Analyzing co-variation patterns between functional and multivariate ecological data – the functional co-inertia analysis
(English)Manuscript (preprint) (Other academic)
- Ecological phenomena are often better represented by mathematical functions than by discrete values. Examples include population trends, temperatures curves, functional responses of predators and seed size distributions. A collection of such functions describing the same phenomenon in different sites or at different points in time constitutes a functional data set. To facilitate the use of functional data sets, we develop a statistical method that allows for the analysis of co-variation between functional and multivariate data sets.
- We extend the multivariate co-inertia analysis framework for analyzing common variation structure between datasets to cases when one or both datasets consist of functional data. We use basis expansions of functions and weighted inner products to extend the concepts of inertia and co-inertia to functional data and present an extension of the RV-coefficient for quantifying the association between datasets. We then derive the functional co-inertia analysis (fCoIA) as a special case of the multivariate method. Using metrics derived from the functions in the basis expansion we express the fCoIA as a multivariate co-inertia analysis of basis expansion coefficients. The new approach is illustrated by coupling non-functional bryophyte species data with a functional dataset describing age-area distributions of young land-uplift islands.
- The technique efficiently summarizes the co-variation structure between the two datasets and provides quantifications and visualizations of the contributions from each data set to the co-variation..An important feature of the results is the graphical illustration of the common variation patterns through plots of approximations of cross-covariance function shapes describing the detailed co-variation of each variable in the multivariate data with the functional data.
- The methodology provides ecologists (potentially also evolutionary biologists) with a new tool for incorporating functional data into ordination analyses and considerably extends the realm of questions that can be addressed. In the future, the approach might be extended to other multivariate methods (e.g….) building on the co-inertia framework (e.g RLQ analysis) and we envision analyses matching environmental data to function valued species traits (e.g “reaction norms” of plastic phenotypic expressions).
functional data analysis, fCoIA, bryophytes, land uplift, co-inertia
Ecology Probability Theory and Statistics
Research subject Ecological Botany; Statistics
IdentifiersURN: urn:nbn:se:umu:diva-121235OAI: oai:DiVA.org:umu-121235DiVA: diva2:932291
FunderSwedish Research Council Formas, 215-2010-998