Biodiv Sci ›› 2019, Vol. 27 ›› Issue (12): 1364-1378.DOI: 10.17520/biods.2019138

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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 Published:2019-12-24
  • Contact: Shi Chunhua


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