Dryland ecosystems are likely to respond discontinuously to gradual changes in environmental conditions. Direct facilitation between plants, whereby plants improve the local environmental conditions for others, has been shown to be a mechanism contributing to these discontinuous ecosystem transitions. Theoretical models describing dryland vegetation dynamics often consider a single plant species and one type of facilitation, namely direct facilitation. However, another type of facilitation–indirect facilitation–is widespread in dryland ecosystems as well; it is performed by plants protected against grazing, the nurses, when this protection extends to other plants growing in their neighbourhood that are deprived of such protection, the protegees. Little is known about the long-term effects of indirect facilitation on dryland dynamics. Here, we developed and analysed a theoretical model including two species–a nurse and a protegee–and indirect facilitation through grazing. We investigated the effects of indirect facilitation on species composition, species spatial clustering and the stability of dryland ecosystems. We showed that indirect facilitation through grazing enables the stable coexistence of the nurse and the protegee and allows the reversibility of the protegee extinction. Surprisingly, the strength of indirect facilitation affected neither the total nor the interspecific vegetation clustering. Our study highlights that spatially explicit grazing protection may affect species composition and the stability of dryland ecosystems and gives hints about how species interactions translate into spatial clustering.

旱地生态系统可能会不连续地响应环境条件的逐渐变化。植物之间的直接促进使植物改善了其他地方的环境条件，这被证明是促成这些不连续的生态系统转变的机制。描述旱地植被动态的理论模型通常考虑单一植物物种和一种便利类型，即直接便利。然而，另一种便利化形式-间接便利化-也普遍存在于旱地生态系统中。它由防止放牧的植物（护士）执行，当这种保护作用扩展到附近生长的其他植物（即蛋白te）时。关于间接促进对旱地动态的长期影响知之甚少。这里，我们开发并分析了一个理论模型，其中包括两个物种（护士和妓女）以及通过放牧间接促进的过程。我们研究了间接促进对物种组成，物种空间聚集和旱地生态系统稳定性的影响。我们表明，通过放牧间接进行的调养可以使护士和蛋白质稳定地共存，并使蛋白质灭绝具有可逆性。出人意料的是，间接促进的强度既不影响总体植被，也不影响种间植被的集群。我们的研究强调，空间上明确的放牧保护可能会影响物种组成和旱地生态系统的稳定性，并暗示物种间的相互作用如何转化为空间集群。