The aDGVM2 required animal presence times, the number of livestock units (LUs), and the dry matter demand per LU to determine daily hectare-based biomass removal. We assumed that animals move from cropland to rangeland 2 weeks before planting and return 2 weeks after the completion of the crop harvest to feed on crop residues during the dry season. SI or SQ crop management did not influence the timing of rangeland grazing simulations, as the timing of sowing and harvest maximum varied by a few days.

We simulated three different scenarios: (1) a rangeland-only scenario (RO) in which animals exclusively graze on rangeland; (2) a rangeland–cropland scenario (RC) in which animals are on rangeland during the cropping season and on cropland during the dry season; and (3) a control scenario (CO) with no cattle presence and very low-intensity background grazing on random days (frequency equal to the mean annual frequency of the RC scenario, animal density equal to 25 % of the mean animal density of the RC scenario), following the scheme described in Pfeiffer et al. (2019), to ensure the development of a grazing-adapted plant community. Based on test runs, we conducted a 310-year spin-up with a randomized climate data sequence from 1980 to 2010 for all scenarios, followed by a 31-year transient simulation from 1980 to 2010. In the RO and RC scenarios, we prescribed grazing between 2000 and 2010 and kept the low-level background grazing from the spin-up for the CO scenario. Natural fire as part of the local rangeland dynamics was allowed during spin-up and transient simulations. Each individual replicate simulation within a scenario was initialized with a unique random seed, creating unique fire occurrence sequences for all simulated hectares. This approach implies small fires that do not fully burn an entire grazing area at a given time and reflects the commonly observed predominance of low-intensity grass layer fires in the region. We used the same set of replicate initializations for all three scenarios, implying that fire event sequences between scenarios were identical up to the start of the grazing treatments but then deviated because the grazing module also uses random numbers and, therefore, alters the sequences between different grazing scenarios. As grazing and fire also interact in the field (e.g., via effects of grazing on fuel availability), we consider this variation as an imitation of the naturally occurring effect.

Based on the herder surveys (see Sect. ), we set livestock to a total of 90 LUs for Gabaza and 87.4 LUs for Selwana. The rangeland area was 1431 ha at Gabaza (15.9 ha per LU) and 2128 ha (24.3 ha per LU) at Selwana. At Gabaza, 71 % of the rangeland was woodland and 29 % was grassland, whereas 55 % was woodland and 45 % was grassland at Selwana (Table ). While rangeland at Selwana is one contiguous area, Gabaza's rangeland includes four sub-areas (A1 to A4) with area sizes of 57, 279, 394, and 683 ha. Lacking detailed information, we assumed equal woodland–grassland partitioning for all sub-areas.

The aDGVM2 required daily information on the LUs visiting a given hectare. The aDGVM2 models vegetation on individual 1 ha stands with no information exchange between different hectares. Spatiotemporal sequences mimicking animal movement on grazed areas were created (see the following subsections for details) to determine the animal effects on each individual hectare on any given day, as explicit animal movement was not tracked. At Gabaza, we established an additional temporal subdivision to determine the duration of animal presence on each sub-area. We assumed active herd relocation between sub-areas (and between rangeland and cropland) and prescribed the use of only one sub-area at a time. Additionally, we partitioned the period of animal presence proportionally to the sub-area size. Thus, due to this size-proportional time split between sub-areas, all rangeland hectares experience approximately the same annual demand, independent of their location in a small or large sub-area, but resting periods are longer for hectares located in the smaller sub-areas. Therefore, differences in the feed deficit size between different sub-areas can be attributed to seasonality, as the grazing load is distributed equally between sub-areas. The grazing periods were prescribed as input to the aDGVM2 grazing routine. Figure  illustrates presence/absence on rangeland for both villages and scenarios (RO and RC). The proportional reduction in the period of animal presence in the RC scenario compared with the RO scenario is illustrated in the Supplement (Fig. S1).

We assigned an index to each hectare in a given area and attributed it to woodland or grassland based on the respective percentages of both vegetation types (Fig. a). We then determined the grazing-affected hectares on a given day by (1) the number of affected hectares (Naff) (“how many?”) and (2) the indices of affected hectares (“which hectares?”). Naff depends on the herd walking range. Cattle typically move between 1 and 13 km d-1 . To link walking distance with the Naff, we assumed that animals moving between hectares walk a minimum of 100 m (the lateral length of a hectare). Based on the typical range of walking distance combined with the spatial scatter of the herd and lacking more detailed information, we defined a mean daily Naff of 50, with a standard deviation of ± 20 ha, and a minimum daily Naff of 10. If the available grazing area was smaller than Naff, animals grazed all hectares in the area. We drew a random number from a normal distribution using the 50 ha mean and 20 ha standard deviation to determine the daily Naff during periods of animal presence in a given area. If a random number was <10, we replaced it with a random uniform number between 10 and 100 ha to ensure the minimum daily Naff of 10. In this way, we created a frequency distribution for the number of visited hectares per day akin to the one shown in Fig. b. Knowing Naff for each day in the 11-year simulation period, we determined the daily indices of affected hectares (Iaff) via daily random uniform subsampling from all available hectare indices of the considered area (Fig. c), i.e., by randomly choosing Naff random indices.

To distribute the LUs across affected hectares using the Iaff, we converted LUs to daily animal units (AUs) by multiplying the minutes per day by the number of LUs (i.e., 1440×90 LUs = 129 000 AUs for Gabaza, and 1440×87.4 LUs = 125 856 AUs for Selwana). This minute resolution considers that animals may spend only part of a day on an individual hectare. For each day, we randomly created between one and five animal subgroups (0<Ng<6) with varying sizes and spatial densities (Fig. d). We placed the group centers randomly on the Naff, as shown in Fig. e using an example with five sub-groups. For each group, we drew the standard deviation around the group center from a random uniform distribution ranging between 0.5 and 1 times the Naff (the colored horizontal lines in Fig. e illustrate the standard deviation, and the vertical lines represent the locations of the individual group centers). We chose this spread around the group center somewhat arbitrarily to describe how tightly the animals within a group stay together. The scatter also influences how strongly subgroups intermingle on the number of affected hectares. We assigned the AUs to the different groups by creating fractional group sizes by first drawing (Ng-1) random uniform numbers between 0 and 1 and then sorting these by size to establish the group breaks. Fractional group sizes were calculated as the differences between the breaks (including 0 and 1 as lower and upper edges) and were multiplied by the number of AUs to obtain the daily AU per group (Fig. f). For each AU group, we applied a random normal distribution using the group's mean and standard deviation (the group center and scatter, as shown in Fig. e) to determine how many AUs are assigned to the hectares around the group mean. We iteratively redistributed AUs whose drawn numbers were <1 or >Naff.

Generating individual distributions for varying numbers of animal groups of changing size allows flexible animal distribution across the affected hectares. The superordinate animal distribution of the herd emerges from superimposing the individual normal distributions (Fig. g) and allows the creation of flexible multi-modal livestock distributions. It imitates the daily livestock group dynamics in a pseudo-explicit manner that does not require exact knowledge of spatial relationships between affected hectares while still creating average long-term characteristics of herd behavior and rangeland usage. When assigning the AUs per hectare to the affected hectares, we sorted the AUs per hectare in descending order and randomly assigned the lower range of the ordered list to the affected woodland hectares to account for the higher feed availability on grassland compared with woodland. For use in aDGVM2, we reconverted the daily assigned AUs for each affected hectare to daily LUs per hectare (Fig. g).

Although we created grazing sequences for all hectares (see the Supplement), computational constraints precluded simulating the total rangeland. Therefore, we simulated different grazing intensity levels based on the total LU visits per hectare during the experiment. For each rangeland (sub-)area, we conducted 150 simulations (75 ha of grassland and 75 ha of woodland), with 15 simulations per area and vegetation type ranging around the minimum, maximum, median, 25th percentile, and 75th percentile of the cumulative LU numbers per hectare over 11 years, respectively. For sub-area A1 at Gabaza, 57 ha (i.e., the complete sub-area) was simulated. For simulated percentages of (sub-)areas, see Fig. a. We conducted 657 simulations for each scenario (CO, RO, and RC), i.e., 1971 simulations in total.

Consumable grass biomass includes living leaves and stalks as well as standing dead and reproductive biomass. A minimum amount of each pool is unavailable to grazers as they cannot graze completely down to the ground. For cattle, we defined a limit of 30 g m-2 of living and dead biomass, respectively, that needs to remain as well as 10 g m-2 of seed biomass see. Feed gaps occur when demand exceeds the available biomass. We calculated the average annual demand, consumption, and deficit across all simulated hectares by vegetation type (i.e., for woodland and grassland hectares) for both villages and for (sub-)areas. In addition, we summed the annual deficits of all simulated hectares per village and divided this sum by the summed demand from all simulated hectares. This ratio characterizes the demand-specific deficit severity and allows comparisons between different years. In the same way, we calculated the ratio between the number of days with a grazing deficit and the sum of rangeland grazing days. As animals in the RC scenario only spent part of the year on the rangeland, we scaled both ratios by the fraction of the year that animals were present on the rangeland for this scenario. We also created hectare-scale overviews for biomass consumption and demand to assess variability between hectares, which allowed for comparisons between both villages as well as sub-areas at Gabaza.

Village-scale grain yields showed considerable interannual variability (Fig. a, b; see Fig. S2 for an individual depiction per crop type). With a larger arable area, Selwana had higher total yields than Gabaza but lower yields per hectare due to the drier conditions (Fig. c, d). The total yield at Gabaza in the SQ scenario varied between 396 t in 2005 and 1253 t in 2006 (mean of 910 ± 251 t). Yields per hectare ranged between 1.2 t ha-1 and 3.7 t ha-1 (mean of 2.7 ± 0.8 t ha-1). SI led to a moderate, non-significant, factor of 1.2 ± 0.1 average yield increase (Fig. f). Straw yield was moderately, but at Selwana not significantly, increased by SI (Fig. e). Maize production at Selwana varied greatly, from 367 t in 2001 to 5739 t in 2004 (mean of 2620 ± 1603 t). Maize grain yields per hectare at Selwana were 53 ± 23 % lower than at Gabaza, ranging between 0.2 and 2.9 t ha-1 (mean of 1.3 ± 0.8 t ha-1). Compared with Gabaza, SI at Selwana led to a slightly higher mean maize yield increase (by a factor of 1.2 ± 0.3, although statistically non-significant), but the response varied considerably between years (Fig. f). The highest yield increase at Selwana (factor of 1.8 increase) occurred in 2005. However, SI reduced maize yield by 11 % compared with the SQ scenario in 2004 and to a lesser extent also in 2002 and 2006. At Gabaza, SI consistently increased maize yields.

The mean cowpea yield in the SQ scenario at Gabaza was 62 ± 24 t, with a minimum of 30 t in 2004 and a maximum of 96 t in 2007, and a mean yield per hectare of 0.7 ± 0.4 t ha-1 (Fig. ). In the SI scenario, grain yield increased by a factor of 1.6 ± 0.0 on average (statistically significant increase at p<0.05; Fig. f). The total mean village cowpea grain yield in the SQ scenario at Selwana was 169 ± 92 t, with a minimum of 36 t in 2005 and a maximum of 328 t in 2008. By hectare, the mean yield was 0.4 ± 0.2 t ha-1 (minimum of 0.1 t ha-1 and maximum of 0.7 t ha-1). SI led to a mean, non-significant, factor of 1.3 ± 0.2 yield increase.

Gabaza had a village-scale peanut yield of 161 ± 27 t, with a minimum of 125 t in 2005 and a maximum of 214 t in 2000 (Fig. b). The mean yield per hectare was 0.9 ± 0.2 t ha-1 (minimum of 0.7 t ha-1 and maximum of 1.2 t ha-1; Fig. d). SI increased the yield by an average factor of 1.2 ± 0.0 (range from 1.1 to 1.3, increase significant at p<0.05; Fig. f). At Selwana, the village-scale peanut yield was 199 ± 74 t, ranging between 63 t in 2003 and 309 t in 2000 (Fig. a). By hectare, the mean yield was 0.5 ± 0.2 t ha-1 (minimum of 0.1 t ha-1 and maximum of 0.7 t ha-1; Fig. c). On average, SI increased peanut yields at Selwana by a factor of 1.3 ± 0.3 (statistically non-significant), with the strongest positive effect in 2001 (factor of 1.7 increase; Fig. f). However, in 2005, yield at Selwana was reduced by more than 50 % compared with the SQ scenario.

For cowpea, SI had a stronger positive effect at Gabaza with respect to relative and hectare-specific increases. Cowpea benefited the most with a factorial increase of 1.6 ± 0.0 (absolute yield increase of 0.6 ± 0.2 t ha-1). With the highest hectare-specific yields of all crops, the moderate factor of 1.2 ± 0.1 increase led to an overall increase of 0.4 t ha-1 for maize, while the relative factor of 1.2 ± 0.0 increase for peanut corresponded to a yield increase of 0.2 ± 0.1 t ha-1. At Selwana, the hectare-specific yield increase was highest for maize (0.2 ± 0.4 t ha-1; factor of 1.2 ± 0.3 relative increase), followed by peanut (1.2 ± 0.1 t ha-1; factor of 1.3 ± 0.3 relative increase) and cowpea (0.1 ± 0.1 t ha-1; factor of 1.3 ± 0.2 relative increase). The crop-type-specific responses also caused a slight shift in the relative contribution of each crop type to the total village-level yield (see Fig. S3).

SI led to a statistically significant increase in village-scale yield at Gabaza for cowpea and peanut, although not for maize (Welch two-sample t test, p<0.05). No crop type at Selwana showed a significant increase. Moreover, the interannual variability in SI-related yield effects was more pronounced and even negative in some years.

Cropland soil organic carbon (SOC) gradually decreased irrespective of management (Fig. ), although somewhat less under SI. At Gabaza, SOC declined by 4.7 %, from 7.5 to 7.2 kg C m-2, in the SQ scenario and by 3.7 % in the SI scenario (7.3 kg C m-2 left in 2010). On average, cropland soil at Selwana stored 1.4 ± 0.1 kg C m-2 less than at Gabaza, and C loss was 6.2 % in the SQ scenario (from 6.1 kg C m-2 in 1998 to 5.7 kg C m-2 in 2010). SI only had a minor effect on SOC loss at Selwana (5.6 % loss, 5.8 kg C m-2 in 2010). At the village scale, cropland soils under SI had 427 t (Gabaza) and 1030 t (Selwana) more carbon stored in 2010 than under SQ management conditions.

The mean green leaf area index (LAI) for cropland varied both seasonally and interannually (Fig. ). Monthly values at Selwana (Fig. a) were generally lower than at Gabaza (Fig. b). SI had a moderately positive but statistically non-significant effect on the LAI, and the highest canopy-cover values occurred during the growing period from December to March. After crop harvest, weed infestation drove the cropland LAI during the dry season.

Extractable soil water (ESW) was generally higher at Gabaza (Fig. c, d). Minimum values occurred in August and September and increased throughout the wet season before gradually declining again. At both locations, SI tended to reduce ESW due to the higher vegetation cover and biomass simulated in the scenario. However, the difference between the SQ and SI scenarios was non-significant.

The hectare-specific mean annual grass biomass demand was lower at Selwana (Figs. , ; for detailed numbers, see Table S2a). There, animals required approximately 300 kg ha-1 yr-1 on average from grassland hectares in the RO scenario but only between 70 and 190 kg ha-1 yr-1 in the RC scenario. The biomass demand on woodland hectares was lower in both scenarios due to animals preferentially visiting grassland hectares with higher biomass availability. Due to the higher stocking density, the annual hectare-specific demand at Gabaza was consistently higher than at Selwana (see panels b–e in Figs.  and ), roughly ranging between 470 and 630 kg ha-1 yr-1 in the RO scenario and between 130 and 340 kg ha-1 yr-1 in the RC scenario on grassland hectares. Due to the fact that the presence period scaling is proportional to the size of the sub-areas at Gabaza, the hectare-specific demand is approximately equal for all sub-areas. Interannual variability in average demand results from the variability in the visit pattern generated according to the description in Sect.  and the fact that only a sample of the total number of rangeland hectares was simulated at each site.

On average, grazers visited each hectare at Selwana on 8–9 d yr-1 in the RO scenario (Table S2b) and on to 2–6 d yr-1 in the RC scenario. On average, at Gabaza, LUs frequented each hectare on 11–14 d yr-1 in the RO scenario and on 3–8 d yr-1 in the RC scenario, except for the smallest sub-area A1 where the average visit frequency was between 7 and 11 d yr-1 in the RO scenario (annual presence on A1 was 15 d yr-1) and between 3 and 6 d yr-1 in the RC scenario (presence on A1 was 3–8 d yr-1, depending on the year).

Despite a similar visit frequency, the average grass biomass consumption on woodland was lower than on grassland (Table S2c) due to the lower number of animals assigned to woodland hectares (see Sect. ). The mean daily grass biomass consumption on affected hectares was comparable between the RO scenario and RC scenario, as the same number of animals per area were present on a per-day basis during both scenarios. Differences in annual grass biomass consumption between scenarios only emerged due to the shortened presence periods per area in the RC scenario (Table S2d).

Across all simulated hectares, the annual demand-specific deficit (gap between supply and demand) at Selwana ranged from 0.2 % to 11.4 % in the RO scenario (Fig. a). In the RC scenario, the deficit declined to values between 0 % and 5.1 %, partially due to the shorter herd presence on rangeland. Gabaza, where the average cattle density per hectare was 1.5 times higher, had higher relative deficits. Moreover, Gabaza has a higher relative woodland proportion (Table ). Demand-specific deficits at Gabaza were between 0.4 % and 17.5 % in the RO scenario (Fig. b) and declined to values between 0 % and 8.0 % in the RC scenario. Years with higher deficits, such as 2002, 2003, 2005, and 2008, coincide with low annual precipitation at both sites (Fig. b). The maximum deficits occurred in 2003, which was the second dry year in a row after 2002. For the respective relative deficits for grassland and woodland hectares, see Fig. S4.

Integrated across all simulated hectares, the time line of the percentage of grazing days with a deficit resembles that of the relative deficits (compare panels c and a and panels d and b in Fig. ). Between 0.6 % and 11.5 % of grazing days had a deficit in the RO scenario at Selwana. The RC scenario reduced this to a range from 0.0 % to 5.2 % of total days. At Gabaza, the higher grazing pressure caused more deficit days. Here, the RO scenario resulted in a range from 0.5 % to 17.0 % of grazing days, with a reduction to 0.0 %–6.6 % in the RC scenario. For a presentation by vegetation type, see Fig. S5. Deficit timing showed a clear seasonal pattern (Fig. e, f). Monthly deficits in the RO scenario were lowest between March and June and highest in October/November before declining towards December. While both villages had a similar seasonal pattern, the demand-specific monthly deficits were higher at Gabaza, particularly from September to November. Cropland pasturing between approximately April to October (see Fig. e, f) avoided deficits during these months. However, it also reduced the deficit size during rangeland presence (compare the RO and RC scenarios in Fig. e, f). Deficits showed a delay of 2–3 months relative to precipitation (Fig. c, d), i.e., the maximum was delayed and occurred after the end of the dry season, when precipitation increased again. Similarly, the lowest deficits in March/April occurred approximately 2 months after peak precipitation.

Consumable grass biomass provision was distinctively seasonal (Figs. , ). Peak biomass occurred between February and March, and the minimum availability developed towards the end of the dry season in October/November. Overall biomass availability was lower at Selwana than at Gabaza, and woodland hectares produced less consumable biomass than grassland hectares. Consumable biomass also greatly varied between years. As the second of 2 consecutive dry years, 2003 had the lowest biomass of the 11 years. Grazing had a minor effect on the across-hectare mean consumable biomass (compare the scenario averages and standard deviations in Figs.  and ). Differences in fire occurrence between grazing scenarios also caused biomass differences (see Figs. S6 and S7).

For Selwana grassland, the average annual GPP in the control ranged between 3.1 ± 1.5 and 11.2 ± 4.1 t ha-1, whereas Gabaza had values between 3.7 ± 1.9 and 15.8 ± 6.5 t ha-1 (Table S3, Fig. S8). On woodland, the hectare-specific grass-layer GPP was lower and ranged between 1.2 ± 0.6 and 3.6 ± 1.7 t ha-1 at Selwana and between 1.3 ± 0.7 and 4.7 ± 1.6 t ha-1 at Gabaza (Table S3, Fig. S9). Differences between scenarios were statistically non-significant (two-sided t test, p<0.05).

Annual grassland NPP at Selwana varied considerably and ranged between 1.2 ± 0.5 and 6.0 ± 2.3 t ha-1 in the control scenario. Annual grassland NPP at Gabaza was higher, with values between 1.4 ± 0.6 and 8.7 ± 3.8 t ha-1 (Table S4, Fig. S10). We also simulated this pattern for woodland hectares, where the mean annual NPP ranged between 0.4 ± 0.3 and 1.9 ± 0.9 t ha-1 at Selwana and between 0.5 ± 0.3 and 3.0 ± 0.9 t ha-1 at Gabaza (Table S4, Fig. S11). The RO and RC scenarios did not differ significantly (two-sided t test, p<0.05) from the control, except for the years 2005 and 2007 in the RC scenario for Selwana grassland hectares and the year 2008 in the RO scenario for the woodland hectares of sub-area A1 at Gabaza.

The GPP normalized for living leaf biomass (LLBM) had annual values of approximately between 7 and 13 g C g-1 (see Table S5 and Figs. S12 and S13), and the NPP normalized for LLBM had values of between 2 and 8 g C g-1 (see Table S6 and Figs. S14 and S15). Values of biomass-specific GPP and NPP were comparable between grassland and woodland, i.e., grass on woodland was as productive as grass on grassland. In contrast to the hectare-specific GPP and NPP values, grazing frequently caused significantly (two-sided t test with p<0.05) higher average biomass-normalized GPP and NPP values relative to the control (see Figs. S12, S13, S14, and S15). This effect was usually stronger in the RO scenario. Based on the sensitivity study in , we suspect that an optimum grazing frequency and intensity likely exists where simulated biomass-normalized productivity is maximized, but we did not explicitly test for this optimum in either the cited or present study. Plot-level GPP and NPP showed pronounced seasonality, and monthly values varied strongly between years (Figs. S16, S17, S18, and S19).

We saw similar seasonality for biomass-specific monthly GPP and NPP (Figs. S20, S21, S22, S23) with minimum values in June and a gradual increase to the December maximum. Values gradually declined from January to March and then rapidly declined towards June. Integrated across all simulated hectares, annual biomass consumption relative to NPP varied between years and was lower at Selwana (Fig. ). The highest ratios occurred in the dry years 2002, 2005, and 2008 (Figs. S10, S11). The annual consumption / NPP ratio was approximately halved in the RC scenario compared with the RO scenario (reduction by a factor of 2.1 ± 0.6 at Selwana and by a factor of 2.1 ± 0.2 at Gabaza).