Complexity and stability of ecological networks: a review of the theory

Abstract

Our planet is changing at paces never observed before. Species extinction is happening at faster rates than ever, greatly exceeding the five mass extinctions in the fossil record. Nevertheless, our lives are strongly based on services provided by ecosystems, thus the responses to global change of our natural heritage are of immediate concern. Understanding the relationship between complexity and stability of ecosystems is of key importance for the maintenance of the balance of human growth and the conservation of all the natural services that ecosystems provide. Mathematical network models can be used to simplify the vast complexity of the real world, to formally describe and investigate ecological phenomena, and to understand ecosystems propensity of returning to its functioning regime after a stress or a perturbation. The use of ecological-network models to study the relationship between complexity and stability of natural ecosystems is the focus of this review. The concept of ecological networks and their characteristics are first introduced, followed by central and occasionally contrasting definitions of complexity and stability. The literature on the relationship between complexity and stability in different types of models and in real ecosystems is then reviewed, highlighting the theoretical debate and the lack of consensual agreement. The summary of the importance of this line of research for the successful management and conservation of biodiversity and ecosystem services concludes the review.

Emergence of weak‐intransitive competition through adaptive diversification and eco‐evolutionary feedbacks

“…This result is tentatively in agreement with May's complexity begets instability principle (May, ), showing that the probability of local stability in a community decreases with number of species and/or number and strength of interactions (Allesina & Tang, ; but see also Grilli, Barabás, Michalska‐Smith, & Allesina, ). However, the exact mechanisms behind the complexity–stability relationship remain uncertain (partly due to the lack of analytical descriptions) and require further non‐trivial investigations that are beyond the scope of our study (Landi, Minoarivelo, Brännström, Hui, & Dieckmann, ; Namba, ). Finally, previous work has shown that increasing intransitivity (3) enables a faster recovery after large perturbations of the system (where species abundance is reduced to few individuals) due to negative frequency dependence mechanisms (Gallien et al., ).…”

Constraints on the distribution of species abundances indicate universal mechanisms of community assembly

“…The second case would demand universal patterns of animal and plant community assembly and might also indicate that observed SADs represent "islands of community stability." Within this interpretation, the unobserved SADs are those that are intrinsically unstable and consequently rare (Allesina & Tang, 2012;Landi, Minoarivelo, Brännström, Hui, & Dieckmann, 2018).…”

Network modelling, citizen science and targeted interventions to predict, monitor and reverse bee decline

“…Network analysis is a mathematical technique widely used for understanding relationships between actors. It has been used to study a diversity of phenomena, from the flow of goods and services between cities and information transfer in social networks, to the movement of nutrients within slimemolds and species interactions in plant–pollinator communities (see review Landi, Minoarivelo, Brännström, Hui, & Dieckmann, ). Network metrics can be used to quantify the importance of relationships between individual actors, the importance of individual actors in the system as a whole, and how the system as a whole responds to the loss of individual actors.…”

“…It is possible to have network edges that are weighted (representing the strength or importance of the interaction) or unweighted (present or absent). Edges can be symmetric (also called undirected; the two species affect each other equally), or asymmetric (also called directed; the two species affect each other differently), and positive or negative (Landi et al, ). When a node changes or adds to its interaction partner(s) this is termed rewiring .…”