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      Indirect Energy Flows in Niche Model Food Webs: Effects of Size and Connectance

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      PLoS ONE

      Public Library of Science

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          Indirect interactions between species have long been of interest to ecologists. One such interaction type takes place when energy or materials flow via one or more intermediate species between two species with a direct predator-prey relationship. Previous work has shown that, although each such flow is small, their great number makes them important in ecosystems. A new network analysis method, dynamic environ approximation, was used to quantify the fraction of energy flowing from prey to predator over paths of length greater than 1 (flow indirectness or FI) in a commonly studied food web model. Web structure was created using the niche model and dynamics followed the Yodzis-Innes model. The effect of food web size (10 to 40 species) and connectance (0.1 to 0.48) on FI was examined. For each of 250 model realizations run for each pair of size and connectance values, the FI of every predator-prey interaction in the model was computed and then averaged over the whole network. A classification and regression tree (CART) analysis was then used to find the best predictors of FI. The mean FI of the model food webs is 0.092, with a standard deviation of 0.0279. It tends to increase with system size but peaks at intermediate connectance levels. Of 27 potential predictor variables, only five (mean path length, dominant eigenvalue of the adjacency matrix, connectance, mean trophic level and fraction of species belonging to intermediate trophic levels) were selected by the CART algorithm as best accounting for variation in the data; mean path length and the dominant eigenvalue of the adjacency matrix were dominant.

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              Allometric scaling relations, including the 3/4 power law for metabolic rates, are characteristic of all organisms and are here derived from a general model that describes how essential materials are transported through space-filling fractal networks of branching tubes. The model assumes that the energy dissipated is minimized and that the terminal tubes do not vary with body size. It provides a complete analysis of scaling relations for mammalian circulatory systems that are in agreement with data. More generally, the model predicts structural and functional properties of vertebrate cardiovascular and respiratory systems, plant vascular systems, insect tracheal tubes, and other distribution networks.

                Author and article information

                Role: Editor
                PLoS One
                PLoS ONE
                PLoS ONE
                Public Library of Science (San Francisco, CA USA )
                5 October 2015
                : 10
                : 10
                [1 ]Division of Life Sciences, UCLA, Los Angeles, CA, United States of America
                [2 ]Tulane-Xavier Center for Bioenvironmental Research, Tulane University, New Orleans, LA, United States of America
                Vrije Universiteit, NETHERLANDS
                Author notes

                Competing Interests: The authors have declared that no competing interests exist.

                Conceived and designed the experiments: JS. Performed the experiments: JS. Analyzed the data: JS. Wrote the paper: JS RR. Wrote the simulation code: RR JS.


                This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

                Figures: 5, Tables: 2, Pages: 14
                The authors have no support or funding to report.
                Research Article



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