scale of the analysis. Considering the whole Upper Paraná floodplain, water transparency followed by electrical conductivity were the strongest predictors for both species. Colonization by submersed plants seems improbable in the Ivinheima subsystem owing to its low water transparency besides frequent localized floods; in the Baía subsystem, it seems inhibited by transparency and low alkalinity. Considering just the Paraná subsystem, the proportion of organic matter in sediment, ten times higher in floodplain lakes than in channels, was the best predictor for H. verticillata occurrence (also related to water pH and transparency), while E. najas was only significantly explained by transparency.