Increasing the amplitude of a bell-shaped, seasonal distribution of DMR by 20%, while keeping the mean annual precipitation constant, decreased the average number of days with >5 mm of rain and increased the number of days with >15 mm and > 25 mm. Correspondingly, the median interval between days with >5 mm rain decreased, but it increased between days with >15 and >25 mm rain. Thus, the manipulation of rain pattern shifted the distribution of daily rain volumes to more frequent heavy rainfalls at the cost of light rains as observed in the Mediterranean 7.

The annual mean longest wet period (LWP) was assessed as an integrative measure of water availability. LWP was defined as the maximum number of consecutive days where the water potential (Ψ) of at least one of the four mineral ("A") soil layers is higher than the permanent wilting point (-3 MPa) representative of the herbaceous plants along the aridity gradient.

LWP varied with DMR depending on interactions with regions and regions × MAP (Tab. 2). In addition, LWP varied with MAP depending on interactions with regions. The average LWP of each region increased in a slightly sigmoid way along the humidity gradient (Fig. 2A). Within sites, LWP increased with MAP. The 'absolute' rate of increase (ΔLWD/ΔMAP) diminished from the arid to the mesic Mediterranean region (Fig. 2B), whereas the 'relative' rate of increase (ΔLWD/10% MAP), indicating the effect of expected relative changes, peaked in the dry Mediterranean region (Additional file 4: RelativeChanges.pdf). LWP increased with DMR when MAP was <600 mm. Beyond this point, LWP did not change significantly with DMR. The highest relative rate of increase occurred around 200 mm MAP. Thus, the relative rate of increase rose with MAP in the arid region, decreased in the semiarid and dry Mediterranean regions, and did not change with MAP in the two most mesic sites.

The results presented here are based on LWP calculated for a permanent wilting point of -3 MPa. Wilting points down to -32 MPa, much lower than the conventional -1.5 MPa for cultivated plants 32, are characteristic for dryland annual species 33. A wilting point of -3 MPa seems representative for a range of annual grass species from dry climates 34. This includes Brachypodium distachyon, a common grass along the precipitation gradient in Israel. The discussion pertains nonetheless to species with low, intermediate, and high permanent wilting points as similar results were obtained for LWP calculated for different wilting points of -1.5 and -5 MPa.

Seedling density was analyzed as an integrative measure of plant responses to DMR via water availability during the early establishment phase. Results reported here, in the preceding and the following section are based on simulations where seed bank density was reset at the beginning of each simulated vegetation year to a value characteristic for each region. The resetting allowed the analysis of rain pattern effects without the influence of inter-annual carry-over effects caused by sequences of wet or dry years. Simulations without seed bank resetting are reported in the section 'Population persistence'.

Seedling density varied with DMR depending on interactions with regions and regions × MAP (Tab. 2). Change of MAP, and its interaction with DMR had no significant effects. The average seedling density of each region increased along the humidity gradient in a hyperbolic fashion (Fig. 2C). Within the arid and semi-arid regions average seedling density increased with MAP, but decreased with increasing MAP in the two most humid regions (Fig. 2D). Increasing DMR at constant nominal MAP increased seedling density in the arid region, whereas increasing DMR generally caused density to decrease in the other regions (Fig. 2D) and did not vary with MAP in the dry Mediterranean region. These contrasting findings suggest that density-dependent germination became more important as water supply increased. The three-way interaction resulted from no effect of MAP on the increase of seedling density with DMR in the arid region, a negative effect of raising MAP on the decrease of density with increasing DMR in the semiarid region, and an on average positive effect of raising MAP on the decrease of density with increasing DMR in the dry to mesic Mediterranean regions.

The effects of rain manipulations on peak shoot mass were similar to that on LWP. Peak shoot mass depended on region, DMR, MAP, and all of their interactions (Tab. 2). The greatest absolute differences among levels were among regions. The average peak shoot mass of each region increased slightly sigmoidally along the humidity gradient. Within each region, mass increased with MAP (Fig. 2E). The 'absolute' rate of increase diminished from the semi-arid to the mesic Mediterranean region (Fig. 2F), whereas the 'relative' rate of increase was greatest in the dry-Mediterranean region (Additional file 4: RelativeChanges.pdf). Further, peak shoot mass (averaged across sites) increased with increasing DMR, but the rate of increase was smaller than that caused by a similar change in MAP. The rate of increase with DMR (averaged across levels of MAP) was greatest in the semiarid region (Fig. 2F). Within the arid region, the effect of increasing DMR was positive and increased with increasing MAP (Fig. 2F). In the other four regions, however, the positive effect of DMR decreased with increasing MAP so that it became insignificant, or sometimes negative, in more mesic regions. In summary, increasing daily mean rain volume and, more strongly, mean annual precipitation both increased peak shoot mass, but their relative effects generally decreased from the semiarid or dry Mediterranean to more arid or more mesic regions.

Simulations with a seed bank that carries over to the following year was conducted to assess the consequences of change of rain pattern on population persistence. In the arid region only 25 of 125 populations persisted until the end of the simulations (30 yr, Fig. 3A). In contrast, in the semiarid region 107 populations (Fig. 3B), in the dry Mediterranean region all but one population (combination -20% MAP, -10% DMR), and in the typical and mesic Mediterranean regions all populations persisted for 30 years. In the arid region, populations persisted with full growth cycles only in the combination +20% MAP, +20% DMR. In the other instances, populations survived up to 30 years via a dormant seed bank without germination. Thus, persistence decreased with increasing MAP (P = 0.04) and increased with the interaction between DMR and MAP (P = 0.001) because persistence was on average higher when both change of DMR and MAP were either both positive or both negative (Fig. 3A). DMR had no significant main effect. In the semiarid region, population persistence increased with DMR when MAP was reduced by 20% (Fig. 3B, P < 0.001). Persistence in other combinations and regions was not assessed statistically because the pattern was obvious.

I compared the effects of DMR and MAP on the coefficients of variation of annual rain volume (CV_R), longest wet period (CV_LWP), and peak shoot mass (CV_mass) because greater environmental and population variability is theoretically related to shorter persistence 3536. I did not include the arid region in this analysis because its CVs were based on less than half the number of years and CV_mass was strongly influenced by a decline in mean mass over time. CV_R varied among regions, decreased with change of MAP, and increased strongly with change of DMR (Tab. 3; each P < 0.0001). These three factors did not interact. CV_R could be predicted by the regression equation CV_R = 19.8 + [3.9 | SA, 1.5 | DM, -1.5 | TM, -3.8 | MM] - 0.084·ΔMAP + 0.128·ΔDMR (adjusted R² = 0.64). CV_LWP varied strongly among regions (Tab. 3; SA: 53, DM: 31, TM: 17, MM: 12) and decreased overall with increasing MAP. The rate of decrease with MAP within regions became smaller along the humidity gradient. The effect of DMR depended on region. CV_LWP decreased with increasing DMR across the semiarid region, did not change with DMR across the dry Mediterranean region, increased with DMR across the typical Mediterranean region, and did not change with DMR across the mesic Mediterranean region. CV_LWP increased with the interaction of MAP and DMR in the semiarid region but in the other regions the interaction effect was not significant. This indicates that water storage in the soil reduced the variability of the rain. The CV of peak shoot mass (CV_mass) behaved in a similar way as CV_LWP (Fig. 4; Tab. 3) except that all interactions were significant. CV_mass decreased along the humidity gradient (Fig. 4A, Tab. 3), with increasing MAP and with increasing DMR. The rate of decrease with MAP became smaller along the humidity gradient. The confidence intervals of the rate of decrease included zero in the mesic Mediterranean region. The average effect of DMR differed among regions because its direction switched from negative to neutral along the humidity gradient (Fig. 4B). The interaction effect on CV_mass by MAP and DMR was positive on average. In addition, the negative effect of DMR diminished with increasing MAP in the semiarid region only, causing a significant three-way interaction.

The CVs of all three variables were positively correlated among each other (Tab. 4). CV_mass was generally correlated more strongly with CV_LWP than with CV_R. The partial correlation between CV_mass and CV_R, accounting for the correlation with CV_LWP, was negative in the semiarid, dry, and typical Mediterranean regions and neutral in the mesic Mediterranean region. The negative partial correlation indicated that soil water storage (via LWP) also reduced the inter-annual effect of rain variability on the variability of shoot mass.

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 27 and from where grassland plants take up most of their water 37. 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 1522 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 1). 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 38. 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 39, which was not considered in the simulations, and plant growth 222540, 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 41 with density-dependent germination fractions 42 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 43. Empirical evidence for this strategy in natural communities is accumulating 424344454647.

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 48. 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.

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.

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 10. Similarly, in tall-grass prairie, doubling the intervals between rainfalls (higher DMR) reduced the standing crop by about 10% 9. Tropical savanna grasses, however, did not respond to watering variance, neither in the field nor in pot experiments (unclipped treatment) 13. 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 18. Greater water volumes applied with longer intervals increased the density of annuals and growth of perennials in an arid pasture 21. The significance of climate was directly shown experimentally 49. 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 49. The climate effect was also shown in a pot experiment using species of Mediterranean and desert origin 16. 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 16.

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 20, 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 9101416.

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 50 has also been observed in the field in arid and semiarid ecosystems 51. 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 28. Furthermore, seed dispersal by animals, wind, and surface runoff from these protected sites would also increase community persistence 52. 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 5 and variability of grassland production increases with the variability of precipitation 535455. 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. 15 that in terms of the pulse-reserve hypothesis 1 "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% 565758. 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.

The present model concentrates on simulating annuals as one functional group. Apparently, the general results also hold for perennial herbs 49. 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 59, 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 12. 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 60. 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 61. Specifically, one could test mechanisms for coexistence proposed by a one-dimensional model for plant functional types in deserts 15, 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 62 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 6364.

The standard model parameters refer to four experimental sites along a 245-km gradient of humidity in Israel: an arid (AR) site near Sedé Boqér (N 30°52' E 34°46', 470 m a.s.l., 90 mm MAP), a semi-arid (SA) site near Lahav (N 31°23' E 34°54', 590 m a.s.l., 300 mm MAP), a "typical" Mediterranean (TM) site near Matta' (N 31°42' E 35°3', 620 m a.s.l., 540 mm MAP), and a mesic Mediterranean (MM) site near 'En Ya'aqov (N 33°0' E 35°14', 500 m a.s.l., 780 mm MAP). Details of rain fall frequency and distribution at nearby climate stations can be found in Additional file 5: ClimateStations.pdf. The soil types range from sandy loam at the AR site to loam at SA and clay at the MM and TM sites (Sarah Pariente, pers. comm.). Mean annual temperatures vary between 19°C and 21°C. Shrub cover increases along the gradient from <5% (AR) to about 80% (MM). Space between shrubs is covered mostly by annuals, while the percentage of bare ground decreases from about 95% to about 5% along the gradient. The vegetation and experimental setup at the sites are described in greater detail by Holzapfel et al. 28.

The four experimental sites are spread more or less evenly along the humidity gradient with a gap between the SA and TM site. Therefore, I used a hypothetical "dry Mediterranean" site (DM) with interpolated site characteristics in the simulations.

The model (version 2.6.0; Additional file 6: AnnualsModelSourceCode.zip) simulates the effect of rainfall variability on soil moisture and annual vegetation. The model is spatially explicit 65 because it includes the competitive interactions among individual neighbouring annual plants and uses principles of cellular automata models. The model's spatial extent is a soil surface of 25 cm × 25 cm per simulated site, divided into 1-cm² cells representing soil columns (Fig. 1A). Each soil column contains a seed bank and space for one plant to reach maturity. The model consists of four modules describing the dynamics of climate, soil, seed bank, and plants (Fig. 1B).

I used five parameter sets to represent the different climates, soils, and plant communities in the five modelled climatic regions (Tab. 1; Additional file 1: ParametersSoil.pdf, Additional file 2: ParametersSeedBank.pdf, Additional file 3: ParametersPlants.pdf). The parameters were determined from experiments at each field site, greenhouse experiments, and published data or by choosing values that reproduced field data (for details see Detailed model description, below). All modelled processes are defined by physical or logical rules for time steps of one day, except for seed dispersal and seed bank mortality, which are evaluated in annual time steps.

The climate module (for details see Detailed model description – Climate module, below) determines daily temperature and precipitation, which are equally distributed in the grid. Temperature is calculated deterministically by a cosine function. Daily values do not vary among years. In contrast, rainfall is generated stochastically by the ReGen algorithm 20 (see below: Precipitation scenarios).

The soil module (for details see Detailed model description – Soil module, below) simulates water infiltration along a slope. A part of the surface water infiltrates into a soil column that consists of one organic (O) layer and four mineral (A) layers. In the simulations excess rain (runoff) was removed from the grid because I was interested in the direct effect of rainfall volume on each cell and similar moisture conditions across the grid. Water is lost to the atmosphere by evapotranspiration. Soil characteristics like hydraulic conductivity, field capacity, residual (minimum) water content, and the parameters of the soil moisture retention curve 66 are kept constant during simulations and are the same for each layer. Infiltration coefficients decrease with soil moisture and increase with vegetation cover.

The seed bank module (for details see Detailed model description – Seed bank module, below) simulates granivory, seed bank mortality, and germination. Before dispersed seeds enter the seed bank, a portion of the seeds in the seed bank dies because of decay, burial, or other causes. A portion of dispersed seeds is eaten before they enter the seed bank if their density is higher than the giving-up density of granivores. I implemented seasonal seed dormancy as an inverse U-shaped function. Germination of germinable seeds is determined by a hydrothermal time approach 4167 that incorporates the average soil moisture and temperature before germination. The actual germination fraction is further controlled by the local density of seeds 4243.

The plant module (for details see Detailed model description – Plant module, below) simulates the growth of individual annual plants. Plant growth is sigmoid, defined by maximum mass and maximum growth rate. The actual growth rate depends on temperature, water availability, the species' permanent wilting point (PWP), and net size-asymmetric competition 68 with neighbours within a radius of up to 2.5 cm. A fixed portion of produced biomass is allocated to reproduction and converted to seeds when the plant dies. Plant mortality is caused by lack of water. Seeds are dispersed with a negative exponential distribution, i.e., the likelihood to disperse farther from the mother plant decreases with distance.

The simulation of soil moisture dynamics and vegetation production by the model was validated by comparison with independent data that were not used to parameterize the model (for details see Additional file 7: Validation.pdf). The sensitivity of the model to changes of the model parameters was tested separately for the abiotic and biotic modules (see Additional file 8: SensitivityAnalyses.pdf).

My model does not take into account increasing annual mean temperatures, CO₂ concentrations or nitrogen deposition from the atmosphere. A multi-factorial field experiment including these factors and precipitation in an annual grassland showed that interactions among these factors become rare over time and nitrogen deposition produced the strongest effect 69. Nonetheless, in the long-term, aboveground production of herbaceous arid communities is most strongly correlated with annual precipitation 70, which is also shown by the tight correlation of community biomass with annual precipitation along the climate gradient (see Validation, below).

I varied the distribution of volume and frequency of daily rainfall for five sets of nominal mean annual precipitation (100, 300, 450, 600, and 800 mm – corresponding roughly to the mean annual precipitation of the field sites) to investigate the effect of the daily rain pattern on the longest wet period (LWP), seedling density, and peak shoot mass of populations of annual plants. The change of daily rain pattern was achieved by increasing the seasonal amplitude of daily mean rain volume (DMR) by -20%, -10%, 0%, 10%, and 20% in the ReGen time series generator 20. Increasing DMR prolongs intervals between rains, reduces the contribution of days with light rains and increases the contribution of rainstorms to the annual rain volume 20. In order to compare the magnitude of this treatment, I also varied the mean annual precipitation volume (MAP) by -20%, -10%, 0%, 10%, and 20% in factorial combination with DMR. I used relative instead of absolute changes of precipitation parameters because regional climate models indicate that the changes will be tightly correlated with current values and that relative changes are remarkably constant along the precipitation gradient (M. Köchy, unpublished results). For example, the RegCM3 circulation model projects for the pessimistic A2 climate change scenario an average increase of DMR by 3% and a decrease of MAP by 13% for 2070–2100 for Israel North of the Negev desert, whereas the optimistic B2 scenario results in an average increase of DMR by 27% and an increase of MAP by 12% between 31° and 33° N (calculations based on 565758).

For the assessment of rain pattern effects on LWP, seedling density, and peak biomass, seed bank density in each region was reset to a constant value at the beginning of each vegetation year (AR: 2000, SA: 16000, DM: 17000, TM: 18000, MM: 20000 seeds/m² corresponding to typical values observed in the field). This constant-seed bank scenario facilitates comparisons among years because carry-over effects of seed bank density due to wet and dry years and mortality are excluded. In a second set of simulations I examined the effect of change of daily rain pattern on population persistence. For population persistence inter-annual seed bank dynamics carry-over effects are important and were included (dynamic-seed bank scenario). To quantify community persistence I recorded the year in which the seed bank had dropped to zero or whether the population survived for the total simulated period.

I simulated 30 years of stochastic rainfall for each combination of levels of DMR and MAP in each climatic region and both seed bank scenarios. This was repeated five times for each combination. I used different random spatial distributions of soil surface heterogeneity in each simulation run. The great detail simulated by the model prevented me from storing daily data and only annual data across the whole lattice was recorded. Therefore, I sometimes phrase interpretations of results cautiously where omniscience of causality in the model could be expected. Among the many vegetation and soil variables simulated by the model, I concentrated on formally analyzing the effect of rain pattern on annual longest wet period (LWP), seedling density, and peak shoot mass (maximum annual aboveground biomass) because each is an integrative measure of, respectively, available soil moisture, establishment, and community performance. The effect of daily rain pattern on LWP, seedling density, and peak shoot mass for the constant-seed bank scenario was examined with analyses of covariance (ANCOVA) across regions. The full-factorial ANCOVA used change of DMR and change of MAP as covariates and regions as a nominal factor. As the data were very heteroscedastic, I used the means across years for each combination of daily pattern × mean annual precipitation × climatic region × repetition. Slopes and means were compared post-hoc using 95% confidence intervals. In addition, I calculated the change of peak shoot mass per 10% change of DMR and per 10% change of MAP to facilitate the comparison of effect sizes.

In the dynamic-seed bank scenario few populations persisted for the total simulation time (30 yr) in the arid region in contrast to the more humid regions. Therefore, an ANCOVA of persistence comprising all sites as for the constant seed bank scenario was not meaningful and I analyzed the arid region only. This turned the ANCOVA for the arid region into a multiple regression. For the other four regions, where time of persistence was almost always the full 30 years of the simulation runs, I compared the coefficient of variation of annual rain volume, longest wet period, and peak shoot mass using an ANCOVA to test how changes in rain pattern affected environmental and production variability. In addition I tested whether the CVs were correlated.