## 3 Results
### Combined Effect of Rainfall and Phenology  
The non-linear relationships between production and both rainfall and phenology, and the positive association between the latter (which results in the absence of values at two types of combinations: early phenology with abundant rainfall, and late phenology with scarce rainfall) result in complex patterns that are best visualized using integrated interaction plots (Figure 4). These plots show the combined effect of both variables (i.e., the sum of their main effects and their interaction) on the production of each of the four vegetation types; the variable ranges where no observations are available are left blank. These are particularly useful for defining the actual ranges of both variables for which  
Figure 3: Predictor effects describing the effect of rainfall, phenology, and herbivore density on the production of the four different vegetation types. Grey-blue bands are confidence bands representing the 95% confident intervals. The small black lines at the bottom of each plot indicate x-values of individual observations in the dataset. The y-axis represents the effect of each variable on the production of each vegetation type. optimal, suboptimal, and minimal production is predicted, which may differ considerably from those based on a direct extrapolation of the effect curves shown in Figure 3.  
The plots show a general pattern for the four vegetation types: production tends to follow a 2D concave downward function, with a local maximum at intermediate values of rainfall and phenology, and decreasing production below and above them. The location of this optimum and the shape of the curve (i.e., whether the decrease is rapid or slow, and more or less asymmetric) varies strongly among vegetation types. Saltmarsh production reaches its maximum when intermediate phenological peaks (days 200-240, i.e., early March-mid April) coincide with medium-high levels of accumulated rainfall (500-650 mm); then decreases strongly towards the lower part of the graph (i.e., at lower levels of rainfall, which take place at both early and intermediate phenologies); and decreases more gradually at higher rainfall levels (which coincide with delayed phenological peaks). Bulrush marsh production also peaks at medium-high levels of accumulated rainfall (500-650 mm) and  
Figure 4: Bi-dimensional effect plots describing the joint effect of phenology (time of the NDVI peak; x-axes) and water availability (rainfall accumulated until the phenological peak; y-axes) on the production of four different vegetation types. The effects displayed in the graph include some of the main effects of both variables and their interaction. Note that the color palette varies among graphs, i.e., the same color does not necessarily indicate the same range of production values in all graphs, and information on production values must be extracted from the contour lines. Ranges of production values shown by contour lines are: 0.14–0.36 for saltmarsh, 0.2–0.4 for bulrush marsh, 0.2–0.38 for shrubland, and 0.1–0.45 for grassland. Green and red lines indicate the observed (1996–2000) and predicted values (MIROC model: 2041–2070) of accumulated rainfall at all possible values of phenology (daily cumulative values, averaged across the aforementioned time series). early phenologies, which, due to the delayed growth cycle of this type of vegetation, take place relatively late in the season (days 200-250, i.e., late March-mid May); and decreases strongly towards the lower (low rainfall) and more moderately towards the upper-right (high rainfall and late phenology) parts of the graph. Shrubland production showed a flatter response, with peaks at medium-high levels of rainfall (450-550 mm) and early phenology (ca. day 120, i.e., early January, close to the earliest values recorded) and a smooth decrease at later phenologies, particularly in combination with increased rainfall.