Energy, Trophic Dynamics and Ecological Discounting.

Ecosystems provide humanity with a wide variety and high economic value-added services, from biomass structuring to genetic information, pollutants' decomposition, water purification and climate regulation. The foundation of ecosystem services is the Eltonian Pyramid, where via prey–predator relationships, energy metabolism and biomass building take place. In the context of existing ecosystem services classification and valuation methods (e.g., CICES, MEA, TEEB), financial investments in ecosystem services essentially address the conservation of trophic pyramids. Our work's main target is to investigate how trophic pyramids' dynamics (stability or instability) impact the long-run discounting of financial investments on ecosystem services' value. Specifically, a trophic pyramid with highly fluctuating populations generates higher risks for the production of ecosystem services, hence for ecological finance instruments coupled to them, due to higher temporal uncertainty or information entropy that should be incorporated into their discount rates. As this uncertainty affects negatively the net present value (NPV) of financial capital on ecosystem services, we argue that the minimization of biomass fluctuations in trophic pyramids via population control should be among the priorities of ecosystem management practices. To substantiate our hypothesis, we construct a logistic predation model, which is consistent with the Eltonian Pyramid's ecological energetics. As the logistic predator model's parameters determine the tropic pyramid's dynamics and uncertainty, we develop an adjusted Shannon entropy index (H(N)_ADJ) to measure this effect as part of the discount rate. Indicatively, we perform a Monte Carlo simulation of a pyramid with intrinsic growth parameter values that yield oscillating population sizes. Finally, we discuss, from an ecological energetics standpoint, issues of competition and diversity in trophic pyramids, as special dimensions and extensions of our analytical framework. [ABSTRACT FROM AUTHOR]