浅水湖泊交替稳态间周期性转变的理论

摘要：浅水湖泊重复的在植被占优势的清水状态和对应的浊水状态间来回变化。通常这种交替发生的十分不规律，但是在某些情况下这种状态间的转换又极其规律。这里我们用一个学者充分研究的荷兰湖泊的数据和一系列简单模型来探索这种循环的可能解释。我们首先用图形模型演示了这种循环在理论上是可能发生的，只要沉水植物在短期内促进了水体变澄清，但是同时引起营养的滞留，预示着营养的长期积累。因此，即使沉水植物通过使水体变清来形成一个有利于自身的正反馈，但是从长期来看，它们可能在逐渐削弱自身的地位，因为它们正造成缓慢的“内源富营养化“。我们用模拟模型探讨了在这种内源富营养化进程中两种不同机制可能的作用：（1）水生植物减少水体P浓度，导致P流失减少，因此提高了P在湖泊沉积物种的积累 （2）长期有机物质的积累导致沉积物需氧量的增加从而引起厌氧情况发生，导致沉积物中P的大量释放。虽然模型表明两种基质都能够使循环发生，但对比荷兰Botshol湖的数据（该湖泊中在过去17年中，规律的循环周期大约为7年），有机物积累引起的循环的周期似乎更实际。

A Theory for Cyclic Shifts between Alternative States in Shallow Lakes

Egbert H. van Nes,1,* Winnie J. Rip,2 and Marten Scheffer1

1Aquatic Ecology and Water Quality Management Group, Wageningen University and Research Center, P.O. Box 8080, NL-6700 DD

Wageningen, The Netherlands; 2Waterboard Amstel, Gooi & Vecht. P.O. Box 1061, NL-1200BB Hilversum, The Netherlands

ABSTRACT

Some shallow lakes switch repeatedly back and forth between a vegetation dominated clear-water state and a contrasting turbid state. Usually such alternations occur quite irregularly, but in some cases the switches between states are remarkably regular. Here we use data from a well-studied Dutch lake and a set of simple models to explore possible explanations for such cyclic behavior. We first demonstrate from a graphical model that cycles may in theory occur if submerged macrophytes promote water clarity in the short run, but simultaneously cause an increased nutrient retention, implying an accumulation of nutrients in the long run. Thus, although submerged plants create a positive feedback on their own growth by clearing the water, they may in the long run undermine their position by creating a slow ‘‘internal eutrophication’’. We explore the potential role of two different mechanisms that may play a role in this internal eutrophication process using simulation models: (1) reduction of the P concentration in the water column by macrophytes, leading to less outflow of P, and hence to a higher phosphorus accumulation in the lake sediments and (2) a buildup of organic matter over time resulting in an increased sediment oxygen demand causing anaerobic conditions that boost P release from the sediment. Although the models showed that both mechanisms can produce cyclic behavior, the period of the cycles caused by the build-up of organic material seemed more realistic compared to data of the Dutch Lake Botshol in which regular cycles with a period of approximately 7 years have been observed over the past 17 years.

Key words: slow–fast cycles; Chara sp.; singular perturbation approach; infinite-period bifurcation; alternative stable states; internal eutrophication.