Interaction strengths in balanced carbon cycles and the absence of a relation between ecosystem complexity and stability.

The strength of interactions is crucial to the stability of ecological networks. However, the patterns of interaction strengths in mathematical models of ecosystems have not yet been based upon independent observations of balanced material fluxes. Here we analyse two Antarctic ecosystems for which the interaction strengths are obtained: (1) directly, from independently measured material fluxes, (2) for the complete ecosystem and (3) with a close match between species and 'trophic groups'. We analyse the role of recycling, predation and competition and find that ecosystem stability can be estimated by the strengths of the shortest positive and negative predator-prey feedbacks in the network. We show the generality of our explanation with another 21 observed food webs, comparing random-type parameterisations of interaction strengths with empirical ones. Our results show how functional relationships dominate over average-network topology. They make clear that the classic complexity-instability paradox is essentially an artificial interaction-strength result.

Reconciling complexity with stability in naturally assembling food webs.

Understanding how complex food webs assemble through time is fundamental both for ecological theory and for the development of sustainable strategies of ecosystem conservation and restoration. The build-up of complexity in communities is theoretically difficult, because in random-pattern models complexity leads to instability. There is growing evidence, however, that nonrandom patterns in the strengths of the interactions between predators and prey strongly enhance system stability. Here we show how such patterns explain stability in naturally assembling communities. We present two series of below-ground food webs along natural productivity gradients in vegetation successions. The complexity of the food webs increased along the gradients. The stability of the food webs was captured by measuring the weight of feedback loops of three interacting 'species' locked in omnivory. Low predator-prey biomass ratios in these omnivorous loops were shown to have a crucial role in preserving stability as productivity and complexity increased during succession. Our results show the build-up of food-web complexity in natural productivity gradients and pin down the feedback loops that govern the stability of whole webs. They show that it is the heaviest three-link feedback loop in a network of predator-prey effects that limits its stability. Because the weight of these feedback loops is kept relatively low by the biomass build-up in the successional process, complexity does not lead to instability.

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.

Beyond connectedness: why pairwise metrics cannot capture community stability.

The connectedness of species in a trophic web has long been a key structural characteristic for both theoreticians and empiricists in their understanding of community stability. In the past decades, there has been a shift from focussing on determining the number of interactions to taking into account their relative strengths. The question is: How do the strengths of the interactions determine the stability of a community? Recently, a metric has been proposed which compares the stability of observed communities in terms of the strength of three- and two-link feedback loops (cycles of interaction strengths). However, it has also been suggested that we do not need to go beyond the pairwise structure of interactions to capture stability. Here, we directly compare the performance of the feedback and pairwise metrics. Using observed food-web structures, we show that the pairwise metric does not work as a comparator of stability and is many orders of magnitude away from the actual stability values. We argue that metrics based on pairwise-strength information cannot capture the complex organization of strong and weak links in a community, which is essential for system stability.

Stability in real food webs: weak links in long loops.

Increasing evidence that the strengths of interactions among populations in biological communities form patterns that are crucial for system stability requires clarification of the precise form of these patterns, how they come about, and why they influence stability. We show that in real food webs, interaction strengths are organized in trophic loops in such a way that long loops contain relatively many weak links. We show and explain mathematically that this patterning enhances stability, because it reduces maximum "loop weight" and thus reduces the amount of intraspecific interaction needed for matrix stability. The patterns are brought about by biomass pyramids, a feature common to most ecosystems. Incorporation of biomass pyramids in 104 food-web descriptions reveals that the low weight of the long loops stabilizes complex food webs. Loop-weight analysis could be a useful tool for exploring the structure and organization of complex communities.