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Metabolic scaling relations in marine ecosystems trophic networks

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. Quo vadis ecosystem ?. or where are you going ecosystem ?

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Metabolic scaling relations in marine ecosystems trophic networks

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  1. 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 L. Palmeri

  2. Quo vadis ecosystem ? or where are you going ecosystem ? Bendoricchio and Palmeri, 2005 Ecological Modelling184: 5–17 L. Palmeri

  3. Each indicator gives a different point of view on systems’ state. Goal Functions are specific (or sectorial), not “global”. Indicators and Goal Functions S (IInd 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 L. Palmeri

  4. Total flow (TST) J13 1 3 J31 J21 2 J32 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) Jikflow originated in i and entering k L. Palmeri

  5. Trophic networks L. Palmeri

  6. 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) L. Palmeri

  7. 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) L. Palmeri

  8. A General Metabolic Growth Model (von Bertalanffy) anabolism = metabolism - catabolism  L. Palmeri

  9. Weight vs. metabolism L. Palmeri

  10. Weight vs. growth L. Palmeri

  11. Allometric Metabolic Scaling • Biomass (B) • Flow out, metabolism (F) • Theorem: Banavar et al. (2002) for an optimal, balanced and direct D-dimensional network L. Palmeri

  12. Supply-demand balance • Cost/BenefitOptimization  Supply and Demand scale isometrically  Supply rate  Demand rate L. Palmeri

  13. Allometric Metabolic Scaling • can be rewritten as • For an optimal network in D dimensions, the Theorem by Banavar et al. (2002) states L. Palmeri

  14. If D = 3  If s1 = 0 from the theorem • If s1 = 0, supply rate independent of Biomass, ´= 2/3 • Ifs1 s2 , less energy is supplied than required, 2/3< ´<3/4 • Optimal condition: s1 = s2 , ´= 3/4 • Ifs1  s2 , more energy is supplied than required, ´> 3/4 Supply-demand balance L. Palmeri

  15. 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 L. Palmeri

  16. 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 L. Palmeri

  17. Quo vadis ecosystem ? According to the theoretical framework developed here, high a values (greater than 0.75 or close to 1) indicate the subsistence of one or several of the following network characteristics: • high supply/demand ratio • highly undirected network • flows redundancies • enhanced recycling • greater system resilience to external perturbations • high costs of maintainance for the network L. Palmeri

  18. Quo vadis ecosystem ? Coversely, low a values (say equal to or less than 2/3) may indicate conditions spanning from ill-defined food web representation to undersupplied networks L. Palmeri

  19. From the black book ofChristensen and Pauly (1993) SDB indicator, calculated for 13 trophic networks: a values in the range 0.29 - 2.50 L. Palmeri

  20. Caribbean coral reef trophic network(S. Opitz) L. Palmeri

  21. L. Palmeri

  22. N Lagoon of VeniceSDB Indicator L. Palmeri

  23. N Lagoon of VeniceSDB Indicator L. Palmeri

  24. N Lagoon of VeniceSDB Indicator L. Palmeri

  25. N Lagoon of VeniceSDB Indicator L. Palmeri

  26. N Lagoon of Venice SDB Indicator (annual) Fusina Sacca sessola Palude della Rosa Petta di Bo’ Ca’ Roman L. Palmeri

  27. 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 !) L. Palmeri

  28. Lagoon of Venice SDB Indicator • SDB reflects DYNAMICS • isable to follow the seasonal succession, i.e. all the networks (except Fusina !) present a similar pattern of variation, i.e.: • Oversupplied in January (pp dormant, … ready to burst) • Balanced during spring (G&D are at a maximum level) • Undersupplied in late summer (decaying season) L. Palmeri

  29. Lagoon of Venice SDB Indicator N 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 • Generality, applicable to very different systems • Sensitivity, distinguishes similar systems L. Palmeri

  30. references • Almaas, E., B. Kovàcs, et al. (2004). “Global organization of metabolic fluxes in the bacterium Escherichia coli.” Nature427: 839-843. • Banavar, J. R., F. Colaiori, et al. (2001). “Scaling, Optimality, and Landscape Evolution.” Journal of Statistical Physics104(1/2). • Banavar, J. R., J. Damuth, et al. (2002). “Supply–demand balance and metabolic scaling.” Proceedings of the National Academy of Sciences99(16). • Banavar, J. R., A. Maritan, et al. (1999). “Size and form in efficient transportation networks.” Nature399: 130-132. • 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.” Nature423: 165-168. • 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 Sciences98(5): 2922-2927. • West, G. B., J. H. Brown, et al. (2001). “A general model for ontogenic growth.” Nature413: 628-631. L. Palmeri

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