## 3 Numerical Simulations and Discussion
### Parameter Values
#### 3.1.2 Effects of Rainfall Timing in Different Regions of Botswana  
In semi-arid areas like Botswana, the rainfall timing significantly affects both plants (forage) and livestock. Timing affects the overall output or harvest of livestock and land vegetation. When considering rainfall timing, it is important to note that the total duration of the rainy season is assumed to remain unchanged in both scenarios (late onset and early onset of the rainy season). For the late onset of the rainy season, seeds may not germinate on time, and existing plants may experience stunted growth or die because of delayed rainfall or a prolonged dry environment [46; 47]. This delay in rainfall will lead to a reduction in biomass production, resulting in less food and water available for livestock. These effects on livestock may cause weight loss, decreased milk production, and increased susceptibility to diseases (see [10] and references therein). Additionally, the reduction in forage availability can disturb reproductive cycles, delay breeding, and reduce birth rates. Moreover, when rainfall occurs later than anticipated, specifically 30 days beyond the expected onset, it adversely affects grass growth, leading to stunted growth and reduced biomass, which ultimately results in a temporary shortage of forage. During such periods of delayed rainfall, farmers can start to rely on stored feed or reduce herd sizes to match the available resources [10; 48]. This is shown in Figure 9a by a drop in livestock number at day 200. This shows that while some cattle may die, some farmers will start to reduce the number of their livestock to match the available feed. Additionally, others have to start livestock mobility [10], hence reducing the number of livestock. Figure 9 shows that after some time, rain will come, which makes grasses grow again, hence improving reproduction success and leading to higher birth rates and healthier offspring. Consequently, the number of livestock starts to grow again.  
On the other hand, when rainfall arrives 30 days earlier than expected, the dry period between the previous and current wet seasons will be short, thereby allowing the plant biomass to recover early. This early rainfall also replenishes soil moisture, supporting the  
Figure 8: Plant–livestock population dynamics in Mabutsane when rainfall intensity is (**a**) decreased by 10%, (**b**) increased by 10%, and (**c**) at baseline.  
growth of deep-rooted plants and making them more resilient to drought stress later in the season. Additionally, the quality of forage is often enhanced, leading to better livestock health, weight gain, and productivity. When rainfall comes early, it reduces the risk of water stress and allows grasses to establish themselves with adequate moisture, providing consistent, high-quality forage for livestock. As a result, livestock benefit from improved nutrition, leading to better overall health, weight gain, and milk production. At the same time, farmers can reduce the need for supplemental feeding, saving costs and resources.  
The effects of both delay and early onset of rainfall, as described above, are shown in Figure 9 for each of the four data points and are compared with the baseline value. As observed in Figure 9a,c, there is a significant effect on the livestock population when rain comes early or is delayed as compared with Figure 9b,d. In Figure 9a,c, when rain comes early, the density of livestock reacts well with it, which means their density increases. However, unless it is well managed, this will result in overgrazing in the area, and the livestock population will eventually decrease significantly. That means the advantage will be lost, as can be observed in Figure 9a. On the other hand, when the onset of rainfall is delayed, livestock will not have enough food, which ends up leading to a decrease in the livestock population.