Stability criteria for complex ecosystems

By Stefano Allesina, Si Tang. Nature, 2011

1,216 citations recorded by the source corpus.

Forty years ago, May proved that sufficiently large or complex ecological networks have a probability of persisting that is close to zero, contrary to previous expectations. May analysed large networks in which species interact at random. However, in natural systems pairs of species have well-defined interactions (for example predator–prey, mutualistic or competitive). Here we extend May’s results to these relationships and find remarkable differences between predator–prey interactions, which are stabilizing, and mutualistic and competitive interactions, which are destabilizing. We provide analytic stability criteria for all cases. We use the criteria to prove that, counterintuitively, the probability of stability for predator–prey networks decreases when a realistic food web structure is imposed or if there is a large preponderance of weak interactions. Similarly, stability is negatively affected by nestedness in bipartite mutualistic networks. These results are found by separating the contribution of network structure and interaction strengths to stability. Stable predator–prey networks can be arbitrarily large and complex, provided that predator–prey pairs are tightly coupled. The stability criteria are widely applicable, because they hold for any system of differential equations.

Subfields: Ecology, Evolution, Behavior and Systematics, Plant Science, Sociology and Political Science

View Paper: https://www.semanticscholar.org/paper/c392b34431cc1cbf26aa972a3776d9dc7d786b0b

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Citations in the corpus

The ecology of the microbiome: Networks, competition, and stability (2015, methodology): “Both measures of stability, therefore, can be determined from the region in the complex plane to which all eigenvalues will be restricted, and we extend the recent analytic results of Allesina and Tang to derive these regions for an ecosystem with any potential mixture of interaction types (18).”
Frugivores at higher risk of extinction are the key elements of a mutualistic network (2014, background): “Highly connected species in nested mutualistic networks may favor the long-term species persistence (Saavedra et al. 2011; but see Allesina and Tang 2012); however, nested networks may be very fragile if generalist species die out (Memmott et al. 2004).”
Biotic interactions in species distribution modelling: 10 questions to guide interpretation and avoid false conclusions (2018, background): “…of abstraction and complexity, ranging from individuals encountering and interacting directly or exploiting a shared resource (e.g., trees competing for light; Lischke, Zimmermann, Bolliger, Rickebusch, & L € offler, 2006) to highly aggregated interaction coefficients (Allesina & Tang, 2012).”
The rise of Network Ecology: Maps of the topic diversity and scientific collaboration (2013, background): “For example, the articles by Allesina and Levine (2011) and Allesina and Tang (2012) are both clearly about Network Ecology.”
The Geography of Complex Knowledge (2017, background): “Typical examples of two-mode networks are individual-event networks (Davis, Gardner, and Gardner 1941), interlocking directorates (Robins and Alexander 2004), predator–prey networks (Allesina and Tang 2012), or firm–projects networks (Balland 2012).”
Complexity and stability of ecological networks: a review of the theory (2018, background): “Accordingly, subsequent work added more structural realism to those random community matrices by including empirical patterns of food web structure and Jacobian elements distributions (see Allesina and Tang 2012; Allesina et al.”
Defining invasiveness and invasibility in ecological networks (2016, methodology): “normally refers to a combined factor of network size (the number of nodes) and connectance (May 1974; Allesina and Tang 2012).”
The stability–complexity relationship at age 40: a random matrix perspective (2015, methodology): “We did so (Allesina and Tang 2012; Tang et al. 2014) by introducing to ecology some basic tools of Random Matrix Theory (RMT) (Bai and Silverstein 2009; Anderson et al.”
Statistical mechanics of ecological systems: Neutral theory and beyond (2015, background): “[5] S.”
Structure–stability relationships in networks combining mutualistic and antagonistic interactions (2014, background): “Our results are thus in agreement with recent studies that question the importance of nestedness for network stability (Allesina and Tang 2012, James et al. 2012).”
Identifying Causes of Patterns in Ecological Networks: Opportunities and Limitations (2017, background): “…matrices with normally distributed interaction strength, s (nC)1/2 1, where s is the standard deviation of the normal distribution from which interaction strengths are drawn, n is the number of species, and C is the connectance of the matrix (see also Sinha 2005, Allesina & Tang 2012).”
Beyond species: why ecological interaction networks vary through space and time (2014, background): “Such a simpliﬁcation does increase the analytical tractability of the problem (Allesina and Tang 2012), but there is little, if any, guar-21 antee that it is ecologically accurate.”