# Spatial and Temporal Dependency of NDVI Satellite Imagery in Predicting Bird Diversity over France
## Material and Method
### Statistical Analysis
GAMs present the advantage to consider non-linear effects between response and predictor variables. Poisson distribution and a _log_ link function were used to calibrate the models. The most parsimonious models (i.e., with the lowest Akaike Information Criterion values) were selected by stepwise backward and forward variable selection [38]. In addition, the procedure was allowed to select from one to four degrees of smoothing (1 = no smoothing) for each quantitative variable in GAMs. The goodness of fit of the models (explanatory performance) was quantified by the amount of explained deviance (%\(D^{2}\)). The independent contribution of each variable to explain species richness was also estimated from a hierarchical partitioning procedure [39]. The predictive performance was calculated by _k_-fold cross-validation [40]. The initial dataset was splitted randomly in three groups of equal size (\(k=3\)). Two groups were used to calibrate the model and the third group was used as a test set to evaluate predictions. The concordance between predictions and observations was measured with the Spearman rank correlations (_Rlo_) ranging from \(-1\) to \(+1\)[41]. The correlation is considered to be weak for \(-1<Rho<0.25\), fair for 0.25 < _Rho_ < 0.50, moderate for 0.50 < _Rho_ < 0.75 and strong for _Rho_ > 0.75 [42]. Cross-validation was repeated 100 times per model to obtain a variance of _Rlo_. The predictive performances between the models were compared using _Wilcoxon rank-sum_ non-parametric tests. In order to assess whether the combination of multiple NDVI time periods lead to higher predictive performances than the use of a single date, a consensus approach was also followed. Because NDVI variables of different time periods were often highly correlated (_Rho_ > 0.70) they could not be included simultaneously into a single model [33]. Alternatively, the consensus approach provides means to combine ensembles of model predictions, and to test if the predictive performance is higher after combination. This approach is usually adopted in species distribution modelling to combine outputs of single modelling techniques and to reduce uncertainty of predictions [43]. Here, the outputs of single-date models were combined with the Weighted Average (WA) consensus method [43]. The predictions were calculated as the mean of predictions of single-date models weighted by their individual predictive performance (mean _Rlo_). The concordance between predictions and observations was evaluated in the same way than the models based on single date. Spatial autocorrelation of residuals was tested for each best model by computing non parametric spline correlograms using the _ncf_ package version 1.1-3 for R [44]. Neighbours were considered until a distance of 300 km. Because a positive inherent autocorrelation was observed only for the very close surveyed plot squares (Spatial autocorrelation < 0.2 within 20 km; average distance of the closest square = 8.15 \(\pm\) 7.01 km; Appendix B), we considered the potential effect as not significant in the analysis [45].