A simplified model of clonal plant growth is formulated, motivated by observations of spatial structures in Posidonia oceanica meadows in the Mediterranean Sea. Two levels of approximation are considered for the scale-dependent feedback terms. Both take into account mortality and clonal, or vegetative, growth as well as competition and facilitation, but the first version is nonlocal in space while the second is local. Study of the two versions of the model in the one-dimensional case reveals that both cases exhibit qualitatively similar behavior (but quantitative differences) and describe the competition between three spatially extended states, the bare soil state, the populated state, and a pattern state, and the associated spatially localized structures. The latter are of two types, holes in the populated state and vegetation patches on bare ground, and are organized within distinct snaking bifurcations diagrams. Fronts between the three extended states are studied and a transition between pushed and pulled fronts identified. Numerical simulations in one spatial dimension are used to determine front speeds and confront the predictions from the marginal stability condition for pulled fronts.

建立了一个简化的克隆植物生长模型，其目的是通过观察海洋波塞冬菌的空间结构在地中海的草地。对于与比例相关的反馈项，考虑了两个近似级别。两者都考虑了死亡率和克隆或无性生长以及竞争和便利，但第一个版本在空间上是非局部的，而第二个版本是在空间上的。在一维案例中对模型的两个版本的研究表明，这两个案例在质量上都表现出相似的行为（但数量上存在差异），并描述了三种空间扩展状态，裸土状态，填充状态和模式状态之间的竞争以及相关的空间局部结构。后者有两种类型，即人口稠密状态的孔洞和裸露的地面上的植被斑块，并组织在不同的蛇形分叉图中。研究了三个扩展状态之间的前沿，并确定了推和拉前沿之间的过渡。在一个空间维度上的数值模拟被用来确定前沿速度，并面对拉动前沿的边际稳定条件的预测。