trophic state indicators from thermodynamics and information … · lasa – laboratorio di analisi...
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Trophic state indicators from
Thermodynamics and Information Theory
Luca Palmeri
Environmental System Analysis Lab
Department of Chemical Processes Engineering
UNIVERSITA’ DI PADOVA
ITALY
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Quo vadis ecosystem ?an overview
• The perspective and the properties
• Definitions: Thermodynamics and Information
Theory
• Calculations
• Application: The Lagoon of Venice food web
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The thermodynamic perspective
� Open systems
� Far from equilibrium
� Dissipative systems
� Locally ordered (information)
� Energy transformation (quantity � quality)
� Growth
� increased biomass
� greater flows
� Development
� Structural change
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Ecosystem indicators
� In steady state a measure or indicator may be defined:
� mathematical properties: continuity, additivity, monotonicity (MAT);
� indicator has to be null at the thermodynamic equilibrium (EQ
0);
� indicator is a physical directly or indirectly observable quantity, defined on the basis of elementary (physical) quantities, it cannot be a characteristic of the sole living systems (OBS ).
� Is a measure of the complexity of the system
� indicator has to be null for maximally ordered and maximally disordered systems (Jørgensen et al., 1992) (NUL);
� indicator cannot be classically extensive (additive) in mass or volume but it has to be (globally) extensive in the processes (Lloyd e Pagels, 1988) (EXP );
� indicator must keep memory of the evolution of the system (Odum, 1988) (MEM).
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Ecosystem indicators
� Because it is a measure of organization:
� indicator has to account for the information transferred with the energy flows (quanta or bit), (Ulanowicz, 1986) (INF);
� indicator must bring to light the intensive characteristic of the network dealing with the structure and not with the actual flows or biomass (NET).
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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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Popular indicators of ecosystem state
� Intensive (information):
AMI - Average Mutual Information
NC - Network capacity
� Extensive (energy, thermodynamic):
EM - Emergy
EX - Exergy
TST - Total System Throughput
ASC - Ascendency
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Thermodynamic potentials
�Classical thermodynamics, the following potentials are defined
� Hentalpy
� Helmoltz free energy
� Gibbs free energy
H �S , p , ni�=U�pV
F �T ,V ,ni�=U�TS
G�T , p ,ni�=U�pV�TS
� Ecosistems (p=cost e V=cost), hentalpy H
� The most appropriate is chosen on the basis of
� imposed constraints
� independent variables considered
(type of transformation)
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Maximum power
� Lotka (1925)
� Energetic approach to ecosystem study
� Power P=X·J
X thermodynamic potential
J material flow
Living systems evolve and react to constraints (e.g. solar light,
temperture, etc.) following the objective of power maximization
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Emergetic analysis
� H.T Odum (1983), energy quality
� hierarchy in energy transformation chains
� energy originated at different hierarchical livels are not
directly comparable
� Transformity Tr, a quality factor for the energy
Quantity of energy of a given type required to
obtain one unit energy of another type
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Emergetic analysis
� Energy transformation chains
� energetic formalism
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Transformity
� Transformity rappresents the quality of energy
� more energy of lower quality to generate
one unit energy of a higher quality
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Emergy
� Allows to compare different types of energy
� J of solar energy to obtain a product
� Em is an expression for “cost”
� Tr is analogous to information [seJ / J] �� [bit]
Em=�i
Tri�E
i[ seJ ]
[Tri ] = [ seJ
J ]Ei = free energy
� Solar transformity, Trs = 1
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Maximum empower principle
� Is a generalization of Lotka’s principle
� Ecosystems maximize energy flows
� Is a compromise between maximal dissipation and
maximal efficiency
Ecosystems evolve along the objective of maximizing empower
at every hierarchical level, i.e. maximizing the transformation
rate of available energy into useful energy
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Emergy calculus
k-th process
Ek
E2·Tr2
E1·Tr1
En·Trn
.
.
.
. Emk=�
i=1
n
Ei�Tr
i
1. Different co-products of a given process possess the same emergy (the total
emergy required for maintaining the father process)
• If a flow of emergy is split, the emergy assigned to each branch is
proportional to the quantity of energy flowing through it.
• The only flows to be considered in emergy calculus for a compartment are
those originated by independents inputs ( feedbacks )
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Emergy calculus
Tr=1
Tr=10
I IIS
1
S
2
I IIS
1
S
2
100
5
90
15
20
10
20
100 100+(200x1/3)
100=(200+100)x1/3
200
200=300x2/3
ENERGY
EMERGY
EmI = 100 + 200 · 1/3 166
EI = 15
TrI 11
EmII = 15 · TrI +20 · TrS2 366
EII = 15
TrII 24
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Exergy
� Ex is a thermodynamic quantity
� distance from equilibrium, energy dissipation
� Evans definition (1965)Ex=T
0�I
I=S0�S=U�p0V�T 0 S��i
µi
0n
i
T 0
� From Gibbs potential
� is a measure of the work ideally obtainable by a system in its
drift toward the thermodynamic equilibrium
� Exergy is not a state function (i.e. an exact differential)
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Exergy
� Energy si conserved
� Energetic cycles are practically balanced
� Exergy variations allow to compare different flows
� Energy, Information and the IInd principle
� Information manipulation requires energy (Exergy)
� This energy is dissipated in order to sustain informational flows
(the constraints)
� Exergy is conserved only in reversible processes
� In natural processes exergy is dissipated
and a net entropy production occurs
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Definition and Measure of
Information
� Shannon’s (1948)
� difference between uncertainty before and after the observation
I=S �Q�X ��S �Q�X ' �
S �Q�X �=�K�i
Piln P
i
� uncertainty on the question Q having the “a priori” knowledge X
� Equivalent to statistical Entropy (Boltzmann order principle)
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Knowledge and Information
� Shannon information
� causes a variation of the probability distribution P
� measures the variation of the uncertainty on Q
� To know
� identify a probability distribution P
� The merit of a channel
� does not depend on how is transmitted a given message
but on how would be transmitted all the others msgs
� The value of information stand in the
� variation of knowledge
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Why the logarithm ?
� Mathematical requirements:
� positive
� increasing
� additive
S �Q�X �=�K�i
Piln P
i
P0=P1�P2
ln P0=ln P1�ln P2
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Uncertainty and entropy
� Distinguishable from the environment � not in equilibrium
� INFORMATION
with S0 entropy of the system at the thermodynamic equilibrium
(for ecological systems Reference State, Shien e Fan 1982)
I=S0�S
� Shannon’s uncertainty
� the definition is based on simple logical criteria
� Thermodynamic entropy Shannon’s uncertainty
� Brillouin (1962) on the basis of mathematical considerations
� the difference is not substaintial, instead is related to the scale
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Units of information
� Defined by the constant K
� The bit, (binary digit)
n possible binary choices (0 or 1)
P=2n total number of possibilities
K=1
ln 2=log
2e=1 bit
� Relation between bit and Joule
N number of elements
kB =1.4 10-23 J/°K Boltzmann’s constantK=NkB
[1 bit ]=1
NkB
ln 2 [ J
° K ]
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� Consider 1 mole (Na=6,02·1023) formed by 2 isotopes in separate phases
of some chemical species
By complete mixing the enropy S becomes
� ~ 6 J/°K or ~ 6 ·1023 bits
� or the number of choices required in order to separate the two
species, starting from an uniform mixing
[1 bit ]=1
NkB
ln 2 [ J
° K ]
Units of information
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Energy and Information
� Energetic balance of the earth
� approximately null (steady state)
� entropy production p 0
Annual information flow: ~ 3,2·1022 J/°K ~ 1038 bits
� maximal limit for information processing
� it is sufficient to guarantee the functioning of
the biosphere
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Energy and Information
� Given a quantity of transmitted information, the energy requirements
(exergy) grows linearly with T
Ex=T0�I
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Exergy
� Energetic type measure
� for complex systems is easier to compute than entropy
� from the informational point of view => signal intensity
� Goal function
� Schneider e Kay (1994)
If a system is brought away from equilibrium (exergy flow) it will
use all the available means to cancel the imposed gradient, i.e. to
dissipate more exergy
� Jørgensen (1997)
Ecosystems maximize exergy dissipation
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Exergy calculus
� Mejer e Jørgensen (1979)
� System represented by N components
� Input of inorganic matter
� Output of inactive organic matter (detritus)
Ex=R�T �
i=0
N
[ci�ln � c
i
ci
eq ���ci�c
i
eq �]c0 concentration of inorganic matter
c1 concentration of dead organic matter
ci concentration of the i-th element
cieq
concentration at the equilibrium of i-th element
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Exergy calculus
� Approximate calculation
� difficult estimation of concentrations cieq
Pi=
cieq
�i=0
Nc
ieq
Pi�
cieq
c0
eq� Inorganic matter prevails
� For dead organic matter (proteins, fats, ...)
c1
c1
eq=e
µ1�µ
1eq
RTP1¿
c1
c0
eqe�
µ1�µ
1eq
RT
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Exergy calculus
� Biotic phase (i=2,...,N)
� probabilities depend on P1 and on the probability of
genetic nature Pi,� ,(� genes)
Pi=P1�P i ,� �2�i�N �
� 20 aminoacids
1 gene = sequence of ~700 aminoacids
Pi ,�=1
20700�
1
20700��
1
20700
��
=20�700�
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Exergy calculus
� Sequencial approximations
Ex
RT��ln � c
1
c0
eq ��i=1
N
c i�� µ1�µ
1
eq
RT ��i=1
N
ci��i=2
N
ci�ln Pi ,�
� Affect only exergy differences, given the same
chemical&physical conditions
Ex
RT�� µ 1�µ 1
eq
RT ��i=1
N
ci��
i=2
N
ci�ln P
i ,�
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Exergy calculus
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Exergy
quality
factors
AFTER
S.E. Jørgensen et al. / Ecological
Modelling 185 (2005) 165–175
Exponential increase
with evolution
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Exergy calculus
� Example of calculation
�Acquatic ecosystem model
COMPARTMENT N. GENES EXERGY FACTOR
Detrito (18 kJ/mole) - 7,42 ·105
Fitoplankton 850 17,8 ·105
Zooplankton 50000 1049 ·105
Pesce 120000 2516 ·105
Ex
RT�7, 34�10
5�c1�c
phyt�c
zoo�c
f��
17 ,8�105c
phyt�1049�10
5c
zoo�2516�10
5c
f
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� Entropy in statistical mechanics (t.dyn equilibrium)
� Maxwell-Boltzmann
� Boltzmann H Theorem
at the equilibrium
fo(v) is a minimum for H
Entropy
Exergy and stochastic processes
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Exergy and stochastic processes
� Generalized entropy (non-equilibrium systems)
� Linear states [Onsager (1931) and Prigogine (1967)]
Entropy production
(IInd principle of t.dyn)
Equilibrium � p=0
� Generalization: Master Equation
Steady states:
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� Generalized entropy (far from equilibrium systems)
�
Exergy and stochastic processes
� GENERALIZED ENTROPY (Van Kampen, 1981)
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Exergy and stochastic processes
GENERALIZED EXERGY � Ex = Ta·�S
� Generalized entropy (far from equilibrium systems)
�
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Emergy/Exergy
� BENEFIT: Exergy
� distance from equilibrium
� COST: Emergy
� solar energy required for a given product
� Bastianoni e Marchettini, 1997
� Emergy/Exergy (Emx)
Greater values of Emx imply less system efficiency
in maintaining the omeostasis
Goal: minimal Emx
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� General model applicable to all the transformation
phenomena occurring in nature
Food webs
Trophic networks
Goods supply
River networks
…..
A network of flows
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A network of flows
� Jik flow originated from i, entering in k
J32
13
2
J13
J31
J21
� Probabilities
J=�i , kJ
ik
Total flow
Pi , k
=J
ik
J
composed
Pi�k=
Jik
�q
Jiq
conditional
Pk
¿=�i
Jik
J
a priori in k
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Average mutual information
� Mutual information exchanged on the average
between network compartments
� Pk* a priori probability that one unit enters in k
� Pk|i conditional probability the emission coming from i
I i�k=S k�i�Sk=K ln Pk�i�K ln Pk¿=K ln
Pk�i
Pk
¿
� Weighting information with composed probability
Pi,k (emission/immission)
AMI=K�i , k
Pi , k
Ii�k
=K�i , k
Pi , k
lnP
k�i
Pk
¿
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� AMI
� Network Capacity
Average mutual information
Everything is connected with everything by equal flows
then
If all compartments are connected in chain by equal flows, then
If all compartments are connected in chain by arbitrary flows,
then
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The domain of AMI
O
A
B
CA
AM
I
NC 2log2N
2log2N
log2N
O
A
BC
D
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Ascendency
� AMI is a characteristic of the network
� circulation of information
� auto-organization
� is an intensive quantity
� Ulanowicz (1986)
Ascendency, Asc=TST·AMI
� measures the activities of growth and development
� is an extensive quantity
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Ascendency
� Ulanowicz e Abarca-Arenas (1997)
Ecosistems pursue the goal (demonstrate a
“propensity”) toward increasing ascendency
� Limiting factors for Asc
� totale throughput TST
� number of compartments
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Popular indicators of ecosystem state� Intensive:
AMI
AMI = NC - Overhead
� Extensive:
EM
EX
ASC
=K�i ,k
Pi , k
Ii� k
=K�i , k
Pi , k
lnP
k�i
Pk
¿[ bit ]
=�i=1
N
Tri�f
i[ J/m2/month ]
=�i=1
N
�i�c
i[ J/m2 ]
= TST · AMI [ bit J/m2/month ]
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Observed correlations
weak correlation
strong correlation
correlation = covariance/(std.dev1•std.dev2)
.
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Correlations
NC EM EX TST ASC
AMI + + - + ++
NC - - - -
EM +++ +++ +++
EX +++ ++
TST +++
� AS C is correlated to TS T and AMI
� EM and EX are correlated to TST (ASC)
� AMI and NC are not correlated to EM, EX e TST
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Benefit/Cost Indicator
� Intensive part: INFORMATION
Development, network articulation
AMI = Benefit NC = Cost
� Extensive part: ENERGY
Growth, catabolism
EX = BenefitEM = Cost
BC = kEX
EM
AMI
NC
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Benefit/Cost Indicator
� Is a measure of production levels and trophic activity
� Variations are more interesting than absolute values
� Generally:
high values of BC � stressed system
positive variations � increased activity
growth and/or development
seasonal variations reflect the dynamic of the
ecological state
BC = kEX
EM
AMI
NC
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Properties of selected indicators
BC = kEX
EM
AMI
NC
MEASURE COMPLEXITY ORGANIZZAT.
Properties: MAT EQo OBS NUL EXP MEM INF NET
Ex � � � � �
Em � � � � �
Ex/Em � � � � � �
AMI � � � � �
NC � � � � �
Asc � � � � �
BC � � � � � � � �
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Observed correlations
weak correlation
strong correlation
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Ecosystem description (Ecological State)
� Ecological � Ecosystem
Network analysis
(flows and storages)
� State � a measurable property
System analysis
Holistic indicators from Thermodynamic and/or Information theory
� Jik flow originated in i and entering k
J32
13
2
J13
J31
J21
J=�i , kJ
ik
Total flow (TST)
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Trophic networks
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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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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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A General Metabolic Growth Model
(von Bertalanffy)
� anabolism = metabolism - catabolism
G=dm
dt=km
��hm�
� Special case with �=1
G=dm
dt=km
��hm
�=0 . 90
�=3
4
�=2
3
�=1
2
�=1
4
G
m
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0 0.2 0.4 0.6 0.8 1
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Weight vs. metabolism
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Allometric Metabolic Scaling
� Biomass (B)
� Flow out, metabolism (F)
� Theorem: Banavar et al. (2002)
for an optimal, balanced
and direct
D-dimensional network
F�B�
�=D
D�1
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Supply-demand balance
� Cost/Benefit Optimization � Supply and Demand scale isometrically
� Supply rate
� Demand rate
F�B[ D
D�1 �1�s1�s
2 �]
r1�B
s1 , s1¿0
r2�B
s2 , s 2¿ 0
F��B r1
r2�
D
D�1
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Allometric Metabolic Scaling� can be rewritten asF�B�
F��Br
1
r2��
=B[��1�s
1�s
2 � ]
� For an optimal network in D dimensions, the Theorem by Banavar et al. (2002) states
�=D
D�1
r1=r
2� s
1=s
2
¿ }¿
¿�F�B
D
D�1 ¿
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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
�'=3
4�1�s
1�s
2 �
s2=
1
D2=
1
9
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� 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
F�B�
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Quo vadis ecosystem ?
The answer:
F�B
3
4
• 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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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:
• high supply/demand ratio
• highly undirected network
• flows redundancies
• enhanced recycling
• greater system resilience to external perturbations
• high costs of maintainance for the network
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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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Food web models
TROPHIC NETWORK: network of exchange of resources between
the elements (biotic and abiotic) of an ecosystem
• Organisms that feed on the same element of the trophic chain are located at the same trophic level
TROPHIC LEVEL:
To each functional group is assigned a fractionary trophic level to determine its position in the trophic web on the basis of the quantitative composition of diet.
� A trophic level 1 is assigned to primary producers and detritus
� For consumers TL=1+ weighted average of trophic levels of preys;
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Food web models
Production + import = predation + yeld + other mortality + migration + biomass increase
� Assumption � Mass balance for the whole web
consumption = predation + non-assimilated food + respiration
� Assumption � Energy balance for each compartment
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Food web models
�Consumption is calculated from apical predators,
hence descending from higher to lower levels of
the trophic web (top-down control).
�The quantity of matter/energy consumed by each
predator, together with diet composition,
determine the quota predated from the lower TL
Detritus = other mortality + non assimilated food
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ECOPATH(Christensen & Pauly 1992)
http://www.ecopath.org
For each compartment:
• Biomass (B)
• Productivity (P) or mortality
• Diet composition and consumptions (Dij)
• Efficiency in the use of resources (EE)
ECOPATH provides the tools for network balancing
and for the analysis of the results
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ECOPATH: BASE INFO
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ECOPATH: DIETS
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ECOPATH: BALANCED NETWORK
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ECOPATH: CONSUMPTIONS
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y = 41,86x0,78
10
100
1000
10000
100000
1 10 100 1000 10000
A Quantitative Model of the Trophic Interactions
in a Caribbean Coral Reef Ecosystem
S. OPITZBiomass fout1 fout2 fout3 fout4 fout5 fout6 fout7 fout8 fout9 fout10 FOUT
Compart g/m2 g/m2/year g/m2/year g/m2/year g/m2/year g/m2/year g/m2/year g/m2/year g/m2/year g/m2/year g/m2/year g/m2/year
Detritus 2000,00 256,80 123,60 7749,00 0,10 1279,30 200,60 24,50 12,90 157,20 9804,00
Benthic autotorophs 1375,00 12839,50 2065,70 27,70 3,80 47,60 240,00 1329,60 370,00 0,10 1294,80 18218,80
Sessile animals 1000,00 177,60 11,40 6,40 472,80 38,30 3,60 0,10 42,00 0,10 8247,70 9000,00
Echinoderms 600,00 0,40 0,01 156,00 824,70 5,50 6,00 65,70 0,10 1200,00 141,60 2400,01
Miscellaneous molluscs/worms 430,00 195,70 1333,00 28,20 672,20 39,30 1,30 49,80 180,70 0,70 509,21 3010,11
Crustaceans 120,00 48,00 0,03 7,20 269,60 3,70 1,60 38,30 0,80 7,20 813,40 1189,83
Large herb. Reef fish 100,00 1719,00 459,10 0,60 7,40 0,90 5,30 49,30 38,40 2280,00
Large carniv. Reef fish 75,00 390,00 4,50 4,90 6,00 0,90 0,80 0,90 112,10 43,80 563,90
Decomposers/microfauna 60,00 3960,00 52,80 171,00 511,70 60,00 1,20 3823,30 4320,00 12900,00
Zooplankton 30,00 261,00 7,20 1,50 1917,40 0,80 65,70 20,50 84,00 18,10 225,00 2601,20
Small schooling fish 30,00 2,40 8,30 10,20 123,90 0,40 0,40 16,40 6,00 0,30 433,30 601,60
Phytoplankton 25,00 99,00 252,80 1,20 990,00 6,00 7,20 393,80 1750,00
Large schooling fish 20,00 0,50 2,70 55,30 0,40 0,50 2,20 6,10 186,60 254,30
Small herb. Reef fish 10,00 2,10 0,10 8,70 4,40 1,20 76,70 281,40 374,60
Small omnivorus reef fish 10,00 1,90 27,70 0,40 3,10 5,50 0,50 0,10 2,40 86,40 128,00
Cephalopods 8,00 0,80 2,40 5,50 0,10 24,40 50,10 10,30 93,60
Scombirds/jacks/sharks 4,40 29,20 8,90 0,10 0,10 0,60 0,30 39,20
Large groupers 4,00 5,90 3,20 0,20 9,30
Large sharks/rays 1,00 0,10 1,10 0,10 3,70 5,00
Sea turtles 0,10 0,20 0,10 0,30
Sea birds 0,01 0,30 0,90 1,20
F
B
• The network has been very carefully
balanced
• Coral reef is a mature system with a
quite direct network (neglecting
higher TLs)
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The SDB exponent (�) for several marine ecosystems
From the book of Christensen, V., and Pauly, D. (1993). “Trophic models of aquatic ecosystems.”
Author Title SDB
1A.A. VAN DAM, F.J.K.T. CHIKAFUMBWA, D.M.
JAMU, B.A. COSTA-PIERCE
Trophic Interactions in a Napier Grass (Pennisetum purpureum)-
fed Aquaculture Pond in Mala? i0,29
2 C.M. ARAVINDAN Preliminary Trophic Model of Veli Lake, Southern India 0,74
3 S. OPITZA Quantitative Model of the Trophic Interactions in a Caribbean
Coral Reef Ecosystem 0,78
4E.A. CHAVEZ, M. GARDUNO, ARREGUIN-
SANCHEZ
Trophic Dynamic Structure of Celestun Lagoon, Southern Gulf of
Mexico 0,82
5D. PAULY, M.L. SORIANO-BARTZ, M.L.D.
PALOMARES
Improved Construction, Parametrization and Interpretation of
Steady-State Ecosystem Model 1,05
6 J. MOREAU, V. CHRISTENSEN, D. PAULY A Trophic Ecosystem Model of Lake Georgia, Uganda 1,05
7M.E. VEGA-CENDEJAS, F. ARREGUIN-SANCHEZ,
M. HERNANDEZTrophic Fluxes on the Vampeche Bank, Mexico 1,08
8 M.R. DELOS REYESFishpen Culture and Its Impact on the Ecosystem of Laguna de
Bay, Philippines (pre Fish pen)1,10
9F. ARREGUIN-SANCHEZ, J.C. SEIJO, E. VALERO-
PACHECO
An Application of ECOPATH II to the North Continental Shelf
Ecosystem of Yucatan, Mexico 1,19
10F. ARREGUIN-SANCHEZ, E. VALERO-PACHECO,
E.A. CHAVEZ
A Trophic Box Model of the Coastal Fish Communities of the
Southwestern Gulf of Mexico 1,24
11 M.R. DELOS REYESFishpen Culture and Its Impact on the Ecosystem of Laguna de
Bay, Philippines (Fish pen period)1,35
12P.D. WALLINE, P. PISANTY, M. GOPHEN, T.
BERMANThe Ecosystem of Lake Kinneret, Israel 1,63
13 P. DEGNBOL The Pelagic Zone of Central Lake Mala? i – A Trophic Box Model 2,50
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The Lagoon of Venice
20 DATASETS:
3 sampling campaigns (Jan, May, Aug / 2001)
in 5 shallow water sampling sites
+ 5 mean annual elaborations
(different temporal scale)
N
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Compartments in the LV food web
1. Pesci carnivori
2. Gobius ophiocephalus
3. Pesci onnivori
4. Liza sp. (cefali)
5. Carcinus mediterraneus
6. Macrobenthos predatore
7. Tapes philippinarum
8. Macrobenthos susp. feeder
9. Macrobenthos detritivor., erbivoro
10. Policheti
11. Micro+mesobenthos
12. Meso+macrozooplancton
13. Microzooplancton
14. Fitoplancton
15. Epifiti
16. Fanerogame
17. Microalghe bentiche
18. Macroalghe
19. Detrito planctonico
20. Detrito bentonico
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Lagoon of Venice trophic network
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AMI & NC
N
� all below 50%
� large N (articulated networks)
� limited n. of preferential pathways
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AMI/NC� Northern stations
� simple networks
� younger systems (develpment)
� Opportunistic species prevail
N
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AMI/NC� Southern stations
� complex networks (high NC)
� older systems (growth)
� stable
N
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EX & EM
N
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EX/EM� Northern stations
� instable
� low production efficiency
� high TST
N
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EX/EM� Southern stations
� stable
� More efficient, less optimized, higher diversity
N
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BC = k
� Extensive � growth
N
EX
EM
AMI
NC
0
100
200
300
400
500
600
700
Jan May Aug Jan May Aug Jan May Aug Jan May Aug Jan May Aug
0
50
100
150
200
250
300
Palude della Rosa Fusina Sacca Sessola Ca' Roman Petta di Bo'
Reti annuali
� Intensive � development
0,5
0
0,5
0
200
0
80
0
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BC = k
� Growth and development
N
0
100
200
300
400
500
600
700
Jan May Aug Jan May Aug Jan May Aug Jan May Aug Jan May Aug
0
50
100
150
200
250
300
Palude della Rosa Fusina Sacca Sessola Ca' Roman Petta di Bo'
Reti annuali
200
0
80
0
EX
EM
AMI
NC
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BC = k
� Normalized to January �
� Normalized to
Sacca Sessola �
N
EX
EM
AMI
NC
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BC = k
� clear distinction between
northern and southern stations
� for southern stations BC is max in may
� Sacca Sessola
mostly stressed
� Ca Roman less stressed
N
EX
EM
AMI
NC
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BC = k Conclusions
� A study on 5 sites of a lagoon ecosystem
� Similar subsystems
� Different ecological state (quality)
� BC clearly identifies the 2 better sites:
Petta di Bo’ & Ca’ Roman
� Follows seasonal dynamics
� It is a sensitive tool
N
EX
EM
AMI
NC
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Lagoon of Venice SDB Indicator
N
January May August Year
Ca’ Roman 0,92 0,77 0,63 0,79
Petta di Bo’ 0,91 0,76 0,67 0,83
Sacca Sessola 0,81 0,77 0,66 0,91
Fusina 0,80 0,85 0,77 0,94
Palude della Rosa 0,89 0,73 0,61 0,88
F = 1,41m0,88
0,001
0,01
0,1
1
10
100
1000
0,001 0,01 0,1 1 10 100 1000
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Lagoon of Venice SDB Indicator
N
January May August Year
Ca’ Roman 0,92 0,77 0,63 0,79
Petta di Bo’ 0,91 0,76 0,67 0,83
Sacca Sessola 0,81 0,77 0,66 0,91
Fusina 0,80 0,85 0,77 0,94
Palude della Rosa 0,89 0,73 0,61 0,88
F = 2,53m0,76
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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Lagoon of Venice SDB Indicator
N
January May August Year
Ca’ Roman 0,92 0,77 0,63 0,79
Petta di Bo’ 0,91 0,76 0,67 0,83
Sacca Sessola 0,81 0,77 0,66 0,91
Fusina 0,80 0,85 0,77 0,94
Palude della Rosa 0,89 0,73 0,61 0,88
F = 2,98m0,66
0,001
0,01
0,1
1
10
100
1000
0,001 0,01 0,1 1 10 100 1000
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Lagoon of Venice SDB Indicator
N
January May August Year
Ca’ Roman 0,92 0,77 0,63 0,79
Petta di Bo’ 0,91 0,76 0,67 0,83
Sacca Sessola 0,81 0,77 0,66 0,91
Fusina 0,80 0,85 0,77 0,94
Palude della Rosa 0,89 0,73 0,61 0,88
F = 14,18m0,86
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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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 1000,0
0
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
31 m a rch 200 9
L. Pa lm e riUn ive rs ità d i Pa dova
LASA – La b ora t orio d i An a lis i de i Sis te m i
Am b ie n ta li
98
Lagoon of Venice SDB IndicatorCa’ Roman 0,63
August Petta di Bo’ 0,67
(decaying season) Sacca Sessola 0,66
Fusina 0,77
Palude della Rosa 0,61
Ca’ Roman 0,77
May Petta di Bo’ 0,76
(growing season) Sacca Sessola 0,77
Fusina 0,85
Palude della Rosa 0,73
Ca’ Roman 0,92
January Petta di Bo’ 0,91
(dormant season) Sacca Sessola 0,81
Fusina 0,80
Palude della Rosa 0,89
Ca’ Roman 0,79
Year Petta di Bo’ 0,83
(averaged values over the year) Sacca Sessola 0,91
Fusina 0,94
Palude 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 !)
31 m a rch 200 9
L. Pa lm e riUn ive rs ità d i Pa dova
LASA – La b ora t orio d i An a lis i de i Sis te m i
Am b ie n ta li
99
Lagoon of Venice SDB IndicatorCa’ Roman 0,63
August Petta di Bo’ 0,67
(decaying season) Sacca Sessola 0,66
Fusina 0,77
Palude della Rosa 0,61
Ca’ Roman 0,77
May Petta di Bo’ 0,76
(growing season) Sacca Sessola 0,77
Fusina 0,85
Palude della Rosa 0,73
Ca’ Roman 0,92
January Petta di Bo’ 0,91
(dormant season) Sacca Sessola 0,81
Fusina 0,80
Palude della Rosa 0,89
Ca’ Roman 0,79
Year Petta di Bo’ 0,83
(averaged values over the year) Sacca Sessola 0,91
Fusina 0,94
Palude 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.:
• Oversupplied in January (pp dormant, … ready to burst)
• Balanced during spring (G&D are at a maximum level)
• Undersupplied in late summer (decaying season)
31 m a rch 200 9
L. Pa lm e riUn ive rs ità d i Pa dova
LASA – La b ora t orio d i An a lis i de i Sis te m i
Am b ie n ta li
100
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
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
31 m a rch 200 9
L. Pa lm e riUn ive rs ità d i Pa dova
LASA – La b ora t orio d i An a lis i de i Sis te m i
Am b ie n ta li
101
Research in progress
How SDB correlates with the other indicators
AS C , TS T , AMI, EM and EX
?