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International audience; Aim. The majority of work done to gather information on the Earth's biodiversity has been carried out using in-situ data, with known issues related to epistemology (e.g., species determination and taxonomy), spatial uncertainty, logistics (time and costs), among others. An alternative way to gather information about spatial ecosystem variability is the use of satellite remote sensing. It works as a powerful tool for attaining rapid and standardized information. Several metrics used to calculate remotely sensed diversity of ecosystems are based on Shannon’s information theory, namely on the differences in relative abundance of pixel reflectances in a certain area. Additional metrics like the Rao’s quadratic entropy allow the use of spectral distance beside abundance, but they are point descriptors of diversity, that is they can account only for a part of the whole diversity continuum. The aim of this paper is thus to generalize the Rao’s quadratic entropy by proposing its parameterization for the first time. Innovation. The parametric Rao’s quadratic entropy, coded in R, (a) allows the representation of the whole continuum of potential diversity indices in one formula, and (b) starting from the Rao’s quadratic entropy, allows the explicit use of distances among pixel reflectance values, together with relative abundances. Main conclusions. The proposed unifying measure is an integration between abundance- and distance-based algorithms to map the continuum of diversity given a satellite image at any spatial scale. Being part of the rasterdiv R package, the proposed method is expected to ensure high robustness and reproducibility.

There is a lack of guidance on the choice of the spatial grain of predictor and response variables in species distribution models (SDM). This review summarizes the current state of the art with regard to the following points: (i) the effects of changing the resolution of predictor and response variables on model performance; (ii) the effect of conducting multi-grain versus single-grain analysis on model performance; and (iii) the role of land cover type and spatial autocorrelation in selecting the appropriate grain size. In the reviewed literature, we found that coarsening the resolution of the response variable typically leads to declining model performance. Therefore, we recommend aiming for finer resolutions unless there is a reason to do otherwise (e.g. expert knowledge of the ecological scale). We also found that so far, the improvements in model performance reported for multi-grain models have been relatively low and that useful predictions can be generated even from single-scale models. In addition, the use of high-resolution predictors improves model performance; however, there is only limited evidence on whether this applies to models with coarser-resolution response variables (e.g. 100 km2 and coarser). Low-resolution predictors are usually sufficient for species associated with fairly common environmental conditions but not for species associated with less common ones (e.g. common vs rare land cover category). This is because coarsening the resolution reduces variability within heterogeneous predictors and leads to underrepresentation of rare environments, which can lead to a decrease in model performance. Thus, assessing the spatial autocorrelation of the predictors at multiple grains can provide insights into the impacts of coarsening their resolution on model performance. Overall, we observed a lack of studies examining the simultaneous manipulation of the resolution of predictor and response variables. We stress the need to explicitly report the resolution of all predictor and response variables.

AimThe majority of work done to gather information on Earth diversity has been carried out by in-situ data, with known issues related to epistemology (e.g., species determination and taxonomy), spatial uncertainty, logistics (time and costs), among others. An alternative way to gather information about spatial ecosystem variability is the use of satellite remote sensing. It works as a powerful tool for attaining rapid and standardized information. Several metrics used to calculate remotely sensed diversity of ecosystems are based on Shannon’s Information Theory, namely on the differences in relative abundance of pixel reflectances in a certain area. Additional metrics like the Rao’s quadratic entropy allow the use of spectral distance beside abundance, but they are point descriptors of diversity, namely they can account only for a part of the whole diversity continuum. The aim of this paper is thus to generalize the Rao’s quadratic entropy by proposing its parameterization for the first time.InnovationThe parametric Rao’s quadratic entropy, coded in R, i) allows to represent the whole continuum of potential diversity indices in one formula, and ii) starting from the Rao’s quadratic entropy, allows to explicitly make use of distances among pixel reflectance values, together with relative abundances.Main conclusionsThe proposed unifying measure is an integration between abundance- and distance-based algorithms to map the continuum of diversity given a satellite image at any spatial scale.