Network trophic dynamics: the modes of energy utilization in ecosystems

Abstract The concept of progressive efficiency is generalized from food chains to food networks of arbitrary structure. Two distinct modes and corresponding pathways of contribution to energy-matter utilization are identified and formulated using continuous time models of energy-matter flows in ecosystems. First passage or root utilization involves first time transfer and transformation (of assimilated substance only) along all direct and indirect food paths originating at a defined source compartment and terminating at a defined destination compartment. First passage paths include acyclic paths plus cyclic paths that do not pass through the destination compartments. Recycling or reutilization involves the subsequent retransformation of previously utilized but not dissipated energy-matter by consumers. Recycling pathways start and end at the defined destination compartment. Total or ultimate utilization by destination compartments is the sum of first passage and recycling utilization. Two properties of ecosystems are demonstrated which depart from those of conventional trophic dynamics. Network virtual amplification is the increase of energy-matter ultimately utilized at destination compartments compared to the quantities originally introduced at source compartments. This is due largely to recycling; no energy is created, no thermodynamic law violated. Network homogenization is the tendency in food cycles for introduced energy-matter to become more or less evenly distributed to all compartments. These properties are illustrated with two models of ecosystem energy-matter flows.

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