Eager Eric Alan, Rebarber Richard, Tenhumberg Brigitte
Mathematics Department, University of Wisconsin-La Crosse, La Crosse, WI, USA,
J Math Biol. 2014 Jul;69(1):1-37. doi: 10.1007/s00285-013-0689-z. Epub 2013 May 28.
Many plant populations have persistent seed banks, which consist of viable seeds that remain dormant in the soil for many years. Seed banks are important for plant population dynamics because they buffer against environmental perturbations and reduce the probability of extinction. Viability of the seeds in the seed bank can depend on the seed's age, hence it is important to keep track of the age distribution of seeds in the seed bank. In this paper we construct a general density-dependent plant-seed bank model where the seed bank is age-structured. We consider density dependence in both seedling establishment and seed production, since previous work has highlighted that overcrowding can suppress both of these processes. Under certain assumptions on the density dependence, we prove that there is a globally stable equilibrium population vector which is independent of the initial state. We derive an analytical formula for the equilibrium population using methods from feedback control theory. We apply these results to a model for the plant species Cirsium palustre and its seed bank.
许多植物种群拥有持久的种子库，种子库由能在土壤中休眠多年的有活力种子组成。种子库对于植物种群动态很重要，因为它们能缓冲环境扰动并降低灭绝概率。种子库中种子的活力可能取决于种子的年龄，因此追踪种子库中种子的年龄分布很重要。在本文中，我们构建了一个一般的密度依赖型植物 - 种子库模型，其中种子库具有年龄结构。我们考虑了幼苗建立和种子生产中的密度依赖，因为先前的研究强调过度拥挤会抑制这两个过程。在关于密度依赖的某些假设下，我们证明存在一个全局稳定的平衡种群向量，它与初始状态无关。我们使用反馈控制理论的方法推导出平衡种群的解析公式。我们将这些结果应用于植物物种沼生蓟及其种子库的模型。
