Cyclic energy pathways in ecological food webs
Introduction
It is clear from both Lindeman's original diagram and text that he envisioned energy flow pathways as cyclical. However, in 1942, Lindeman did not have the methodological tools to simultaneously investigate the complex conceptual network that he used to represent the energy pathways in the Cedar Bog Lake ecosystem, and therefore, out of practicality, reduced the analysis to a series of two parallel trophic chains. As a result, food web ecology has developed largely along this paradigm in which matter–energy flow transfers mostly sequentially from basal to intermediate to top species (e.g., Paine, 1980, Cohen et al., 1990, Pimm, 2002). Some exceptions were evident, especially in marine ecosystems (e.g., Pomeroy, 1974, Wiegert and Owen, 1971, Ulanowicz, 1983, Wetzel, 1995, and notably in a related series of papers called network trophic dynamics literature, e.g., Patten, 1985, Burns, 1989, Burns et al., 1991, Higashi et al., 1988, Higashi et al., 1991, Higashi et al., 1993a, Higashi et al., 1993b, Patten et al., 1990, Whipple and Patten, 1993, Whipple, 1998, Whipple, 1999). In flow analysis of food webs, cycling affects, for instance, residence time and the total system throughflow (Fath et al., 2004). For example, Patten (1985) used network flow analysis to show energy is available and cycling in the Okefenokee Swamp ecosystem (some “trophic” transfers were over 20 steps in length). Recently, this detrital pathway has recently garnered renewed attention within the ecological community (see Moore et al., 2004), but the data requirements for a flow analysis similar to Patten (1985) are great which has impeded the application of this methodology to many systems. In fact, most published food webs or models have structural data (i.e., connectance), but not functional data (flow or interaction strength). Therefore, it is useful to have a metric that identifies the cyclic pathways based only on the connectance pattern. This paper adds to the network trophic dynamics paradigm some novel results for structural networks that are under growing discussion in recent literature.
A structural cycle is the presence of a pathway in the ecological network in which matter–energy passes through biotic or abiotic stores returning for availability to the same or lower trophic levels. Structural cycling is present in food webs due to intraguild predation, cannibalism, or other predation events that connect laterally or backwards in the hierarchy. Many empirical food web descriptions capture these cycles, and also assembly models such as the Constant Connectance (Martinez, 1992) and Niche model (Williams and Martinez, 2000) allow for internal structural cycles. Common to these models and many empirical data sets, is that all the structural cycling is due to “traditional” predation, and that they ignore the extra feedback connections caused by flows to detritus and back to the system through detritus feeders. Flows to detritus include many pathways such as death, excrement, or exfoliation. The detritus feedback loop is a fixed cyclic structure. It assures a certain amount of cycling, and it is fundamentally different from other cyclic structures in the system since it allows energy to flow from any trophic level including top predators to lower trophic levels.
In this paper we investigate 26 empirically derived ecological food webs with and without detrital interconnections ranging in size from 6 to 220 compartments to demonstrate the importance of the detritus feedback loop and we compare the results to the structural cycling generated by five different community assembly rules.
Section snippets
Structural cycling
Common network analysis properties include network size (n) and connectance (C). Connectance is defined as C = L/n2, where L is the number of links and n2 is the possible number of connections in the network. Furthermore, nC = L/n, which is the property known as linkage density. A newly developed and important property is network structural cycling (Fath, 1998, Jain and Krishna, 2003). This measures the presence and strength of cyclic pathways in a strongly connected component (SCC) of a network.
Data sources
In a well-studied set of 17 food webs (Dunne et al., 2002, Dunne et al., 2004), 10 of the webs explicitly include detritus compartments as source compartments (out-degree greater than zero), but with no input (in-degree equal to zero)2; the other seven webs excluded detritus entirely. This gives the image of two parallel food chains, one
Community assembly rules
Due to the difficulty in acquiring the requisite data for fully developed empirical food webs, researchers have developed community assembly rules that recreate, as best as possible, the perceived structural characteristics of food webs. These provided null-models to investigate fundamental questions of community structure and organization, attempting to link the ecological observed process to underlying pattern. Here we consider five such models, Constant Connectance (Martinez, 1992), Cascade (
Results
The maximum eigenvalue was calculated using the data for the empirical food webs without detritus (E1), in which n ranges from 30 to 220 (Table 1). The data have relatively low λmax (range from 0 to 10.25) and no readily apparent pattern regarding structural cycling (Fig. 2a). However, as stated above, although the webs include detritus in the categorical description, it is only treated as a primary food source in the structure. By reconnecting the rest of the food web to detritus such that it
Discussion
While there are many important links in the ecological networks, in this work, we have shown that passive flows to detritus and from detritus back into the system give an important contribution to the total structural cycling in the system, and increases the trend that cycling increases with the product nC, both in models and empirics. Although this web-like structure was evident in Lindeman's original trophic dynamic analysis, it was lost as food webs were constructed according to a food chain
Acknowledgments
We are grateful to Stuart Borrett, and indirectly Jennifer Dunne, for providing the unmodified data set used in Fig. 2a, and to Bernie Patten, Stefano Allesina, and anonymous reviewers for comments on the manuscript. GH was a participant in IIASAs Young Scientist Summer Program and was awarded the Mikhalevich Scholarship in part for this research.
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