## 3 Functional Diversity and Ecological Function  
Functional diversity is broadly defined as the value and range of functional traits in a community [116, 117], and its importance cannot be overstated. In practical terms, functional diversity facilitates comparisons at multiple scales. In conceptual terms, there is increasing evidence that functional diversity greatly contributes to the stability of ecological function [117, 118, 119, 120, 121] and to ecosystem resilience within and across scales [122, 123], that functional diversity is influenced by the intensity of disturbance [124, 125], and that functional diversity and species diversity are related [126, 127, 125]. This may explain efforts aimed at developing qualitative and quantitative measures [128, 129] to characterize within (local or alpha), between (landscape or beta), and overall (regional or gamma) [130, 131, 132] functional diversity and understand their scale dependency in space [133, 134, 135, 120] and time [136, 137] in response to changing environmental conditions. It is important to emphasize that functional diversity is a community property [128, 138] and therefore, when using spatially explicit remotely sensed data, functional diversity is estimated in communities or neighborhoods of pixels [15, 56, 66]. In high-resolution airborne images (e.g., 1-5 m), single or few pixels represent individual trees, whereas the size of the neighborhoods, field sampling units, or plots capture community structure and processes in any given region. The development of metrics to quantify functional diversity mirrors similar efforts aimed at characterizing spectral diversity, i.e., the variability in spectral reflectance, a dimension of diversity linked to plant taxonomic and phylogenetic diversity [139, 140, 141, 142, 143]. Therefore, the metrics described below, although focusing mainly on functional diversity, will also include references to spectral diversity (Figure 2b, Stage 5; Files S1 and S2: Table S2). Quantifying functional diversity may use single or multiple functional traits to identify functional groups, i.e., groups of species sharing similar traits and most likely performing similar functions or exhibiting similar ecological strategies within ecosystems [121, 144, 145, 146, 147, 148, 149]. One large-scale functional grouping of plants uses categorical traits such as life form, leaf type, and leaf phenology to identify plant functional types (PFT); these traits are currently retrievable from remotely sensed data [150]. Another functional grouping of plants used continuous traits, more specifically canopy functional traits derived from airborne hyperspectral data and cluster analyses to identify functional forest classes (FFC) and functional forest groups (FFG) that were subsequently scaled at a country level (Figure 2b Stage 5; Files S1 and S2: Table S2; [12]). Identifying these classes is a prerequisite to characterize alpha and beta diversity, as shown by work on spectral diversity [56, 151]. Functional diversity is more commonly expressed by metrics or indices that use as input single or multiple functional traits that can take discrete and/or continuous values [135, 136, 152, 153, 154]. A common metric based on single traits is the community weighted mean of trait values (CWM) that expresses the importance of a trait based on species abundances; when estimated for many communities, it can be used to understand trait-environment relationships. In the context of this review, CWM has been used to scale leaf- and plant-level traits derived from field, laboratory, and spectroscopy measurements to canopy or plot scales (Figure 2b, Stage 5; Files S1 and S2: Table S2; [5; 47; 80]). Subsequently, the plot-level traits are used with multispectral or hyperspectral data to develop predictive models for trait mapping purposes.