生物多样性 ›› 2019, Vol. 27 ›› Issue (12): 1364-1378.doi: 10.17520/biods.2019138

• 综述 • 上一篇    下一篇

复杂性-稳定性研究: 数学模型的进展

徐光华1, 李小玉2, 施春华1, *()   

  1. 1 浙江农林大学暨阳学院, 浙江诸暨 311800
    2 浙江农林大学林业与生物技术学院, 浙江临安 311300
  • 收稿日期:2019-04-22 接受日期:2019-07-29 出版日期:2019-12-20
  • 通讯作者: 施春华 E-mail:shichunhua7924@163.com
  • 基金项目:
    浙江农林大学暨阳学院人才启动项目(RQ1911F10)

The complexity-stability relationship: Progress in mathematical models

Guanghua Xu1, Xiaoyu Li2, Chunhua Shi1, *()   

  1. 1 Jiyang College of Zhejiang Agriculture and Forestry University, Zhuji, Zhejiang 311800
    2 College of Forestry and Biotechnology, Zhejiang Agriculture and Forestry University, Lin’an, Zhejiang 311300;
  • Received:2019-04-22 Accepted:2019-07-29 Online:2019-12-20
  • Contact: Shi Chunhua E-mail:shichunhua7924@163.com

对自然生态系统的观察给人们以复杂的群落更稳定的直观印象, 但数学模型却得出了截然相反的结论。这一“悖论”使得复杂性-稳定性研究自20世纪70年代以来成为长期的热点。本文对这一领域的数学模型研究进行简要综述。首先对这一论题进行概念剖析, 然后将各类模型分为线性和非线性两大类, 前者即群落矩阵法, 后者包括相互作用矩阵法、复杂网络数值模拟法和食物网构件动力学法。它们分别基于不同的群落构建方法和稳定性判断标准, 探求各物种是如何相互作用并实现共存的。总体而言, 在随机构建的群落模型中, 多样性和连接度的增长不利于系统稳定; 而在更接近真实自然群落的模型中, 相互作用方式、网络拓扑结构、相互作用强度分布等方面的机制提供了稳定效应, 按此组织的生态网络可达到很高的复杂度。然而, 复杂性-稳定性的研究还远未结束, 当前的模型仍不足以反映自然群落中的复杂相互作用, 稳定性的概念也有待拓展。对这一议题的深入研究在生态学理论和生态系统管理实践方面都具有重大价值。

关键词: 复杂性-稳定性, 持久性, 群落矩阵, 分室, 食物网

In the 1970s, the intuition that complex communities are more stable than simple ones was challenged by mathematical models which gave diametrically opposing conclusions. Since then, this “paradox” has been heavily researched making the complexity-stability relationship of continued interest. Here, we analyzed the concepts of “complexity” and “stability” and classified the half-century of mathematical models generated by this field into linear approach and nonlinear approaches. The former is also referred to as community matrix, while the latter could be further classified into interaction matrix, numerical simulation of complex network, and food web module dynamics. Based on different community construction methods and adopting different stability criteria, together they provide a rich knowledge of how species interact and coexist, enabling us to reveal the vain of the paradox. In general, species diversity and connectivity play a negative role in the stability of randomly constructed community models. However, in models that mimic natural, empirical communities, several characteristics (including network topology, interaction intensity distribution, and interaction mode) provide mechanisms for maintaining stability, enabling these communities to reach higher levels of complexity. The study of complexity-stability is far from over. The complex interactions in natural communities is still beyond the reach of current models, and the concept of stability also needs to be expanded. The in-depth study of this topic will contribute both ecological theory and ecosystem management practice profoundly.

Key words: complexity-stability, persistence, community matrix, compartments, food web

图1

可能群落空间与真实群落"

图2

消费者-资源相互作用(改绘自McCann, 2010)。其中R和C分别表示资源和消费者种群密度, r为资源内禀增长率, K为承载力, a为攻击率, R0是资源的半饱和密度, e是转化为消费者生物量的比例, m为消费者的个体死亡率。"

图3

食物网的空间等级结构。椭圆表示各营养级物种的空间尺度及其所覆盖的栖息地(改绘自McCann, 2010)。"

表1

复杂性?稳定性研究模型方法"

方法名称
Approach name
群落构建方法
Community construction method
群落规模
Community size
稳定性衡量
Stability measurement
群落矩阵法
Community matrix approach
指定物种数、连接度、平均相互作用强度, 随机给出或指定网络结构和相互作用分布
Species number, connectivity, average interaction intensities are designated; web structure and interaction distribution rule are random or designated
适用大型生态网络
Suitable for large ecological networks
局部稳定性, 稳定网络的百分比(PSW)
Local stability, percentage of stable webs (PSW)
相互作用矩阵法
Interaction matrix approach
指定物种数, 网络结构可随机给出或指定, 随机给出每单位相互作用强度
Species number is designated, web structure can be designated or random, per unit interaction intensities are random
适用大中型生态网络
Suitable for large and middle-sized ecological networks
局部稳定性+可行性, 稳定网络的百分比(PSW)
Local stability and feasibility, percentage of stable webs (PSW)
复杂网络的数值模拟法
Numerical simulation of complex network
指定物种数, 网络结构由专门模型生成, 相互作用强度参数通过与体型比给出, 或在一定范围内变动
Species number is designated, web structure is generated by model, parameters of interaction intensity are given by the ratio to body size, or vary within a certain range
适用中型生态网络
Suitable for middle-sized ecological networks
持久性(共存的物种数占比)
Persistence (the proportion of coexisting species)
食物网构件动力学法
Food web module dynamics approach
所有参数都直接指定
All parameters are designated
适用小型构件, 但可通过构件组合推测大型食物网的稳定性
Suitable for small web module, but could be used to infer the stability of large food webs
永久性+波动程度
Permanence and variability
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