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.
Empirical quantification of biodiversity changes remains a challenge even in well surveyed groups such as birds. This may be because the change depends on spatio-temporal scales, specifically on spatial grain (i.e. area of a sampling unit), geographic extent (i.e. size of the area of interest), temporal grain (i.e. duration of a sampling event), and temporal extent (i.e. length of the time series). Further, different metrics of biodiversity may exhibit different trends. Here we review global literature assessing the temporal trends of avian biodiversity from ca 1900 AD to present, focusing on studies summarising trends across many locations within a larger region (i.e. spatially replicated). From each study we extracted direction of average trend (increase, decrease, stable), spatial and temporal grains and extents at which trends have been assessed, metrics of biodiversity, and location. We then discuss the trends as a function of the spatio-temporal grains and extents they are defined at. We found 59 trends of 12 metrics, where each trend is an average of trends from multiple sites (spatial replicates). There was a tendency of biodiversity metrics to increase at local and regional spatial scales, and to not increase globally. We thus confirmed that biodiversity dynamics can have opposite trends at different spatial scales. Concerning temporal grain, it was poorly documented across the studies, with inconsistent definitions, and we suggest a common framework to better understand the link between temporal scales and biodiversity dynamics. We have also identified underrepresented regions (those outside North America and Europe), periods (those before the 70’s), and biodiversity metrics that need further attention. We highlight the importance of considering both spatial and temporal scaling jointly in any assessment of biodiversity change, and provide guidelines for how to do this effectively both in birds, and in other taxa.
This article addresses the propagation of constitutive uncertainties between scales occurring in the multiscale modelling of fibre-reinforced composites. The amplification of such uncertainties through upward or downward transitions by a homogenisation model is emphasized and exemplified with the Mori-Tanaka model. In particular, the sensitivity to data uncertainty in the inverse determination of constituent parameters based on downward transitions is stressed on an example. Then a database improvement method, which exploits simultaneously the available information on constitutive uncertainties at all scales instead of just propagating those associated with one scale, is presented and shown to yield substantial reductions in uncertainty for both the constitutive parameters and the response of structures. The latter finding is demonstrated on two examples of structures, with significant gains in confidence obtained on both.
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