Trophic state indicators from Thermodynamics and Information … · LASA – Laboratorio di Analisi...

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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

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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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� 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)

�


� GENERALIZED ENTROPY (Van Kampen, 1981)

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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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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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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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N


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


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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N


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


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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N


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


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

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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


Ca’ Roman 0,92

January Petta di Bo’ 0,91

(dormant season) Sacca Sessola 0,81

Fusina 0,80


Ca’ Roman 0,79

Year Petta di Bo’ 0,83

(averaged values over the year) Sacca Sessola 0,91

Fusina 0,94


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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Lagoon of Venice SDB IndicatorCa’ Roman 0,63

August Petta di Bo’ 0,67

(decaying season) Sacca Sessola 0,66

Fusina 0,77


Ca’ Roman 0,77

May Petta di Bo’ 0,76

(growing season) Sacca Sessola 0,77

Fusina 0,85


Ca’ Roman 0,92

January Petta di Bo’ 0,91

(dormant season) Sacca Sessola 0,81

Fusina 0,80


Ca’ Roman 0,79

Year Petta di Bo’ 0,83

(averaged values over the year) Sacca Sessola 0,91

Fusina 0,94


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)

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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

for the indicator values and very general convergence schemes

N


� Generality, applicable to very different systems

� Sensitivity, distinguishes similar systems

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Research in progress

How SDB correlates with the other indicators

AS C , TS T , AMI, EM and EX

?

Trophic state indicators from Thermodynamics and Information … · LASA – Laboratorio di Analisi...

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Transcript of Trophic state indicators from Thermodynamics and Information … · LASA – Laboratorio di Analisi...