università di padova lasa – laboratorio di analisi dei sistemi ambientali 1 incofish, 14...
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INCOFISH, 14 September 2006
L. PalmeriUniversità di PadovaLASA – Laboratorio di Analisi dei Sistemi Ambientali
1
Metabolic scaling relations in marine ecosystems trophic networks
Luca Palmeri
Yuri Artioli
Environmental System Analysis LabDepartment of Chemical Processes Engineering
UNIVERSITA’ DI PADOVA
ITALY
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INCOFISH, 14 September 2006
L. PalmeriUniversità di PadovaLASA – Laboratorio di Analisi dei Sistemi Ambientali
2
Quo vadis ecosystem ?
or
where are you going ecosystem ?
Bendoricchio and Palmeri, 2005Ecological Modelling 184: 5–17
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INCOFISH, 14 September 2006
L. PalmeriUniversità di PadovaLASA – Laboratorio di Analisi dei Sistemi Ambientali
3
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
Each indicator gives a different point of view on systems’ state. Goal Functions
are specific (or sectorial), not “global”.
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INCOFISH, 14 September 2006
L. PalmeriUniversità di PadovaLASA – Laboratorio di Analisi dei Sistemi Ambientali
4
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)
Jik flow originated in i and entering k
J32
1 3
2
J13
J31
J21
ki ikJJ,
Total flow (TST)
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INCOFISH, 14 September 2006
L. PalmeriUniversità di PadovaLASA – Laboratorio di Analisi dei Sistemi Ambientali
5
Trophic networks
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INCOFISH, 14 September 2006
L. PalmeriUniversità di PadovaLASA – Laboratorio di Analisi dei Sistemi Ambientali
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)
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INCOFISH, 14 September 2006
L. PalmeriUniversità di PadovaLASA – Laboratorio di Analisi dei Sistemi Ambientali
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)
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INCOFISH, 14 September 2006
L. PalmeriUniversità di PadovaLASA – Laboratorio di Analisi dei Sistemi Ambientali
8
A General Metabolic Growth Model (von Bertalanffy)
anabolism = metabolism - catabolism
hmkmdt
dmG
kmFmetabolism
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INCOFISH, 14 September 2006
L. PalmeriUniversità di PadovaLASA – Laboratorio di Analisi dei Sistemi Ambientali
9
Weight vs. metabolism
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INCOFISH, 14 September 2006
L. PalmeriUniversità di PadovaLASA – Laboratorio di Analisi dei Sistemi Ambientali
10
Weight vs. growth
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INCOFISH, 14 September 2006
L. PalmeriUniversità di PadovaLASA – Laboratorio di Analisi dei Sistemi Ambientali
11
Allometric Metabolic Scaling
Biomass (B)
Flow out, metabolism (F)
Theorem: Banavar et al. (2002)
for an optimal, balanced
and direct
D-dimensional network
BF
1
D
D
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INCOFISH, 14 September 2006
L. PalmeriUniversità di PadovaLASA – Laboratorio di Analisi dei Sistemi Ambientali
12
Supply-demand balance
Cost/Benefit Optimization Supply and Demand scale isometrically
Supply rate
Demand rate
2111
ssD
D
BF
0, 111 sBr s
0, 222 sBr s
1
2
1
D
D
r
rBF
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INCOFISH, 14 September 2006
L. PalmeriUniversità di PadovaLASA – Laboratorio di Analisi dei Sistemi Ambientali
13
Allometric Metabolic Scaling can be rewritten asBF
211
2
1 ssBr
rBF
For an optimal network in D dimensions, the Theorem by Banavar et al. (2002) states
1
2121
1
D
D
BFssrr
D
D
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INCOFISH, 14 September 2006
L. PalmeriUniversità di PadovaLASA – Laboratorio di Analisi dei Sistemi Ambientali
14
Supply-demand balance
If D = 3
If s1 = 0 from the theorem
If s1 = 0, supply rate independent of Biomass, ´= 2/3
If s1 s2 , less energy is supplied than required, 2/3<
´<3/4
Optimal condition: s1 = s2 , ´= 3/4
If s1 s2 , more energy is supplied than required, ´> 3/4
2143 1 ss
911
2 2 D
s
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INCOFISH, 14 September 2006
L. PalmeriUniversità di PadovaLASA – Laboratorio di Analisi dei Sistemi Ambientali
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
BF
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INCOFISH, 14 September 2006
L. PalmeriUniversità di PadovaLASA – Laboratorio di Analisi dei Sistemi Ambientali
16
Quo vadis ecosystem ?
One answer might be:
43
BF
• 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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INCOFISH, 14 September 2006
L. PalmeriUniversità di PadovaLASA – Laboratorio di Analisi dei Sistemi Ambientali
17
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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INCOFISH, 14 September 2006
L. PalmeriUniversità di PadovaLASA – Laboratorio di Analisi dei Sistemi Ambientali
18
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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INCOFISH, 14 September 2006
L. PalmeriUniversità di PadovaLASA – Laboratorio di Analisi dei Sistemi Ambientali
19
From the black book ofChristensen and Pauly (1993)
SDB indicator, calculated for 13 trophic networks:
values in the range 0.29 - 2.50
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INCOFISH, 14 September 2006
L. PalmeriUniversità di PadovaLASA – Laboratorio di Analisi dei Sistemi Ambientali
20
Caribbean coral reef trophic network(S. Opitz)
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INCOFISH, 14 September 2006
L. PalmeriUniversità di PadovaLASA – Laboratorio di Analisi dei Sistemi Ambientali
21
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INCOFISH, 14 September 2006
L. PalmeriUniversità di PadovaLASA – Laboratorio di Analisi dei Sistemi Ambientali
22
Lagoon of Venice SDB Indicator
N
January May August YearCa’ Roman 0,92 0,77 0,63 0,79Petta di Bo’ 0,91 0,76 0,67 0,83Sacca Sessola 0,81 0,77 0,66 0,91Fusina 0,80 0,85 0,77 0,94Palude della Rosa 0,89 0,73 0,61 0,88
F = 1,41m 0,88
0,001
0,01
0,1
1
10
100
1000
0,001 0,01 0,1 1 10 100 1000
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INCOFISH, 14 September 2006
L. PalmeriUniversità di PadovaLASA – Laboratorio di Analisi dei Sistemi Ambientali
23
Lagoon of Venice SDB Indicator
N
January May August YearCa’ Roman 0,92 0,77 0,63 0,79Petta di Bo’ 0,91 0,76 0,67 0,83Sacca Sessola 0,81 0,77 0,66 0,91Fusina 0,80 0,85 0,77 0,94Palude della Rosa 0,89 0,73 0,61 0,88
F = 2,53m 0,76
0,001
0,01
0,1
1
10
100
1000
10000
0,001 0,01 0,1 1 10 100 1000
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INCOFISH, 14 September 2006
L. PalmeriUniversità di PadovaLASA – Laboratorio di Analisi dei Sistemi Ambientali
24
Lagoon of Venice SDB Indicator
N
January May August YearCa’ Roman 0,92 0,77 0,63 0,79Petta di Bo’ 0,91 0,76 0,67 0,83Sacca Sessola 0,81 0,77 0,66 0,91Fusina 0,80 0,85 0,77 0,94Palude della Rosa 0,89 0,73 0,61 0,88
F = 2,98m 0,66
0,001
0,01
0,1
1
10
100
1000
0,001 0,01 0,1 1 10 100 1000
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INCOFISH, 14 September 2006
L. PalmeriUniversità di PadovaLASA – Laboratorio di Analisi dei Sistemi Ambientali
25
Lagoon of Venice SDB Indicator
N
January May August YearCa’ Roman 0,92 0,77 0,63 0,79Petta di Bo’ 0,91 0,76 0,67 0,83Sacca Sessola 0,81 0,77 0,66 0,91Fusina 0,80 0,85 0,77 0,94Palude della Rosa 0,89 0,73 0,61 0,88
F = 14,18m 0,86
0,001
0,01
0,1
1
10
100
1000
10000
0,001 0,01 0,1 1 10 100 1000
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INCOFISH, 14 September 2006
L. PalmeriUniversità di PadovaLASA – Laboratorio di Analisi dei Sistemi Ambientali
26
Lagoon of Venice SDB Indicator (annual)
N Petta di Bo’
Sacca sessola
Ca’ Roman
Fusina Palude della Rosa
y = 12,50x0,79
0,1
1
10
100
1000
10000
0,00 0,10 10,00 1000,00
y = 13,68x0,83
0,1
1
10
100
1000
10000
0,01 0,1 1 10 100 1000
y = 15,87x0,91
0,1
1
10
100
1000
10000
0,001 0,1 10 1000
y = 16,77x0,94
0,10
1,00
10,00
100,00
1000,00
10000,00
0,01 0,10 1,00 10,00 100,00 1000,00
c y = 13,43x0,88
0,01
0,10
1,00
10,00
100,00
1000,00
10000,00
0,001 0,100 10,000 1000,000
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INCOFISH, 14 September 2006
L. PalmeriUniversità di PadovaLASA – Laboratorio di Analisi dei Sistemi Ambientali
27
Lagoon of Venice SDB IndicatorCa’ Roman 0,63
August Petta di Bo’ 0,67 (decaying season) Sacca Sessola 0,66
Fusina 0,77Palude della Rosa 0,61Ca’ Roman 0,77
May Petta di Bo’ 0,76 (growing season) Sacca Sessola 0,77
Fusina 0,85Palude della Rosa 0,73Ca’ Roman 0,92
January Petta di Bo’ 0,91 (dormant season) Sacca Sessola 0,81
Fusina 0,80Palude della Rosa 0,89Ca’ Roman 0,79
Year Petta di Bo’ 0,83(averaged values over the year) Sacca Sessola 0,91
Fusina 0,94Palude della Rosa 0,88
From the Lagoon of Venice Ecosystems (ARTISTA study)
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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INCOFISH, 14 September 2006
L. PalmeriUniversità di PadovaLASA – Laboratorio di Analisi dei Sistemi Ambientali
28
Lagoon of Venice SDB IndicatorCa’ Roman 0,63
August Petta di Bo’ 0,67 (decaying season) Sacca Sessola 0,66
Fusina 0,77Palude della Rosa 0,61Ca’ Roman 0,77
May Petta di Bo’ 0,76 (growing season) Sacca Sessola 0,77
Fusina 0,85Palude della Rosa 0,73Ca’ Roman 0,92
January Petta di Bo’ 0,91 (dormant season) Sacca Sessola 0,81
Fusina 0,80Palude della Rosa 0,89Ca’ Roman 0,79
Year Petta di Bo’ 0,83(averaged values over the year) Sacca Sessola 0,91
Fusina 0,94Palude della Rosa 0,88
From the Lagoon of Venice Ecosystems (ARTISTA study)
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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INCOFISH, 14 September 2006
L. PalmeriUniversità di PadovaLASA – Laboratorio di Analisi dei Sistemi Ambientali
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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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L. PalmeriUniversità di PadovaLASA – Laboratorio di Analisi dei Sistemi Ambientali
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• 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: 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.” Nature 423: 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 Sciences 98(5): 2922-2927.
• West, G. B., J. H. Brown, et al. (2001). “A general model for ontogenic growth.” Nature 413: 628-631.