Cycling emergy: computing emergy in trophic networks

• Arguments are presented supporting inclusion of feedbacks in emergy algebra.
• The inclusion of feedbacks in the accounting methodology does not contradict emergy theory.
• When cycling is included, total available emergy is increased.
• The order of components in the transformity hierarchy is changed when cycling is included.

While cycles are a very important phenomena of ecosystems, they represent a methodological challenge in emergy accounting. The relevance of feedbacks is acknowledged in emergy evaluations, however they are not considered by the emergy algebra. In this paper, we present supporting arguments in favor of an update in the emergy accounting methodology. We argue that including the contribution of feedback emergy is essential to understand a system's internal functioning, thus studies interested in better capturing these features should consider emergy cycling. Feedbacks represent emergy that entered the system in the past (therefore it is not double counting), and they enable additional organization and work above that supported by input emergy alone.To evaluate the effect upon system properties of including feedbacks, we compared two different methods for calculating transformities using trophic networks as case studies. One method followed the classic emergy rules where feedbacks were not included, and the other included the feedbacks (we refer to them as static and network method, respectively). The comparison between the resulting transformities and system emergy patterns showed that (1) transformities and system emergy were significantly higher with the network method, and (2) this increase affected the network compartments unevenly, altering their position in the emergy hierarchy. Estimating relative importance of the system's components or their true emergy requirements are only possible by evaluating the total emergy that flows through them.