The use of matrix models for calculating sustainable utilization rates of natural resources

Many rural communities living in savannas on the outskirts of the Kruger National Park suffer
from poverty and unemployment. These communities are surrounded by large areas of
communal lands which often offer a vast array of natural resources. The Italian funded project
aimed to address these differences and come up with ways of increasing the social, economic
and environmental benefits from the area. The communal area surrounding Malumalele was
visited and the main floral components were assessed to determine potentially utilizable
resources. A spreadsheet model was constructed to determine sustainable stocking rates for
livestock based on the grass productivity. Matrix models were constructed for three woody
species; Acacia nigrescens, Peltophorum africanum and Dichrostachys cineria. These were
then used to ascertain the most suitable size classes for harvesting and sustainable harvesting
rates. Our preliminary models suggest that current livestock stocking rates are appropriate and
could possibly even be increased. The grass model predicts that approximately R550
000/annum from livestock alone could be generated from 5000 hectares. The matrix models
predict that approximately 10% or seven adult A. nigrescens trees could be harvested per
hectare. While 15% of all juvenile P. africanum and D. cinerea plants (approximately 40
plants per hectare) could also be sustainably harvested. However more data would need to be
collected to determine the necessary time interval between harvesting events for each species.

居住在克鲁格国家公园（Kruger National Park）周边稀树草原地带的诸多乡村社区，普遍深陷贫困与失业困境。这些社区被大片公有土地环绕，这类土地往往蕴藏着极为丰富的自然资源。此项由意大利资助的研究项目，旨在针对性解决上述问题，探寻提升该区域社会、经济与环境效益的可行路径。研究团队对马卢马莱莱（Malumalele）周边的公有区域开展了实地考察，并对区域内主要植物区系进行了评估，以甄别具有开发利用价值的自然资源。研究人员构建了电子表格模型，基于草地生产力测算牲畜的可持续载畜量。针对黑刺金合欢（Acacia nigrescens）、非洲盾柱木（Peltophorum africanum）以及灰毛二蕊相思（Dichrostachys cinerea）这三种木本物种，研究团队构建了矩阵模型，随后利用这些模型确定了最适宜的采伐尺寸等级与可持续采伐率。初步模型结果显示，当前的牲畜载畜量处于合理区间，甚至具备进一步提升的空间。草地模型预测，在5000公顷的土地上，仅通过畜牧业每年即可创造约55万南非兰特的收益。矩阵模型则预测，每公顷土地可采伐约10%的成年黑刺金合欢（约7株/公顷）。此外，每公顷土地上约15%的非洲盾柱木与灰毛二蕊相思幼株（约40株/公顷）也可实现可持续采伐。不过，仍需收集更多数据，以确定各物种所需的采伐间隔周期。