Potential of GLMM in modelling invasive spread.

Abstract

Abstract Utilization of generalized linear mixed models (GLMM) in invasion biology has increased exponentially during the last 5-10 years. GLMM are useful tools that can handle data with various distributions as well as spatial or temporal dependence, which are involved in many study designs. We review the current state-of-the-art of GLMM with special focus on applications in invasion biology. This review covers all steps of data analysis with GLMM. We address frequently encountered practical problems, such as failure of convergence, and put some emphasis on validation of model assumptions. Further, we point towards possibilities of analysing zero-heavy data using combined GLMM. More detailed insight into practical applications of GLMM is provided in three worked examples in the supplementary material. Regarding applications of GLMM in invasion biology, a literature analysis showed that random effects are mostly used to account for non-independence of observations through study design, but rarely for estimation of random variation. There may be some potential in using random-effect estimation more consciously, as in some recent studies of genetic variation of invasive species. Often, invasion biologists have to deal with count data or proportions. In such cases, several methods of parameter estimation are available, but their suitability depends on characteristics of the data at hand and, hence, they should be chosen carefully. Also, repeated measures are common in invasion biology. In GLMM frameworks, the auto-correlation of such data can be modelled by structured co-variance matrices. This opportunity, however, has seldom been used.