Ecological Applications of Cycle Analysis

The recycling of energy-matter is an important process that occurs in every ecosystem. Cycling is believed to be a buffering mechanism that allows ecosystems to face shortage of nutrient inflows. This process, however, has been neglected in many theoretical models, which concentrated on communities rather than ecosystems, and which usually comprised just a few species due to constraints of modeling techniques. Food web ecologists always had an ambivalent attitude toward cycling. For example, the first collection of food webs published (which contained poorly resolved food webs with just a few nodes) showed that cycles are very rare. This was justified by the fact that cycles are likely to destabilize a system, because they introduce positive feedbacks. This result was, however, challenged by the discovery of many cycles in larger food webs, and the role of cannibalism in age-structured population dynamics. In recent times, the importance of cycles in food webs has been reconsidered, thanks to the switch of focus from local stability dynamics toward a more comprehensive approach to ecosystems persistence and nonlinear dynamics. Moreover, a greater attention has been devoted to the microbial loop, which, in some aquatic ecosystems, receives more than 50% of the primary production, remi-neralizes it and feeds it back to higher trophic levels.

Ecosystem oriented modeling, on the other hand, included cycles as the very foundation of the discipline. The first clear reference to the importance of cycling in ecological network comes from the work of Lindeman who, in his seminal paper in 1942, described food webs as cycling material and energy. Odum then included the amount of recycling as one of the 24 criteria for evaluating if an ecosystem is 'mature' (i.e., developed).

The request for a quantification of cycling was then answered by the FCI illustrated above. Modified versions of the FCI, including biomass storage, utilizing the so-called 'total dependency and contribution matrices' were published, increasing the possibilities for modelers and therefore the number of applications of such indices to empirical studies.

Recently, it was pointed out how all these calculations ignore some cycling that involves just off-diagonal terms in the Leontief matrix. Unfortunately, in order to compute the exact amount of cycling in an ecosystem one should utilize a computationally intensive method, which is therefore unfit to be applied to large ecosystem networks. Fortunately, studies conducted on many small networks showed that the total amount of cycling and the FCI seem linearly related, with the total cycling being around 1.14 times the FCI.

The relation between cycling and maturity of ecosystems was challenged by the work of Ulanowicz. He showed how cycling could be inversely related to the developmental status of an ecosystem, and how perturbations could be reflected into a higher cycling index. These considerations suggest that cycling could be seen as a homeostatic response to stress: impacts on ecosystems free nutrients from the higher trophic levels; this freed matter is then recycled into the system by microorganisms, generating cycles at the lower trophic levels. In this view, responding to stress ecosystem would show a decrease in cycle length and an increase in total cycling. It is therefore important to know the distribution of cycle lengths together with the total amount of cycling in the ecosystem when one wants to assess the ecosystem status and maturity. Ulanowicz also presented important insights on cycling as autocatalytic processes. The cycling feature of ecosystems is at the basis of the views of several authors on ecosystem function and dynamics, such as, for example, the work of Patten and colleagues.

Another aspect of cycling is represented by the com-partmentalization into SCCs. Although ecosystems comprise myriad interactions, they still can be divided into a few subsystems that are connected by linear chains of energy transfers. In several aquatic food webs, SCC analysis shows a subdivision into pelagic and benthic components of the ecosystem. This result is, however, dependent on the way the ecosystem is modeled, with particular emphasis on the importance of including several detritus compartments.

Summarizing, cycling is an important aspect of ecosystem dynamics. Although cycles seem to be rare in published community food webs and models, their number is very large when detritus compartments are considered. Moreover, it is important to stress that the role of the so-called microbial loop, neglected in studies that concentrate on larger organisms, can dramatically change the cycling performance of the system. These considerations lead ecosystem ecologists to the formulation of the amount of cycling in ecosystem networks. The FCI, even though it is a biased count of the cycling in ecosystems, has found wide application in ecosystem studies. The problem of measuring the exact amount of cycling in an ecosystem is still an open problem, as it could be possible to ameliorate the algorithms for finding and removing cycles. Finally, the network building process is likely to determine the outcome in terms of cycling. It would therefore be important to have shared rules for network building that would result in the comparability between different networks and ecosystems.

See also: Autocatalysis; Cannibalism; Ecological Network Analysis, Ascendency; Stability.

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