Mixed effects models and extensions in ecology with R

Abstract

No sooner, it seems, had our first book Analysing Ecological Data gone to print, than we embarked on the writing of the nearly 600 page text you are now holding. This proved to be a labour of love of sorts-we felt that there were certain issues sufficiently common in the analysis of ecological data that merited more detailed description and analysis. Thus the present book can be seen as a 'sequel' to Analysing Ecological Data but with much greater emphasis on these very issues so commonly encountered in the collection of, and analysis of, ecological data. In particular, we look at different ways of analysing nested data, heterogeneity of variance, spatial and temporal correlation, and zero-inflated data. The original plan was to write a text of about 350 pages, but to do justice to the sheer range of problems and ideas we have well exceeded that original target (as you can see!). Such is the scope of applied statistics in ecology. In particular, partly on the back of reviewer's comments, we have included a chapter on Bayesian Monte-Carlo Markov-Chain applications in generalized linear modelling. We hope this serves as an informative introduction (but no more than an introduction!) to this interesting and increasingly relevant area of statistics. We received lots of positive feedback on the approach and style we used in Analysing Ecological Data, especially the combination of case studies and a theory section. We have therefore followed the same approach with this book. This time, however, we have provided the R code used for the analysis. Most of this R code is included in the text, but where the code was particularly long, it is only available from the book's website at www.highstat.com. In the case studies, we also included advice on what to write in a paper.

Intercolony variations in movement patterns and foraging behaviors among herring gulls (Larus argentatus) breeding in the eastern Wadden Sea

“…To obtain and validate the optimal model, predictor selection was performed using the best‐subset method and based on the Akaike information criterion (AIC) value. A reasonable definition of the AIC based on mixed models is problematic (Korner‐Nievergelt, 2015; Zuur, Ieno, Walker, Saveliev, & Smith, 2009), and we therefore neglected the random effects solely for this predictor selection process, thus reducing the models to fixed effects. Model selection revealed that all the proposed predictors should be used as predictors within the final regression model.…”

Spatial and climatic patterns of the relative abundance of poisonous vs. non-poisonous plants across the Northern Tibetan Plateau

“…Here, we did not apply any data transformation for the three responsible variables because the relationship between responsible and explanatory variables might be changed due to data transformation. Instead, we hypothesized that the residuals of the best-fitted models are normally distributed and that the explanatory variables cause the non-normality (Zuur et al 2009). …”

“…7). Therefore, we accepted the alternative solution of Zuur et al (2009) that generalized additive models (GAMs) can cope with problems mentioned above. A linear equation can easily be extended into an additive model with multiple explanatory variables when smoothing functions are used to replace the slopes of the linear regressions:…”

“…Then, we carried out a backward selection approach process to identify the optimal models. Specifically, we dropped the least significant term, refitted the model, and continued this loop until all terms were significant as suggested by Zuur et al (2009). Meanwhile, we followed the lowest Akaike information criteria (AICs), which is generally used to measure goodness of fit and model complexity, to pick out the best-fitted GAM.…”

Nearly 200 years of sustained selection have not overcome the leaf area–stem size relationship in the poinsettia

“…We then fit another model allowing population/varieties to have a random slope in addition to a random intercept. We compared these two models (random intercept vs. random slope and intercept) using likelihood ratio tests and the Akaike Information Criterion (Zuur, Ieno, Walker, Saveliev, & Smith, 2009). Once the best model was chosen based on the random component, we examined whether cultivated and wild individuals differed in their leaf area–stem volume allometry testing the significance of the log 10 stem volume wild/cultivated interaction term.…”