Community matrix

The predictability of qualitative food web dynamics in response to extinction and invasion

Food webs are extraordinarily complex, containing myriad direct interactions and indirect effects. Determining how this network of interactions and effects influences a food web’s qualitative dynamics is a challenging task, especially because data …

Exact probabilities for the indeterminacy of complex networks as perceived through press perturbations

We consider the goal of predicting how complex networks respond to chronic (press) perturbations when characterizations of their network topology and interaction strengths are associated with uncertainty. Our primary result is the derivation of exact …

Rapid and direct recoveries of predators and prey through synchronized ecosystem management

One of the twenty-first century’s greatest environmental challenges is to recover and restore species, habitats and ecosystems. The decision about how to initiate restoration is best-informed by an understanding of the linkages between ecosystem …

Characterizing species interactions to understand press perturbations: What is the community matrix?

The community matrix is among ecology's most important mathematical abstractions, formally encapsulating the interconnected network of effects that species have on one another's populations. Despite its importance, the term “community matrix” has …

Complexity increases predictability in allometrically constrained food webs

All ecosystems are subjected to chronic disturbances, such as harvest, pollution, and climate change. The capacity to forecast how species respond to such press perturbations is limited by our imprecise knowledge of pairwise species interaction …

Predicting community responses to perturbations in the face of imperfect knowledge and network complexity

How best to predict the effects of perturbations to ecological communities has been a long‐standing goal for both applied and basic ecology. This quest has recently been revived by new empirical data, new analysis methods, and increased computing …