# Spatial and Temporal Dependency of NDVI Satellite Imagery in Predicting Bird Diversity over France
## Material and Method
### Statistical Analysis  
In a first time, we built models at national scale using the total filtered bird dataset (\(n=759\)). We compared explanatory and predictive performances of NDVI data at several time periods with DHI data. For each of the four species richness metrics, we first constructed a model with only the climate variable, i.e., the dominant climate region of the bird plot, as predictor (e.g., SR\({}_{woodland}\)\(\sim\)Climate). Then, we added into the climate model both NDVI variables (Avg and SD) of each time period in five separate models (e.g., SR\({}_{woodland}\)\(\sim\)Climate + Avg.NDVI\({}_{065}\) + SD.NDVI\({}_{065}\)). Finally, we fitted a final model including DHI variables (6 predictors related to the Avg and SD of the three DHI components, see above) and the climate predictor. In a second time, we examined whether the best time period of NDVI depended on the plot land cover context. This analysis was only applied to woodland and farmland species richness that were the best explained bird metrics at national scale. We partitioned bird national data into subsets, according to the dominant land cover of the bird plot squares. Landscape composition in each plot was calculated as the proportion of area occupied by four land covers: woody vegetation (including hedgerows), permanent grasslands, winter crops (mainly wheat and barley) and summer crops (mainly maize and sunflower). Because agricultural blocks of the land cover map (RPG) may cover partially the bird plot squares, only the blocks included by at least 70% in the plots were conserved for the estimation. Based on the land cover proportions, four subsets of bird plots were defined with the constraint to obtain a sample size large enough (i.e., with \(n>100\)) and a high dominance of a specific land cover (Table 1). For each subset, we built models with climate and NDVI variables of each date as for the national scale. Relationships between bird species richness and predictors were explored using generalized additive models (GAMs) with R version 3.1.0 software ([PERSON], 2015) and the _gam_ package ([PERSON], 2015). The general expression of GAM model is ([PERSON], 2015):  
\[g(E(Y|X_{1},X_{2},...,X_{p}))=f_{0}+f_{1}(X_{1})+f_{2}(X_{2})+...+f_{p}(X_{p})= f_{0}+\sum_{i=1}^{p}f_{i}(X_{i}) \tag{1}\]  
where \(Y\) is the response variable, \(X_{i}\) the predictors, \(f_{i}\) the non-parametric smooth functions and \(g\) the link function relating to the expected value of \(Y\). \begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & \multicolumn{2}{c}{**Plots Dominated by**} & \multicolumn{3}{c}{**Plots Dominated by**} \\  & \multicolumn{2}{c}{**Woodlands**} & \multicolumn{3}{c}{**Grasslands**} \\ \hline \(n=114\) & **Min–Max** & **Mean (SD)** & \(n=127\) & **Min–Max** & **Mean (SD)** \\ \hline \% Tree cover & **80–100** & **94.2 (5.8)** & \% Tree cover & 0–64 & 25.5 (14.3) \\ \% Grass cover & 0–9 & 0.7 (1.8) & \% Grass cover & **25–82** & **38 (11.6)** \\ \% Winter crops & 0–3 & 0.1 (0.4) & \% Winter crops & 0–56 & 7.7 (8.8) \\ \% Summer crops & 0–14 & 0.6 (2.1) & \% Summer crops & 0–25 & 3.6 (4.9) \\ \hline \hline  & \multicolumn{2}{c}{**Plots Dominated by**} & \multicolumn{3}{c}{**Plots Dominated by**} \\  & \multicolumn{2}{c}{**Winter Crops**} & \multicolumn{3}{c}{**Summer Crops**} \\ \hline \(n=149\) & **Min–Max** & **Mean (\(\pm\)SD)** & \(n=106\) & **Min–Max** & **Mean (\(\pm\)SD)** \\ \hline \% Tree cover & 0–58 & 18.2 (11.5) & \% Tree cover & 0–70 & 17.2 (11.5) \\ \% Grass cover & 0–48 & 4.8 (7.6) & \% Grass cover & 0–41 & 6.3 (8.2) \\ \% Winter crops & **25–77** & **39.9 (10.7)** & \% Winter crops & 0–57 & 21.7 (12.1) \\ \% Summer crops & 0–35 & 9.8 (8.5) & \% Summer crops & **15–73** & **22.9 (8.4)** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Distribution of the landscape composition in the four subsets of bird plots dominated by woodlands, grasslands, winter crops and summer crops. The average proportion is given with its range (min-max) and standard deviation (SD).