A detailed description of the simulation model SGM and previous results have been presented elsewhere (see [17, 18]). SGM has been previously validated with empirical data and simulates population dynamics of Grewia flava under specific land use, fire and rain scenarios in southern Kalahari semiarid savannas. However, to facilitate a better understanding of the current results we will briefly describe the study species and relevant aspects of the simulation model.
The study species
In the open savannas of the southern Kalahari, Grewia flava typically grows beneath the dominant tree species Acacia erioloba , because bird-mediated seed dispersal predominately confines new establishments to woody plant microsites. However, occasionally large individuals may be found in the open grassland matrix at former tree sites, suggesting high longevity of Grewia flava. Under high cattle grazing a substantial proportion of seeds may be distributed into the open matrix vegetation, since cattle feed on the foliage and fleshy fruits of Grewia flava . This may result in a substantial increase in Grewia cover, particularly around boreholes (e.g. ). Grewia flava has excellent resprouting capabilities after fire  and low drought mortality rates . Size class distributions suggest a demographic bottleneck in early life stages due to low rates of emergence and high juvenile mortality .
General model structure
The computer model SGM (see [17, 18]) represents a grid-based approach iteratively simulating population dynamics of Grewia flava in annual time steps for a period of 500 years. Based on empirical demographic and spatial data from the Kimberley region of the southern Kalahari (see ), an initial population of 15 shrubs ha-1 was distributed on a 200 × 200 cell grid, with each cell representing 5 m × 5 m of savanna vegetation. The SGM grid is developed in two layers: a landscape and a population layer. In the first layer micro-site types of the savanna vegetation may change in the course of time. In the second layer SGM simulates population dynamics of Grewia flava. A cell type was classified as either tree (T) (i.e. occupied by Acacia erioloba) or matrix type (M) (i.e. grassland vegetation). However, it switched from T to M status when a tree died after a mean life span of 200 years. The converse occurred where a new tree establishes. Initial tree distribution and spatial recruitment pattern was random with a constant density of 5 trees ha-1 for the entire simulation period. In each time step, SGM simulated important life history stages, environmental conditions and the key ecological processes of Grewia flava, the majority of which are governed by annual rainfall patterns (see Figure 1). For example in the model, rainfall directly determines the likelihood of a fire, drought and fire mortality, fruit crop size, emergence and annual shrub growth rate.
Annual rainfall in the southern Kalahari is highly variable, with precipitation ranging between 200 and 700 mm yr-1. Rain falls almost exclusively during summer (November to April) with an inter-annual mean of 417 mm for the period 1940 – 2000 (Kimberley airport, South African Weather Service 2001, unpublished data). For this period we defined a threshold value of 150 mm below and above the long-term mean to classify years into 'low', 'average' and 'high' rainfall years (thresholds of 267 mm yr-1and 567 mm yr-1, respectively) (see ). Accordingly, frequency of extreme rainfall years resulted in an annual probability of P
= 0.15 for low and P
= 0.13 for high rainfall years (P
= 0.72). Similar classifications have been applied in other studies, e.g. in a spatial simulation model of Acacia raddiana in the Negev Desert .
Fruit production and seed dispersal
Fruit production rates are based on mean crop size of Grewia size classes and may vary depending on the annual rainfall (see ). Seed dispersal is mostly zoochorous and spatially aggregated with a large proportion of seeds deposited in woody plant microsites. It is a crucial factor for the population dynamics and long-term viability of Grewia flava  and represented by two parameters: probability of seeds removed from a shrub and deposited in cell type M, P
, and cell type T, P
varies randomly per year between 0.1–0.01% and represents occasional seed distribution through, e.g. small mammals. P
refers to bird-mediated seed dispersal with a range of 1–5% in high rainfall years, 2.5–7.5% in average and 5–10% in low rainfall years. Based on estimates from empirical data , the assumption of relatively constant seed dispersal rates may be reasonable as the proportion of seeds removed is most likely to be higher in years of lower fruit set. Fruit production typically varies more than bird abundances, and unless birds switch in exactly compensatory fashion to other fruits to the degree that Grewia flava becomes less abundant, fruit removal may be higher in years of low population size.
Even though microsite types differ markedly in micro-environmental conditions, they do not differ in emergence rates of Grewia flava seeds  suggesting a similar emergence probability for cell type M and T. However, depending on annual rainfall conditions, the probability of emergence in the model may vary between 1–2% in average and 2–4% in high rainfall years (no emergence occurs in low rainfall years). As survival of Grewia flava seeds in the soil is very low, seeds that do not emerge are assumed to die.
Fire and drought
The occurrence and intensity of a fire depends on the amount of rainfall, since precipitation determines annual grass biomass production and thus fuel load . In the SGM, fire was simulated probabilistically for the entire grid and may only occur in high and average rainfall years. Average frequency of 7.9 years in the model is supported by fire intervals reported from similar savannah types . The impact of fire varies spatially and demographically: a seedling in the matrix vegetation has a 95% chance of being killed in a fire, compared with 4% for adult shrubs which largely resprout in the following year. For T cells, fire mortality probability is 0% for adults and 75% for seedlings. These model assumptions are realistic, since grass fuel accumulation and fire severity beneath trees is less than in tree inter-spaces (e.g. [40, 41]). In the SGM, the probability of drought mortality varies between life stages and the annual rainfall conditions (see also model description in ). Annual drought mortality for adults is restricted to low rainfall years with a probability of 3% for both cell types. This assumption is based on data from O'Connor  and Schurr . For seedlings the annual drought mortality probability is 90% for average and 50% for high rainfall years (see ). All seedlings are assumed to die in years with low rainfall conditions.
In the model, each shrub was assigned a size class with an average canopy cover. For definition of shrub size classes we used the canopy volume to group Grewia flava individuals into categories of small (Grewia
; <1 m3), medium-sized (Grewia
; 1–10 m3) and large plants (Grewia
; >10 m3) as well as seedlings (Grewia
; temporary state after emergence, transforming to Grewia
with the following year). We assumed a maximum age for each size class member with MaxAge
= 5 years for small and MaxAge
= 25 years for medium-sized shrubs. These estimates are based on annual shoot growth rates and aerial photograph analysis of the study area (see ). In each annual time step an individual can accumulate a growth year and, if MaxAge is reached, attain the next size class with Ptransition(S)= 0.2 for small and Ptransition(M)= 0.1 for medium-sized shrubs. No growth occurs in low rainfall years.
Carrying capacity and competition
To incorporate intra-specific competition we used a simple causal approach that incorporates cell-based shrub cover. Therefore, we defined a carrying capacity of K = 25 m2 as maximum total cell shrub cover. If shrub cover exceeded K, individuals in the cell died. Density-dependent mortality was simulated annually by removing the smallest individuals first, i.e. in descending order of size class, until shrub cover <K (for further details see ). Inter-specific competition between Grewia flava seedlings and the grass layer were neglected: empirical tests showed that emergence rates were similar within and outside of the grassy vegetation matrix (see ). For the adult stage, inter-specific competition with other woody plants is of low importance because Grewia flava often occurs as a mono-dominant species, particularly on bush encroached rangelands.
The standard scenario of the model, based on rainfall for the period 1940 – 2000, led to stable population dynamics (Figure 2). As standard deviation was generally high we performed 100 replicate simulation runs (± 0.0173 for the standard scenario, see Figure 2). To determine and compare population trends between the climate change scenarios we then used a simple linear regression of years vs. shrub density to calculate the z-value, i.e. the slope of the year – shrub density relationship. This is a reasonable approach for analyzing time-abundance relationships (e.g. ). When population dynamics were stable for 500 years, i.e. z was ≅ 0, the number of new recruits more or less resembled the number of fire- and drought-killed shrubs (Figure 2). Significant recruitment events mostly occurred in high rainfall years without fire.
Based on the standard scenario we performed simulation experiments for each of the four different scenarios of climate change with variation in inter-annual mean of precipitation, coefficient of inter-annual variation, and temporal auto-correlation (see Table 1):
(1) increase in precipitation, i.e. stepwise increase of P
resulting in a higher probability of high rainfall years (increase in recruitment events). Probability of low rainfall years is constant whereas frequency of average years is reduced, accordingly.
(2) decrease in precipitation, i.e. stepwise increase of P
resulting in a higher probability of low rainfall years (increase in drought events),
(3) increase in inter-annual variation of precipitation, i.e. stepwise increase of P
resulting in a higher probability of low and high rainfall years at the cost of average years (unaltered inter-annual mean),
(4) increase in temporal auto-correlation of rainfall with 'good' and 'poor' phases.
For the scenario (4) we varied two parameters:
(4a) introduction of rain cycles with increasing period length PL, i.e. longer phases of favorable and unfavorable rain conditions and,
(4b) increase in intra-cycle variation ICV, i.e. increasing variation between alternating favorable and unfavorable periods within one rain cycle.
For PL we applied a period length of 10, 20, 50, 100 and 250 years, respectively, with each period subdivided into a similarly long 'good' and 'poor' phase. For example, a 10-year period length was subdivided into a 5-year period of superior and a 5-year period of poor conditions. For an increase in ICV we alternately increased and decreased high and low rainfall probabilities in each period, respectively (see 4a and 4b in Table 1). For example, for an ICV value of 100% P
equaled 0.00 and P
0.26 in a 'good' phase, whereas values were 0.30 and 0.00, respectively for a 'poor' phase. Through this procedure inter-annual mean and variation of rainfall probabilities were identical for each scenario and the default set of rainfall probabilities. Combined increase in PL and ICV resulted in an increase of positive auto-correlation. Near-decadal epochs of above- and below-normal rainfall have been identified for the period 1955–1991  and may increase in ICV under predicted climate change.