Abstract
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.
Highlights
Ecological systems are characterized by multivariate and stochastic dynamics at varying scales
When there was no difference between group means both methods performed and slightly underestimated the hypervolume
All but one transition plot fell inside the coniferous woodland hypervolume; this plot had a combination of low specific leaf area (SLA) and average canopy height that was not typical of coniferous woodland habitat
Summary
Ecological systems are characterized by multivariate and stochastic dynamics at varying scales. It is challenging to identify when change determined by an environmental or external driver has resulted in a shift to a new state (Kowalchuk et al 2003). Analyses that focus solely on univariate responses risk being unable to detect and predict emergent phenomena that result from the positive or negative covariance between system properties. A perturbation could cause a change that is only observable in a multivariate context (Kersting 1984). It would be desirable to consider changes in multiple ecosystem characteristics simultaneously, requiring an ability to theoretically and empirically evaluate high-dimensional responses. We follow convention by referring to the high-dimensional space of interest as the hypervolume (Blonder 2018)
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