I simulated the change of stochastic daily rain patterns by increasing the seasonal amplitude of daily mean rain volume (DMR) matched by a decrease in the seasonal occurrence of rainy days so that the mean annual volume remained unchanged. As a result of the increase of DMR, heavy rainfalls contributed more and light rainfalls less to annual precipitation than under current conditions.
The shift of rain pattern had clear effects on the average longest wet period (LWP; Fig. 2A, B). The effect of changing mean annual precipitation (MAP) was stronger than that of changing DMR and keeping MAP constant but the orders of magnitude were similar. The increase of LWP based on absolute change of MAP became flatter along the humidity gradient (Fig. 2B) because additional rain was less important for maintaining the soil moisture of an already moist soil in the more humid regions. In addition, the soil became saturated and additional water drained to lower soil layers or ran off at the surface. The increase of LWP with relative change of MAP was unimodal and greatest in the dry Mediterranean region (Additional file 4: RelativeChanges.pdf) because absolute changes of MAP were smaller in the more arid regions and the effect of increasing MAP diminished with the humidity of the region.
Changing DMR produced a complex response of LWP. In almost all instances, a greater amplitude of DMR, i.e., more days with rainstorms, prolonged the wet period but the effect size decreased with the humidity of the region. The effect of DMR occurred to a small degree because a higher likelihood of rainstorms advanced and delayed the average dates of the first and last rainstorms, correspondingly, prolonging the wet period. More importantly, rainstorms filled up the soil immediately and to a greater depth than did light rains, especially in the more arid regions with sandier soils. The depth of recharge considered in the model is within the soil's A layer (extending to 16–31 cm, depending on region), where annuals have most of their roots  and from where grassland plants take up most of their water . The water in deeper parts of the A layer evaporated more slowly than it would do near the surface, because the soil dried out from the surface downwards and dry soil was less permeable than wet soil. This response of LWP to a change in DMR was due to the texture-dependent, non-linear relation between soil water potential and soil water content as shown by the high ranks of retention-curve parameters in the sensitivity analysis (see Sensitivity analyses, below). It corroborates other simulations and experimental results [15, 22] that sandier soils have deeper soil water recharge from rainstorms than clayey soils, whose water availability is increased by more regular rainfalls (inverse-texture effect ). The latter effect did not appear in my simulations because the clayey soils were restricted to the more humid climates, where the mean interval between rainfalls > 2 mm (3 d) was sufficient to keep the soil's A layer above the LWP threshold of -3 MPa. The relative effect of soil texture on peak shoot mass is comparable to that of ± 20% change of DMR in simulations . Therefore, the parameters of the soil module should be adapted when simulations are carried out for other target sites. The relation between soil texture and water holding capacity also affects nutrient availability , which was not considered in the simulations, and plant growth [22, 25, 40], which will be discussed farther down.
In summary, the effects of changing MAP and DMR on soil water supply to plants were additive, depended on soil texture, and increased with the aridity of the region. Changes in DMR became important only when they were strong and the change in MAP was small.
Seedling density increased among regions along the humidity gradient (Fig. 2C, D) because the number of seeds was a fixed input parameter that increased from the arid to the mesic Mediterranean region and germination rates did not differ enough among sites to change this pattern. The increase of seedling density with MAP within regions was positive in the arid and semiarid regions but negative in the Mediterranean regions (Fig. 2D). This was the outcome of combining the concept of hydrothermal time for germination  with density-dependent germination fractions  in the model. Evidently, additional rain enhanced the number of days when conditions for germination were met and increased establishment in the arid and semiarid regions. In contrast, more rain in the Mediterranean regions did not greatly improve the conditions for germination. More rain, however, raised the germination fraction (Detailed model description – Seed bank module, eq. 2) so that competition among germinating seeds intensified and relative seedling density decreased with increasing MAP in the Mediterranean regions. Test simulations without density regulation showed that heavy rainfalls would cause mass germination in the mesic regions and later strong competition among adult plants. Therefore, density-dependent germination is an evolutionary stable strategy . Empirical evidence for this strategy in natural communities is accumulating [42–47].
Independent of changes to MAP, increasing DMR increased seedling density in the arid region, but decreased density in the other regions. In all regions, germination fractions increased with more regular rainfalls according to the applied hydrothermal time concept, but seedlings had access only to water in the upper 5 cm of the soil, which dried out quickly. Therefore, successful establishment of seedlings in the arid region was mostly controlled by access of seedling roots to water provided by rainstorms (high DMR). The increase of seedling density with less frequent watering was also observed in dry temperate grassland, but the effect was attributed to the breaking of seed dormancy . In the less arid regions more regular rainfalls increased the germination fraction and rainstorms were less important for providing water for seedlings. In summary, seedling density was determined mostly by seed availability, density-dependent germination, number of rainstorms under arid conditions, and regularity of rain under more mesic conditions.
Peak shoot mass
Generally, the effect of rain manipulations on peak shoot mass (Fig. 2E) followed a similar pattern as that on LWP (Fig. 2A), showing the strong control that water as a limiting resource exerted on growth. The change of peak shoot mass with relative change of MAP was greatest in the dry Mediterranean region. There, more seeds could germinate and more rain improved soil moisture conditions during establishment than in the more arid regions. On the other hand, individuals grew more sparsely so that competitive effects were weaker than in the typical and mesic Mediterranean regions. In general, the importance of rainstorms (high DMR) for growth decreased via LWP, whereas the importance of competition and the density of individuals increased along the humidity gradient. This change of ranking also showed in the sensitivity analysis (see Sensitivity analyses, below).
The decrease of seedling density with MAP in the non-arid regions did not cause a similar decrease in peak shoot mass. Instead, competition for water among established plants reduced their density. Since the effect of competition decreased with increasing LWP, the final density of mature individuals increased in the semiarid to typical Mediterranean regions but still decreased with LWP in the mesic Mediterranean region. In this region the decrease of density, however, was compensated by higher production per individual so that peak community shoot mass still increased with MAP.
To summarize, the sigmoid increase of community mass with MAP resulted from a similar increase of LWP with relative change of MAP along the humidity gradient, a larger effect of additional rain on establishment in arid than in non-arid regions, and increasing importance of competition for water. The increase of community mass with DMR was the sum of a positive effect of rainstorms on establishment in more arid regions, a negative effect on germination in non-arid regions, and a positive effect on LWP resulting in more intense competition but also higher production with increasing MAP.
Comparison with experiments
The result that the effect of daily rain distribution on the growth of annuals depends on the climatic humidity of the region was also found in experiments where the temporal distribution of water applications was varied independent of the total amount. In more mesic regions, plant growth either remains unaffected or increases with more evenly distributed water applications (lower DMR). For example, in a temperate grassland, water applications every second day vs. monthly more than doubled plant biomass . Similarly, in tall-grass prairie, doubling the intervals between rainfalls (higher DMR) reduced the standing crop by about 10% . Tropical savanna grasses, however, did not respond to watering variance, neither in the field nor in pot experiments (unclipped treatment) . In contrast, plant growth in arid regions tends to be enhanced by stronger pulses with longer intervals (higher DMR). Irrigation every two weeks instead of daily increased the yield of onions by about 40% in sub-Sahelian Burkina Faso . Greater water volumes applied with longer intervals increased the density of annuals and growth of perennials in an arid pasture . The significance of climate was directly shown experimentally . Increasing DMR by increasing intervals between water applications reduced community productivity in a mesic tall-grass prairie but increased it in the drier mixed- and short-grass prairie . The climate effect was also shown in a pot experiment using species of Mediterranean and desert origin . The two desert species grown with low total seasonal water supply had highest survival rates when pulse intervals after establishment were long (11 or 23 d). In contrast, the two Mediterranean species grown with higher total seasonal water supply survived better when time between pulses was 23 d rather than 3 d .
Obviously, intervals between rains cannot be extended indefinitely without having a negative effect on plant production. The intervals used in this model (3 d [mesic Mediterranean] - 7 d [semi-arid], 18 d [arid]) are similar to those found in nature , where longer intervals between rainstorms are interrupted by light rainfalls. In contrast, 'long interval' treatments in experiments are often regularly spaced and much longer than either natural or projected frequencies for a given location; a factor which may have contributed to the observation of negative correlations between productivity and interval length in mesic climates [9, 10, 14, 16].
In the second set of simulations, using a dynamic seed bank that included carry-over effects between years, communities in semi-arid to mesic Mediterranean regions persisted for the full simulation time (30 yr) in almost all combinations of change to MAP and DMR. In these regions, the communities produced enough seeds to compensate for low seed production in drought years. The storage effect of the seed bank to buffer environmental variability  has also been observed in the field in arid and semiarid ecosystems . Since annual precipitation was not autocorrelated, sequences of drought years were rare and community mass recovered within a few years. Most communities failed to recover in the arid region. Average seed production was not high enough to compensate for drought years. In natural sites in arid regions, populations persist for more than 30 yr because shrubs, crevices, and shade of rocks facilitate the establishment of annuals by indirectly increasing soil moisture . Furthermore, seed dispersal by animals, wind, and surface runoff from these protected sites would also increase community persistence . This continuous replenishment of the seed bank from external sources corresponds to the constant seed bank scenario and underlines the importance of external seed input.
Although populations in the Mediterranean regions persisted for at least 30 years, rainfall variability affected community dynamics across years. The annual variability of peak shoot mass decreased along with the variability of annual precipitation and LWP as MAP increased (Fig. 4). Generally, annual rainfall is less variable in more humid climates  and variability of grassland production increases with the variability of precipitation [53–55]. Increasing DMR increased the variability of annual rain volume but decreased the variability of LWP and peak shoot mass in drier regions and had neutral or positive effects in the more mesic regions. The negative correlation of DMR with the variability of community mass via LWP on the decadal time scale was in line with the beneficial effect of DMR on community mass at the annual scale, despite the increase of annual rainfall variability with DMR. This supports Reynolds et al.  that in terms of the pulse-reserve hypothesis  "pulse" ([sensu 15] must refer directly to the resource as it is available to the plant and not to the resource as it is supplied. In this case, the pulse must be sought in the soil moisture reservoir and not in the rain.
How does precipitation change projected by global climate models translate into community change along the gradient? The RegCM3 climate model generally predicts a 10 to 20% increase of DMR for the Middle East, but change of MAP varies between -20 and +10% [56–58]. Although the community response to an increase of DMR would have an opposite trend to the response to a decrease in MAP, the latter is much stronger. Consequently, the net effect is negative unless the decrease in MAP is small and the increase in DMR is strong. At sites with soils that cause a negative response of community mass to the increase of DMR, however, the effect of decreasing MAP would be amplified.
Model extensions and suggestions for further research
The present model concentrates on simulating annuals as one functional group. Apparently, the general results also hold for perennial herbs . Simulating this growth form would require an adaptation of parameters but only small changes to model structure. Vegetative reproduction would have to be introduced and the possibility that one individual may occupy more space than one grid cell. Although herbs take up water mostly from upper soil layers , potential uptake from deeper layers could be explored by increasing the parameter for layer thickness or by adding additional layers, requiring just small changes to the soil and plant modules. The model already includes structures for simulating competition for light and nitrogen and interactions with shrubs, although they have not yet been validated. This would allow studying competitive relationships with woody plants in relation to soil moisture distribution . The model can be parameterized for different annual species. Simulations for characteristic species from each climatic region showed that all species responded in a similar way to rain pattern, but some were more sensitive than others . Extending the model to simulate individuals of several species or functional types simultaneously would allow studying effects of rain pattern on, e.g., community composition or invisibility. This would improve our understanding of how different functional types coexist along a gradient of aridity . Specifically, one could test mechanisms for coexistence proposed by a one-dimensional model for plant functional types in deserts , especially seasonal differences in water use, differences in preparedness for water flushes, and differences in spatial uptake of water from upper soil layers. The model can also be used in a hierarchical modelling approach  to specify the reactions of the herbaceous vegetation for a larger area and coarser scale. For this end I carried out simulations for specific seed bank and rain volume scenarios to obtain transition probabilities of biomass production that were used in models of landscape productivity [63, 64].