Model-based hypervolumes for complex ecological data.

Developing a holistic understanding of the ecosystem impacts of global change requires methods that can quantify the interactions among multiple response variables. One approach is to generate high dimensional spaces, or hypervolumes, to answer ecological questions in a multivariate context. A range of statistical methods has been applied to construct hypervolumes but have not yet been applied in the context of ecological data sets with spatial or temporal structure, for example, where the data are nested or demonstrate temporal autocorrelation. We outline an approach to account for data structure in quantifying hypervolumes based on the multivariate normal distribution by including random effects. Using simulated data, we show that failing to account for structure in data can lead to biased estimates of hypervolume properties in certain contexts. We then illustrate the utility of these "model-based hypervolumes" in providing new insights into a case study of afforestation effects on ecosystem properties where the data has a nested structure. We demonstrate that the model-based generalization allows hypervolumes to be applied to a wide range of ecological data sets and questions.