Looplessness in networks is linked to trophic coherence

Complex systems such as cells, brains, or ecosystems are made up of many interconnected elements, each one acting on its neighbors, and sometimes influencing its own state via feedback loops. Certain biological networks have surprisingly few such loops. Although this may be advantageous in various ways, it is not known how feedback is suppressed. We show that trophic coherence, a structural property of ecosystems, is key to the extent of feedback in these as well as in many other systems, including networks related to genes, neurons, metabolites, words, computers, and trading nations. We derive mathematical expressions that provide a benchmark against which to examine empirical data, and conclude that "looplessness" in nature is probably a consequence of trophic coherence.