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Università di Padova LASA – Laboratorio di Analisi dei Sistemi Ambientali 1 INCOFISH, 14 September 2006 L. Palmeri Metabolic scaling relations in marine ecosystems trophic networks Luca Palmeri Yuri Artioli Environmental System Analysis Lab Department of Chemical Processes Engineering UNIVERSITA’ DI PADOVA ITALY

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Università di Padova LASA – Laboratorio di Analisi dei Sistemi Ambientali 2 INCOFISH, 14 September 2006 L. Palmeri Quo vadis ecosystem ? or where are you going ecosystem ? Bendoricchio and Palmeri, 2005 Ecological Modelling 184: 5–17

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Università di Padova LASA – Laboratorio di Analisi dei Sistemi Ambientali 3 INCOFISH, 14 September 2006 L. Palmeri Indicators and Goal Functions S(II nd TD law) Maximum entropy equilibrium W (Lotka) Maximum power energy dissipation p(Prigogine) Minimal entropy production linear regime Em(Odum) Maximum empower energy quality (solar) Ex(Jørgensen) Maximum Exergy distance from equilibrium AMI, NC e Asc (Ulanowicz) Propensity to maximal Ascendency network organization Emx(Bastianoni & Marchettini) Minimum Em/Ex cost/benefit Each indicator gives a different point of view on systems’ state. Goal Functions are specific (or sectorial), not “global”.

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Università di Padova LASA – Laboratorio di Analisi dei Sistemi Ambientali 4 INCOFISH, 14 September 2006 L. Palmeri Ecosystem description (Ecological State) Ecological Ecosystem Network analysis (flows and storages) State a measurable property System analysis Holistic indicators from general system properties (e.g. allometries) J ik flow originated in i and entering k J J 13 J 31 J 21 Total flow (TST)

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Università di Padova LASA – Laboratorio di Analisi dei Sistemi Ambientali 5 INCOFISH, 14 September 2006 L. Palmeri Trophic networks

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Università di Padova LASA – Laboratorio di Analisi dei Sistemi Ambientali 6 INCOFISH, 14 September 2006 L. Palmeri Ecosystem optimization Ecosystems try to optimize the flows and biomass Optimal networks show a balance between flows and biomass (lets say between costs and benefits)

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Università di Padova LASA – Laboratorio di Analisi dei Sistemi Ambientali 7 INCOFISH, 14 September 2006 L. Palmeri Network optimization COST: supply the energy Increase the quality of energy (higher trophic levels) Foster energy transport (network articulation) BENEFIT: respond to energy demand catabolism anabolism development OPTIMIZATION of Stored energy (Biomass) Supply/demand of resources (metabolites, energy flowing in the network)

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Università di Padova LASA – Laboratorio di Analisi dei Sistemi Ambientali 8 INCOFISH, 14 September 2006 L. Palmeri A General Metabolic Growth Model (von Bertalanffy) anabolism = metabolism - catabolism

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Università di Padova LASA – Laboratorio di Analisi dei Sistemi Ambientali 9 INCOFISH, 14 September 2006 L. Palmeri Weight vs. metabolism

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Università di Padova LASA – Laboratorio di Analisi dei Sistemi Ambientali 10 INCOFISH, 14 September 2006 L. Palmeri Weight vs. growth

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Università di Padova LASA – Laboratorio di Analisi dei Sistemi Ambientali 11 INCOFISH, 14 September 2006 L. Palmeri Allometric Metabolic Scaling Biomass (B) Flow out, metabolism (F) Theorem: Banavar et al. (2002) for an optimal, balanced and direct D-dimensional network

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Università di Padova LASA – Laboratorio di Analisi dei Sistemi Ambientali 12 INCOFISH, 14 September 2006 L. Palmeri Supply-demand balance Cost/Benefit Optimization Supply and Demand scale isometrically Supply rate Demand rate

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Università di Padova LASA – Laboratorio di Analisi dei Sistemi Ambientali 13 INCOFISH, 14 September 2006 L. Palmeri Allometric Metabolic Scaling can be rewritten as For an optimal network in D dimensions, the Theorem by Banavar et al. (2002) states

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Università di Padova LASA – Laboratorio di Analisi dei Sistemi Ambientali 14 INCOFISH, 14 September 2006 L. Palmeri Supply-demand balance If D = 3 If s 1 = 0 from the theorem If s 1 = 0, supply rate independent of Biomass, ´= 2/3 If s 1 s 2, less energy is supplied than required, 2/3< ´<3/4 Optimal condition: s 1 = s 2, ´= 3/4 If s 1 s 2, more energy is supplied than required, ´> 3/4

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Università di Padova LASA – Laboratorio di Analisi dei Sistemi Ambientali 15 INCOFISH, 14 September 2006 L. Palmeri as an Indicator of Trophic Network State For biological systems D=3 Generally: 2/3 For a system, with B-independent supply: = 2/3 undersupplied: < 3/4 in optimal condition: = 3/4 oversupplied: > 3/4

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Università di Padova LASA – Laboratorio di Analisi dei Sistemi Ambientali 16 INCOFISH, 14 September 2006 L. Palmeri Quo vadis ecosystem ? One answer might be: Unfortunately ecosystems are not always represented by direct networks they usually show feedbacks and matter recycling A network with ¾ scaling could not correspond to an optimum and stable state In that case the system could not employ overhead supply to compensate vulnerabilities to external pressures

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Università di Padova LASA – Laboratorio di Analisi dei Sistemi Ambientali 17 INCOFISH, 14 September 2006 L. Palmeri Quo vadis ecosystem ? According to the theoretical framework developed here, high values (greater than 0.75 or close to 1) indicate the subsistence of one or several of the following network characteristics: 1.high supply/demand ratio 2.highly undirected network 3.flows redundancies 4.enhanced recycling 5.greater system resilience to external perturbations 6.high costs of maintainance for the network

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Università di Padova LASA – Laboratorio di Analisi dei Sistemi Ambientali 18 INCOFISH, 14 September 2006 L. Palmeri Quo vadis ecosystem ? Coversely, low values (say equal to or less than 2/3) may indicate conditions spanning from ill-defined food web representation to undersupplied networks

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Università di Padova LASA – Laboratorio di Analisi dei Sistemi Ambientali 19 INCOFISH, 14 September 2006 L. Palmeri From the black book of Christensen and Pauly (1993) SDB indicator, calculated for 13 trophic networks: values in the range

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Università di Padova LASA – Laboratorio di Analisi dei Sistemi Ambientali 20 INCOFISH, 14 September 2006 L. Palmeri Caribbean coral reef trophic network (S. Opitz)

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Università di Padova LASA – Laboratorio di Analisi dei Sistemi Ambientali 21 INCOFISH, 14 September 2006 L. Palmeri

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Università di Padova LASA – Laboratorio di Analisi dei Sistemi Ambientali 22 INCOFISH, 14 September 2006 L. Palmeri Lagoon of Venice SDB Indicator N

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Università di Padova LASA – Laboratorio di Analisi dei Sistemi Ambientali 23 INCOFISH, 14 September 2006 L. Palmeri Lagoon of Venice SDB Indicator N

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Università di Padova LASA – Laboratorio di Analisi dei Sistemi Ambientali 24 INCOFISH, 14 September 2006 L. Palmeri Lagoon of Venice SDB Indicator N

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Università di Padova LASA – Laboratorio di Analisi dei Sistemi Ambientali 25 INCOFISH, 14 September 2006 L. Palmeri Lagoon of Venice SDB Indicator N

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Università di Padova LASA – Laboratorio di Analisi dei Sistemi Ambientali 26 INCOFISH, 14 September 2006 L. Palmeri Lagoon of Venice SDB Indicator ( annual) N Petta di Bo’ Sacca sessola Ca’ Roman Fusina Palude della Rosa

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Università di Padova LASA – Laboratorio di Analisi dei Sistemi Ambientali 27 INCOFISH, 14 September 2006 L. Palmeri Lagoon of Venice SDB Indicator SDB is SENSITIVE accounting for very little differences in the same type of shallow water ecosystems, in different seasons (Fusina is different !)

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Università di Padova LASA – Laboratorio di Analisi dei Sistemi Ambientali 28 INCOFISH, 14 September 2006 L. Palmeri Lagoon of Venice SDB Indicator SDB reflects DYNAMICS is able to follow the seasonal succession, i.e. all the networks (except Fusina !) present a similar pattern of variation, i.e.: 1.Oversupplied in January (pp dormant, … ready to burst) 2.Balanced during spring (G&D are at a maximum level) 3.Undersupplied in late summer (decaying season)

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Università di Padova LASA – Laboratorio di Analisi dei Sistemi Ambientali 29 INCOFISH, 14 September 2006 L. Palmeri Conclusions Relatively easy to apply to “arbitrarily large” real networks, without increasing computational demands increasing the number of free parameters Allometric principles provide limit intervals (thresholds) for the indicator values and very general convergence schemes N Lagoon of Venice SDB Indicator Generality, applicable to very different systems Sensitivity, distinguishes similar systems

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Università di Padova LASA – Laboratorio di Analisi dei Sistemi Ambientali 30 INCOFISH, 14 September 2006 L. Palmeri references Almaas, E., B. Kovàcs, et al. (2004). “Global organization of metabolic fluxes in the bacterium Escherichia coli.” Nature 427: Banavar, J. R., F. Colaiori, et al. (2001). “Scaling, Optimality, and Landscape Evolution.” Journal of Statistical Physics 104(1/2). Banavar, J. R., J. Damuth, et al. (2002). “Supply–demand balance and metabolic scaling.” Proceedings of the National Academy of Sciences 99(16). Banavar, J. R., A. Maritan, et al. (1999). “Size and form in efficient transportation networks.” Nature 399: Bendoricchio, G. and Palmeri, L. (2005) “Quo vadis ecosystem?” Ecological Modelling 184: 5–17. Garlaschelli, D., G. Caldarelli, et al. (2003). “Universal scaling relations in food webs.” Nature 423: Niklas, K. J. and B. J. Enquist (2001). “Invariant scaling relationships for interspecific plant biomass productrion rates and body size.” Proceedings of the National Academy of Sciences 98(5): West, G. B., J. H. Brown, et al. (2001). “A general model for ontogenic growth.” Nature 413:

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