Network systems provide humans with essential services but can crash dramatically, a case in point being the financial collapse in 2008. Can these crises be predicted before it is too late? The answer is yes, and the key tool is network theory.
Re-EcoNetis an UCD based multidisciplinary collaboration between theoretical ecologists, applied mathematicians, physicists, geomorphologists, and biologists who use network science to discover the processes that confer stability and resilience on ecosystems.
The structure of ecological networks determines the expression of ecological functions. For example, the structure of a food web controls energy flux through the foodweb. Network structure and their functions naturally fluctuate over time (green line). Perturbations alter the structure of the network and so their functions. If the perturbation is released, the network may reassemble, either to return to the previous state or maybe settle into a new state. Aspects of network structure are topology (who connects to whom) and link weights (ammount of fluxes or strength of interaction between nodes). Key challenges in ecology are: i) describe fluctuations of networks, especially typical vs. anomalous states; ii) connect variable structure to variable functions to detect the functional implications of structural variation (figure credit: Bardgett and Caruso 2020).
The overarching goal is the formulation of a research platform to develop large scale projects (e.g. a COST Action) focusing on the detection of the onset of systemic crises in ecosystems under global change threats.
Network statistical mechanics adapts theory and mathematical formalism from physics to network theory. The resulting models allow the construction of ensembles of networks compatible with given sets of constraints. There are two complementary goals: one is the definition of the minimal set of constraints necessary to reproduce key structural features of empirical networks (i.e. network reconstruction), and the other is the construction of unbiased null models that randomise network properties under a set of constraints. Both for network reconstruction and null model formulation, the most interesting constraints are at the node level. For example, the degree sequence, that is the number of links of each node, node by node. Or also, node strength sequence, which in a food web would be the total incoming and outcoming energy or C flux of a species (species by species). In classical ecological null models, the observed network is generally used to define a set of deterministic constraints. For example, if a plant of a plant-pollinator network has 5 pollinators, all null randomised networks will assign exactly 5 species to that plant, and just randomise the identity of the plant-partners. This means that the network structural properties are not allowed to fluctuate, which is very unlikely and generally unobserved in replicated observations of the same network. For example, the plant we considered before might have 5 partners in certain locations or at certain times only on average, with some locations and some times having 4 or 3 partners, or maybe more than 5 partners. Fluctuations in quantitative aspects such as energy fluxes between consumers and resources are perhaps even more likely. In Re-EconNet, we are working with an approach known in physics as “canonical ensemble”, in which maximum entropy and likelihood are used to find the most typical network configurations subject to constraints observed on the empirical network (e.g. degree sequence) but with the ensmeble respecting the constraints only on average (meaning the fluctuations over time or across locations are now allowed). This approach resolves all the statistical issues of classical rewiring algorithms and offers, in our view, a more robust and complete set of null models for ecological networks.
