Linking saturation, stability and sustainability in food webs with observed equilibrium structure

Stability of a dynamic equilibrium in a predator-prey system depends both on the type of functional response and on the point of equilibrium on the response curve. Saturation effects from Holling type II responses are known to destabilise prey populations, while a type III (sigmoid) response curve has been shown to provide stability at lower levels of saturation. These effects have also been shown in multi-trophic model systems. However, stability analyses of observed equilibria in real complex ecosystems have as yet not assumed non-linear functional responses. Here, we evaluate the implications of saturation in observed balanced material-flow structures, for system stability and sustainability. We first make the effects of the non-linear functional responses on the interaction strengths in a food web transparent by expressing the elements of Jacobian ‘community’ matrices for type II and III systems as simple functions of their linear (type I) counterparts. We then determine the stability of the systems and distinguish two critical saturation levels: (1) a level where the system is just as stable as a type I system and (2) a level above which the system cannot be stable unless it is subsidised, separating a stable materially sustainable regime from an unsustainable one. We explain the stabilising and destabilising effects in terms of the feedbacks in the systems. The results shed light on the robustness of observed patterns of interaction strengths in complex food webs and suggest the implausibility of saturation playing a significant role in the equilibrium dynamics of sustainable ecosystems

Competitive hierarchies in bryozoan assemblages mitigate network instability by keeping short and long feedback loops weak

Competitive hierarchies in diverse ecological communities have long been thought to lead to instability and prevent coexistence. However, system stability has never been tested, and the relation between hierarchy and instability has never been explained in complex competition networks parameterised with data from direct observation. Here we test model stability of 30 multispecies bryozoan assemblages, using estimates of energy loss from observed interference competition to parameterise both the inter- and intraspecific interactions in the competition networks. We find that all competition networks are unstable. However, instability is mitigated considerably by asymmetries in the energy loss rates brought about by hierarchies of strong and weak competitors. This asymmetric organisation results in asymmetries in the interaction strengths, which reduces instability by keeping the weight of short (positive) and longer (positive and negative) feedback loops low. Our results support the idea that interference competition leads to instability and exclusion but demonstrate that this is not because of, but despite, competitive hierarchy

Stability and Fluctuations in Complex Ecological Systems

From 08-12 August, 2022, 32 individuals participated in a workshop, Stability and Fluctuations in Complex Ecological Systems, at the Lorentz Center, located in Leiden, The Netherlands. An interdisciplinary dialogue between ecologists, mathematicians, and physicists provided a foundation of important problems to consider over the next 5-10 years. This paper outlines eight areas including (1) improving our understanding of the effect of scale, both temporal and spatial, for both deterministic and stochastic problems; (2) clarifying the different terminologies and definitions used in different scientific fields; (3) developing a comprehensive set of data analysis techniques arising from different fields but which can be used together to improve our understanding of existing data sets; (4) having theoreticians/computational scientists collaborate closely with empirical ecologists to determine what new data should be collected; (5) improving our knowledge of how to protect and/or restore ecosystems; (6) incorporating socio-economic effects into models of ecosystems; (7) improving our understanding of the role of deterministic and stochastic fluctuations; (8) studying the current state of biodiversity at the functional level, taxa level and genome level.Comment: 22 page

Matrix scaling and tipping points

To assess which ecosystems are most vulnerable it is necessary to compare the resilience of complex interaction networks in a meaningful way. A fundamental problem for the comparative analysis of ecological stability is that the organisms in ecological networks operate on different time scales. A conventional solution to this problem has been to assume the intraspecific interaction strengths in the dynamical system (and diagonal elements in the community matrix) have the same value, ignoring the time scale differences, and therefore disregarding vital ecological information. In this paper, we consider two methods that have previously been developed to deal with community matrices arising from populations with widely different time scales and which contain differing self-regulation terms (diagonal entries). One approach considers the critical self-regulation in a system by proportionally adjusting the diagonal entries until the tipping point is found. The other is a scaling procedure that translates the intraspecific information on the diagonal on to the off-diagonal entries. We show the relation between the leading eigenvalue of the latter, and the numerical diagonal parameter of the former, which in many ecologically relevant networks is exact. In addition, we show for 3x3 scaled competitive systems how the feedback determines whether the leading eigenvalue is real- or complex-valued, which is important for knowing when the scaling procedure remains ecologically sensible. While arising from an ecological setting, this work has wider implications in network theory and linear algebra

Feedback spectra of soil food webs across a complexity gradient, and the importance of three-species loops to stability

It has been shown that in real food webs, the strongest omnivorous feedback, a three-link positive feedback, is a good indicator of system stability, suggesting that the strongest positive feedback in a food web could be the Achilles heel of stability. However, the complete spectrum of feedbacks in observed food webs has never been analyzed. Here, we have quantified all the feedbacks in 32 soil food webs along a complexity gradient, including trophic feedbacks and feedbacks resulting from recycling of organic matter. We found that, although the maximum omnivorous feedback was rarely the strongest positive feedback in a system, it stood out over longer and stronger feedbacks as the indicator of stability. The results emphasize the importance of small substructures in complex networks

Stability and Fluctuations in Complex Ecological Systems

From 08-12 August, 2022, 32 individuals participated in a workshop, Stability and Fluctuations in Complex Ecological Systems, at the Lorentz Center, located in Leiden, The Netherlands. An interdisciplinary dialogue between ecologists, mathematicians, and physicists provided a foundation of important problems to consider over the next 5-10 years. This paper outlines eight areas including (1) improving our understanding of the effect of scale, both temporal and spatial, for both deterministic and stochastic problems; (2) clarifying the different terminologies and definitions used in different scientific fields; (3) developing a comprehensive set of data analysis techniques arising from different fields but which can be used together to improve our understanding of existing data sets; (4) having theoreticians/computational scientists collaborate closely with empirical ecologists to determine what new data should be collected; (5) improving our knowledge of how to protect and/or restore ecosystems; (6) incorporating socio-economic effects into models of ecosystems; (7) improving our understanding of the role of deterministic and stochastic fluctuations; (8) studying the current state of biodiversity at the functional level, taxa level and genome level