Science 25 July 2014:
Vol. 345 no. 6195 pp. 1253497-0
Research Article

On the structural stability of mutualistic systems

Rudolf P. Rohr, Serguei Saavedra, Jordi Bascompte | 2 Comments

In ecology, structural stability influences the range of perturbations mutualistic networks can withstand. [Also see Perspective by ]

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Avoid graphics that make you question the scientific soundness of a paper

“Visualisations and graphics are fundamental to studying complex subject matter.” That’s the first sentence in an opinion paper by McInerny et al. (1) on visualisation for science and policy. If however graphics are presented like in the figure accompanying the structured abstract of Rohr et al. (25 July, p. 416) (, one might better do without. The figure is intended to explain the structural stability of nested networks, accompanied by the statement that “the nested networks observed in nature—illustrated here by the network at the bottom—lead to a maximum structural stability”. If we look at the mentioned network in more detail, then we can observe that i) the network above the one at the bottom has exactly the same basic structure after slightly rearranging the positions of the butterflies and the plants while not changing the interactions; ii) literally spoken such a network cannot be observed in nature as the species used in the figure do not overlap in their distributions. It is misleading to use symbols for butterflies which are clearly identifiable species, namely from left to right: Papilio machaon (Holarctic), Papilio ulysses (Australian / New Guinean) and Danaus plexippus (mainly Central and North-American); and iii) we have to keep in mind that butterflies are not really good examples for pollinators (2), which however was the main interaction dealt with in the paper. Fortunately the figure used in the perspective by Pawar (25 July, p. 383) does not have these shortcomings and also gives a much easier access to the messages behind the really fascinating findings by Rohr et al.

Josef Settele* and Martin Wiemers

Helmholtz Centre for Environmental Research–UFZ, 06120 Halle, Germany and iDiv, German Centre for Integrative Biodiversity Research, 04103 Leipzig, Germany *Author for correspondence. E-mail:

References (1) G. J. McInerny et al., Trends in Ecology & Evolution 29, 148-157 (2014). (2) "Butterfly Pollination.” USDA Forest Service Celebrating Wildflowers.

Submitted on Sun, 09/21/2014 - 14:21

Structural stability means evolutionary, but not ecological, stability

May’s [Nature 238:413] theory that complexity entails instability has generated considerable debate among ecologists. A significant aspect of this debate surrounds the different perspectives of nestedness in the stability of mutualistic networks. Using Lyapunov stability, Allesina and Tang [Nature 483:205] reconfirmed that “stability is negatively affected by nestedness in bipartite mutualistic networks”. The tide of evidence has been reversed however by Rohr et al. [Science 345:1253497] who showed that mutualistic communities maximize their structural stability through potentially enhanced nestedness. However, we argue that such a comparison is much like comparing apples with oranges.

Lyapunov stability is a measure of ecological stability while structural stability is an indicator of evolutionary stability. This is clear since the perturbation reflects different processes and responses. For Lyapunov stability, the perturbation involves small changes in population sizes, caused by disturbances and stochasticity. How an ecological network responds to such perturbation is the typical indicator of ecological stability. In contrast, perturbation in structural stability is variability in vital rates (e.g. growth rates). Yet population growth rates change at an evolutionary scale, and the perturbation therefore means forces of directional or disruptive selection that divert species from their original evolutionary trajectory.

Since Lyapunov and structural stability reflect different aspects of interaction networks, they have different implications for understanding network resilience. This is highlighted in evolutionary invasion analysis (e.g. adaptive dynamics) where ecological and evolutionary stability are clearly distinguished and handled separately [Nature 421:259]. Indeed, at ecological timescales, an ecosystem dominated by mutualistic interactions is likely unstable and species poor. By contrast, at evolutionary timescales, mutualistic interactions can act as a stabilizing force and restrict diversification [Am. Nat. 183:363]. The complexity-stability debate will be better resolved once these two stability concepts are differentiated for the unique value that each captures in describing interaction networks and the resilience thereof.

Cang Hui and John S. Terblanche

Stellenbosch University, and African Institute for Mathematical Sciences, Cape Town 7945, South Africa

Submitted on Fri, 08/15/2014 - 03:32