Predicting global community properties from uncertain estimates of interaction strengths.

The community matrix measures the direct effect of species on each other in an ecological community. It can be used to determine whether a system is stable (returns to equilibrium after small perturbations of the population abundances), reactive (perturbations are initially amplified before damping out), and to determine the response of any individual species to perturbations of environmental parameters. However, several studies show that small errors in estimating the entries of the community matrix translate into large errors in predicting individual species responses. Here, we ask whether there are properties of complex communities one can still predict using only a crude, order-of-magnitude estimate of the community matrix entries. Using empirical data, randomly generated community matrices, and those generated by the Allometric Trophic Network model, we show that the stability and reactivity properties of systems can be predicted with good accuracy. We also provide theoretical insight into when and why our crude approximations are expected to yield an accurate description of communities. Our results indicate that even rough estimates of interaction strengths can be useful for assessing global properties of large systems.