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September 2022 Spatial functional data modeling of plant reflectances
Philip A. White, Henry Frye, Michael F. Christensen, Alan E. Gelfand, John A. Silander
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Ann. Appl. Stat. 16(3): 1919-1936 (September 2022). DOI: 10.1214/21-AOAS1576


Plant reflectance spectra, the profile of light reflected by leaves across different wavelengths, supply the spectral signature for a species at a spatial location to enable estimation of functional and taxonomic diversity for plants. We consider leaf spectra as “responses” to be explained spatially. These reflectance spectra are also functions over wavelength that respond to the environment. Our motivating data are gathered for several plant families from the Greater Cape Floristic Region (GCFR) in South Africa and lead us to develop rich novel spatial models that can explain spectra for genera within families. Wavelength responses for an individual leaf are viewed as a function of wavelength, leading to functional data modeling. Local environmental features become covariates. We introduce a wavelength, covariate interaction, since the response to environmental regressors may vary with wavelength, as may variance. Formal spatial modeling enables prediction of reflectances for genera at unobserved locations with known environmental features. We incorporate spatial dependence, wavelength dependence, and space–wavelength interaction (in the spirit of space–time interaction). We implement out-of-sample validation for model selection, finding that the model features above are informative for the functional data analysis. We supply ecological interpretation of the results under the selected model.

Funding Statement

Data collection efforts were made possible by funding from National Science Foundation grant DEB-1046328 to J.A. Silander. Additional support was provided by NASA FINESST grant award 19-EARTH20-0266 to H.A. Frye and J.A. Silander.


We thank Matthew Aiello-Lammens, Douglas Euston-Brown, Hayley Kilroy Mollmann, Cory Merow, Jasper Slingsby, Helga van der Merwe, and Adam Wilson for their contributions in the data collection and curation. Special thanks to Cape Nature and the Northern Cape Department of Environment and Nature Conservation for permission for collection leaf spectra and traits.


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Philip A. White. Henry Frye. Michael F. Christensen. Alan E. Gelfand. John A. Silander. "Spatial functional data modeling of plant reflectances." Ann. Appl. Stat. 16 (3) 1919 - 1936, September 2022.


Received: 1 March 2021; Revised: 1 August 2021; Published: September 2022
First available in Project Euclid: 19 July 2022

Digital Object Identifier: 10.1214/21-AOAS1576

Keywords: Environmental regressors , Functional data analysis , Heterogeneity , hierarchical model , interaction , kernel weighting , reflectance , spatial confounding

Rights: Copyright © 2022 Institute of Mathematical Statistics


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Vol.16 • No. 3 • September 2022
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