How collectively integrated are real ecological communities? Are population dynamics of a species determined only by its direct interactions - who it eats, pollinates, or competes with? Or must we consider indirect feedbacks rippling across the whole network? These questions illustrate a spectrum of behaviors which can be found in different communities.
To formalize this question, we propose a set of measures that quantify the degree of collective integration of a community. Three important measures are perturbation depth, interaction horizon and response predictability.
Perturbation depth is the average network distance travelled by long-term effects of perturbing (e.g. removing) a species. In more collectively integrated communities, species further away from the perturbed species can respond significantly.
Interaction horizon measures the contribution of indirect effects in the response to an environmental stressor.
Response predictability is the degree of accuracy with which the short term response to a perturbation can be extrapolated to the long term.
These measures quantify aspects of collective behavior that [are important/can be observed] in different empirical contexts.
Our mathematical analysis will reveal that all these notions are strongly related to one another, and to a more formal measure of collective integration. The latter will allow us to deduce the drivers of collective behaviour, and investigate its empirical prevalence.
The answers to these questions will clarify when reductionist perspectives, focusing on particular species and small interaction motifs, suffice or fail when applied to natural ecosystems.