Structural stability: Concepts, methods, and applications

doi:10.17520/biods.2020110

Abstract

Abstract:

Ecological networks—how species interactions are organized within ecological communities—are highly structured, which has motivated generations of ecologists to elucidate how these structures affect species coexistence. Unfortunately, we still do not have a clear and consistent answer about the link between network structure and species coexistence. A possible explanation is that most of the studies do not take into account that the environment affects both network structure and species coexistence due to the multidimensional and changing nature of environmental factors. In this context, the structural stability approach provides a theoretical framework grounded on biological realism to quantitatively link network structure, species coexistence, and environmental factors. I begin by an overview of the heated debates in the study of ecological networks. Then I introduce the theoretical framework and computational tools of the structural stability approach in a nutshell. Then I show the empirical applications in different ecological questions across a broad range of ecological systems. Overall, the structural stability approach provides a new perspective to understand the maintenance of biodiversity in ecological communities.

Key words: community structure, species coexistence, structural stability, environmental gradient, environmental stress

Chuliang Song. Structural stability: Concepts, methods, and applications[J]. Biodiv Sci, 2020, 28(11): 1345-1361.

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URL: https://www.biodiversity-science.net/EN/10.17520/biods.2020110

https://www.biodiversity-science.net/EN/Y2020/V28/I11/1345

Figures/Tables 4

Fig. 1 Two ecological community structures. Here we present an illustration of two hypothetical network structures. The community structure is represented as a matrix. The columns correspond to different plant species while the rows correspond to different pollinators (in Panel A) or herbivores (in Panel B). A species interaction is represented as a gray grid. Panel (A) illustrates the nested structure. The defining feature of a nested structure is that highly connected species interact with both highly connected and poorly connected species, while poorly connected species interact almost exclusively with highly connected species. The nested structure is widely conceived as a universal structure in mutualistic communities. Panel (B) illustrates the modular structure. The defining feature of the modular structure is that in which groups of species have many interactions among them, but few interactions with the rest of the species in the network. The modular structure is widely conceived as a universal structure in food webs.

Fig. 2 The debates in the study of community structures. Three different schools of thought coexist in linking nestedness and species coexistence in mutualistic communities. The first school (Panel A) argues that nestedness is a key factor to support the biodiversity in mutualistic communities, the second school (Panel B) argues there is no causal relationship between the nested pattern and biodiversity, and the third school (Panel C) argues that nested patterns are not universal in observed mutualistic communities, thus makes the whole question a straw man.

Fig. 3 The mathematical framework of the structural stability approach. To compute the structural stability (SS) of an ecological community, we need two pieces of information: the coexistence domain (CD) and the environment domain (ED). The coexistence domain (denoted in blue; region A) is the full range of parameters that are compatible with species coexistence. The coexistence domain is determined by the community structure via the ecological dynamics. The environment domain (denoted in green; region B) is the full range of parameters constrained by the given environmentally conditions. The environment domain is determined by the environmental factors. Structural stability is defined as the relative size of the coexistence domain comparing to the environment domain. The larger the structural stability is, the more likely species can coexist under the given environmental conditions.

Fig. 4 The structural stability approach for understanding multispecies coexistence. The nodes denote the key elements in ecological dynamics: species pool, community structure, environmental factors, and species coexistence. The links represent the ecological processes (denoted in blue) that connect these elements: community assembly, structural change, ecological dynamics, environmental gradient, and environmental stress. The structural stability approach aims to integrate these ecological processes under a unified framework. For each process, the structural stability approach provides new theoretical predictions, which are validated by experimental and/or observational data.

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