@misc{BeckBallesterosMejiaBuchmannetal.2012,
  author    = {Beck, Jan and Ballesteros-Mejia, Liliana and Buchmann, Carsten M. and Dengler, J{\"u}rgen and Fritz, Susanne A. and Gruber, Bernd and Hof, Christian and Jansen, Florian and Knapp, Sonja and Kreft, Holger and Schneider, Anne-Kathrin and Winter, Marten and Dormann, Carsten F.},
  title     = {What's on the horizon for macroecology?},
  series = {Ecography : pattern and diversity in ecology ; research papers forum},
  volume    = {35},
  journal   = {Ecography : pattern and diversity in ecology ; research papers forum},
  number    = {8},
  publisher = {Wiley-Blackwell},
  address   = {Hoboken},
  issn      = {0906-7590},
  doi       = {10.1111/j.1600-0587.2012.07364.x},
  pages     = {673 -- 683},
  year      = {2012},
  abstract  = {Over the last two decades, macroecology the analysis of large-scale, multi-species ecological patterns and processes has established itself as a major line of biological research. Analyses of statistical links between environmental variables and biotic responses have long and successfully been employed as a main approach, but new developments are due to be utilized. Scanning the horizon of macroecology, we identified four challenges that will probably play a major role in the future. We support our claims by examples and bibliographic analyses. 1) Integrating the past into macroecological analyses, e.g. by using paleontological or phylogenetic information or by applying methods from historical biogeography, will sharpen our understanding of the underlying reasons for contemporary patterns. 2) Explicit consideration of the local processes that lead to the observed larger-scale patterns is necessary to understand the fine-grain variability found in nature, and will enable better prediction of future patterns (e.g. under environmental change conditions). 3) Macroecology is dependent on large-scale, high quality data from a broad spectrum of taxa and regions. More available data sources need to be tapped and new, small-grain large-extent data need to be collected. 4) Although macroecology already lead to mainstreaming cutting-edge statistical analysis techniques, we find that more sophisticated methods are needed to account for the biases inherent to sampling at large scale. Bayesian methods may be particularly suitable to address these challenges. To continue the vigorous development of the macroecological research agenda, it is time to address these challenges and to avoid becoming too complacent with current achievements.},
  language  = {en}
}
@article{DormannElithBacheretal.2013,
  author    = {Dormann, Carsten F. and Elith, Jane and Bacher, Sven and Buchmann, Carsten M. and Carl, Gudrun and Carre, Gabriel and Garcia Marquez, Jaime R. and Gruber, Bernd and Lafourcade, Bruno and Leitao, Pedro J. and M{\"u}nkem{\"u}ller, Tamara and McClean, Colin and Osborne, Patrick E. and Reineking, Bjoern and Schr{\"o}der-Esselbach, Boris and Skidmore, Andrew K. and Zurell, Damaris and Lautenbach, Sven},
  title     = {Collinearity a review of methods to deal with it and a simulation study evaluating their performance},
  series = {Ecography : pattern and diversity in ecology ; research papers forum},
  volume    = {36},
  journal   = {Ecography : pattern and diversity in ecology ; research papers forum},
  number    = {1},
  publisher = {Wiley-Blackwell},
  address   = {Hoboken},
  issn      = {0906-7590},
  doi       = {10.1111/j.1600-0587.2012.07348.x},
  pages     = {27 -- 46},
  year      = {2013},
  abstract  = {Collinearity refers to the non independence of predictor variables, usually in a regression-type analysis. It is a common feature of any descriptive ecological data set and can be a problem for parameter estimation because it inflates the variance of regression parameters and hence potentially leads to the wrong identification of relevant predictors in a statistical model. Collinearity is a severe problem when a model is trained on data from one region or time, and predicted to another with a different or unknown structure of collinearity. To demonstrate the reach of the problem of collinearity in ecology, we show how relationships among predictors differ between biomes, change over spatial scales and through time. Across disciplines, different approaches to addressing collinearity problems have been developed, ranging from clustering of predictors, threshold-based pre-selection, through latent variable methods, to shrinkage and regularisation. Using simulated data with five predictor-response relationships of increasing complexity and eight levels of collinearity we compared ways to address collinearity with standard multiple regression and machine-learning approaches. We assessed the performance of each approach by testing its impact on prediction to new data. In the extreme, we tested whether the methods were able to identify the true underlying relationship in a training dataset with strong collinearity by evaluating its performance on a test dataset without any collinearity. We found that methods specifically designed for collinearity, such as latent variable methods and tree based models, did not outperform the traditional GLM and threshold-based pre-selection. Our results highlight the value of GLM in combination with penalised methods (particularly ridge) and threshold-based pre-selection when omitted variables are considered in the final interpretation. However, all approaches tested yielded degraded predictions under change in collinearity structure and the folk lore'-thresholds of correlation coefficients between predictor variables of |r| >0.7 was an appropriate indicator for when collinearity begins to severely distort model estimation and subsequent prediction. The use of ecological understanding of the system in pre-analysis variable selection and the choice of the least sensitive statistical approaches reduce the problems of collinearity, but cannot ultimately solve them.},
  language  = {en}
}