Grass and tree cover responses to intra-seasonal rainfall variability vary along a rainfall gradient in African tropical grassy biomes

Although it is well known that mean annual rainfall (MAR) and rainfall seasonality have a key role in influencing the distribution of tree and grass cover in African tropical grassy biomes (TGBs), the impact of intra-seasonal rainfall variability on these distributions is less agreed upon. Since the prevalent mechanisms determining biome occurrence and distribution change with MAR, this research investigates the role of intra-seasonal rainfall variability for three different MAR ranges, assessing satellite data on grass and tree cover, rainfall and fire intervals at a sub-continental scale in sub-Saharan Africa. For MAR below 630 mm y−1, rainfall frequency had a positive relationship with grass cover; this relationship however became mostly negative at intermediate MAR (630–1200 mm y−1), where tree cover correspondingly mostly increased with rainfall frequency. In humid TGBs, tree cover decreased with rainfall intensity. Overall, intra-seasonal rainfall variability plays a role in determining vegetation cover, especially in mesic TGBs, where the relative dominance of trees and grasses has previously been largely unexplained. Importantly, the direction of the effect of intra-seasonal variability changes with MAR. Given the predicted increases in rainfall intensity in Africa as a consequence of climate change, the effects on TGBs are thus likely to vary depending on the MAR levels.

: Map of the spatial distribution of the three mean annual rainfall ranges Table S1: Pearson's r coefficients between explanatory variables in the three mean annual rainfall ranges Table S2: Generalized linear models for tree cover in the low mean annual rainfall range Table S3: Generalized linear models for grass cover in the low mean annual rainfall range Table S4: Generalized linear models for tree cover in the intermediate mean annual rainfall range Table S5: Generalized linear models for grass cover in the intermediate mean annual rainfall range Table S6: Generalized linear models for tree cover in the high mean annual rainfall range Table S7: Generalized linear models for tree cover without filtering by mean annual rainfall ranges Table S8: Generalized linear models for grass cover without filtering by mean annual rainfall ranges Note S1: Supplementary information for the residual analysis. Method and Results Table S9: Generalized linear models for the residual analysis Figure S2: Results of the residual analysis Figure S1: Geographical distribution of 0.5° grid cells in areas of tropical grassy biomes in sub-Saharan Africa (determined as explained in the Material and Methods section in the main text) within the three mean annual rainfall ranges R1 (0-630 mm y -1 ), R2 (630-1200 mm y -1 ) and R3 (1200-2500 mm y -1 ).  Table S1: Pearson's r coefficients between explanatory variables in the three mean annual rainfall (MAR) ranges. Pearson's r between MAR, rainfall seasonality index (SI), logarithmic average fire intervals (log10(AFI)), wet-season rainfall intensity (aw) and frequency (lw) for R1 (MAR≤630 mm y -1 ), R2 (630 mm y -1 <MAR < 1200 mm y -1 ) and R3 (MAR ≥ 1200 mm y -1 )  Table S2: GLMs for tree cover in the low mean annual rainfall range (MAR≤630 mm y -1 ). Explanatory variables are: MAR, rainfall seasonality index (SI), logarithmic average fire interval (log10(AFI)), wet-season daily rainfall intensity (aw) and wet-season rainfall frequency (lw). Among all the possible combinations of predictors, only models with Akaike information criterion (AIC) smaller than the intercept-only model are shown. For each case we report the coefficients of the predictors (x1-x4), the explained deviance (R 2 ) and the AIC differences (DAIC). Note that predictor variables were standardized such that in the GLMs their coefficient magnitude is a measure of their importance in the model. See Material and Methods in the main text for a detailed description of the statistical model analysis.

METHOD
In order to understand the effective dependence of the vegetation cover variables on the intraseasonal rainfall variables (i.e. whether this dependence was or not influenced by other explanatory variables due to collinearity) we performed a residual analysis for the cases where the best models for vegetation cover included the wet-season rainfall intensity (aw) or frequency (lw) (See Table 1 in the main text).
To this end, given V the vegetation cover (tree cover T or grass cover G) and R the intra-seasonal rainfall variables (aw or lw), we computed: (1) The multi-variable GLM of V with mean annual rainfall (MAR), rainfall seasonality index (SI) and average fire intervals in logarithmic scale (log10(AFI)), included as linear terms (see also Material and Method section in the main text, and Table S2-S6 for the results).
(2) The deviance residuals of the GLM for V (V').
(3) The multi-variable GLM of R with MAR, SI, log10(AFI), included as linear terms (see Table S9 below). lw was fitted assuming binomial error distribution with a logit function, because, like vegetation cover, it is limited between 0 and 1, while aw was fitted assuming normal error distribution. (4) The deviance residuals of the GLM for R (R').
(5) The linear fit between V' and R', evaluated using the R 2 . A high R 2 implied that the dependence of V on R was direct and not only influenced by the other variables. Table S9 below summarizes the GLMs for aw or lw (see step 3 of the procedure described above) and the GLMs for tree and grass cover for the intermediate rainfall range (see step 1 above), which are not included in Tables S2-S6 for the following reason: in the intermediate range the best GLM for T with lw was a parabolic logit fit (Table 1), thus we computed the residual analysis for data below and above the parabolic logit fit minimum (lw=0.45 d -1 ), in order to investigate the effective tendency (i.e. increase or decrease) of tree cover with respect to lw. Since also G had a parabolic logit dependence on lw , quite specular to trees, we computed, as done for trees, the residual analysis for data below and above the parabolic logit fit maximum (lw=0.55 d -1 ), even though this model was the third selected model (DAIC=1.72, see Fig. 3b and Table S5). Table S9: Generalized linear models for the residual analysis. GLMs for mean daily rainfall intensity in the wet-season (aw) or mean rainfall frequency in the wet season (lw) in the three mean annual rainfall (MAR) ranges: low MAR (R1, MAR≤630 mm y -1 ), intermediate MAR (R2, 630 mm y -1 <MAR < 1200 mm y -1 ) and high MAR (R3, MAR ≥ 1200 mm y -1 ). GLMs for tree and grass cover in R2 are also reported. Predictors are: MAR, rainfall seasonality index (SI), logarithmic average fire interval (log10(AFI)). The explained deviance (R 2 ) is reported for each case. Note that predictor variables were standardized such that in the GLMs their coefficient magnitude is a measure of their importance in the model. After the computation of the residuals of the GLMs for vegetation cover and for intra-seasonal rainfall variables (see steps 2,4 in the procedure above), we computed the linear fits between these two residual sets (see step 5 in the procedure above). Figure S2 shows the scatterplot of the residuals along with the linear fits and the R 2 for the different MAR ranges. Figure S2: Results of the residual analysis. (a) Scatter plot between the deviance residuals of the grass cover GLM (y-axis) and the deviance residuals of lw GLM (x-axis) at low mean annual rainfall (MAR ≤630 mm y -1 ). Continuous line is the linear fit between the two residual sets; (b) Scatter plot between the deviance residuals of the grass cover GLM (y-axis) and the deviance residuals of lw GLM (x-axis) computed for lw < 0.55 d -1 (blue circles) and lw ³ 0.55 d -1 (red circles) at intermediate mean annual rainfall (630 mm y -1 <MAR < 1200 mm y -1 ). Lines are the linear fits between the two