人类活动影响下具有Allee效应的非自治种群演化模式的研制及其应用——以丹顶鹤为例

Non-autonomous population dynamics model for single species with Allee effect affected by human activities and its application: A case study of red-crowned cranes Grus japonensis

提出“中国的丹顶鹤是否是一活着的灭绝物种(活死者) ?”这一重大科学问题。要回答这个问题,首先必须建立有关丹顶鹤种群演化与人类活动、栖息地斑块平均面积和斑块数关系的动力学模式,其次必须对丹顶鹤种群的大小进行动力学预测。前者涉及到所谓的“相互作用的标度理论”,后者则属于“物种多样性动力学预测”这一崭新的研究领域。首次应用标度理论,阐述了单个物种环境容量(K)与斑块数(P)的标度性质,并用实测的小三江平原的丹顶鹤资料进行了验证发现,K∝P0 .7。同时,在对logistic模式改进的基础上,引进人类活动累积效应及其作用的时间因素,首次提出了人类活动影响下具有Allee效应的非自治种群演化模式。并以丹顶鹤为例,模拟了其种群演化特征,预测了其灭绝时间。模拟结果发现:对于我国的珍稀物种丹顶鹤,其繁殖率的相对高低对物种灭绝的影响并不显著,但Allee效应对其物种灭绝的影响却是明显的,Allee效应越弱,物种灭绝时间越长。如果小三江平原湿地的生境质量得不到有效的恢复和提高,该区丹顶鹤将有可能会在330～4 2 8a后走向灭绝,即丹顶鹤的灭绝对现有栖息地毁坏的响应具有330～4 2 8a的时间滞后性。因此,认为丹顶鹤是一种典型的“活着的灭绝物种”,这一点必须引起政府、科学家和公众的高度重视。

The scientific question whether Grus japonensis is a “living dead” species has been put forward in this paper. To answer this question, firstly, it is necessary to build the dynamical models about the relations among population dynamics of red-crowned cranes, human activities, average area of patches, and the number of patches. Secondly, it is needed to predict the population size of red-crowned cranes. The former refers to the scaling theory of interaction, and the latter refers to the new research field of dynamical prediction of species diversity. The scaling property of environmental capacity of single species (K) with the number of patches (P) has been introduced by applying scaling theory in this paper based on the investigated data of red-crowned cranes in Small Three River Plain. The results show that if the average patch area is definite, the maximum capacity of red-crowned cranes scales the number of patches to power 0.7, i.e., K∝P^(0.7). By incorporating the scaling of environment capacity with the number of patches, human activities effect and its time function into the Logistic Growth Model, a non-autonomous population model for single species with Allee effect affected by human activities is put forward. The simulation results show: (1) when habitat is highly fragmented with small patch area leading to little capacity, and the higher colonization rate brings about stronger interspecific density-dependence, the extinction rate will be higher, and species will go extinct more quickly. In spite of all, colonization rate has little influence on extinction time. Thus in high fragmented landscape, the effect of increasing colonization rate to avoid species extinction proves to be very slim. The fragmented landscape must be improved to escape red-crowned crane extinction. (2) The greater the Allee effect is, the longer the extinction time will be. (3) If the habitat quality is not recovered and improved, the number of red-crowned cranes in Small Three River Plain would be less than 20 after 2100 and they would go extinct in 330～428a, i.e., there is a time delay of 330～428 years for the red-crowned crane extinction in response to past habitat loss and fragmentation. Therefore, we think the red-crowned crane is a typical “living dead” species, and more attention must be taken to it from the government, scientists, and the public.