Transcript Ecological Modelling and Management: Opportunities

Identifying Existing Weaknesses,
Theoretical Constraints, and Needed
Advances in Ecosystem Modeling
Robert E. Ulanowicz
Emeritus, University of Maryland
Center for Environmental Science
Courtesy Professor, University of Florida
Arthur R. Marshall Laboratory
Department of Botany and Zoology
Ecosystem Modeling Workshop
CaRA, GCOOS, GOMA, and SECOORA
October 15, 2009
St. Petersburg, FL
Single Species/Process Models
Photosynthesis (P) by phytoplankton as function of light (I)
Jassby & Platt Limnol. Oceanogr. 21 (1976)


PB  PmB tanhI / PmB  RB
 = uptake coeff.
b = saturation
Single Species/Process Models
• Work rather well (Calibrate & Verify)
• Used widely for prediction and
interpolation.
Leslie Matrix Models
Leslie Matrix Models
• Derived from Actuarial practice
• Heavily used in fisheries and game
management
• Calibration and verification straightforward
• Decent predictions
Cellular Automata
Von Neuman
Neighborhood
Moore
Neighborhood
Landscape Grid
Migration with Diffusion
Ti 10,i  UBi 10  DBi 10  Bi 
Ti ,i 10  UBi  DBi  Bi 10 
Migration around Barrier (t=2)
Migration around Barrier (t=10)
Migration around Barrier (t=100)
Vectors of Animal Movement
Animal Densities (t=100)
Landscape Models
Landscape models are highly useful for
developing and virtually testing new
hypotheses in landscape ecology.
Their value for purposes of prognostication is
growing. Successes are more frequent when
single process dominates the dynamics.
Hydrodynamic Models
Hydrodynamic Models
Hydrodynamic models often give quite reliable
results. Numerical models often equal or
exceed the accuracy of physical analogs.
They are employed effectively for a host of
engineering applications, such as distribution of
salinity, suspended particles, temperature, etc.
Water Quality Models
Chlorophyll a vs N & P
Water Quality Models
Nitrogen levels in Cape Cod Bay
Water Quality Models
Water quality models predict well when the
dynamics are dominated by a single process –
physical, chemical or biological.
Water quality models begin to lose their
effectiveness whenever two or more biological
processes come into play.
Individual Based Models (IBMs)
Introduces individuals with programmed
behavior patterns into a virtual habitat
and traces the fate of each individual
over time and space.
An embellishment of cellular automata.
<http://www.red3d.com/cwr/ibm.html>
Autonomous Agent Models
An autonomous agent is a programmed
system that is part of a virtual
environment. It senses that environment,
and acts on it, over time, in pursuit of its
own agenda.
A slight refinement on IBMs.
IBMs and Autonomous Agent Models
IBMs and autonomous agent models are still
used primarily to test ideas about single species.
For example, whether hydroperiod affects nesting
success in woodstorks, or how alligator
populations respond to thermal stress.
IBMs of multiple populations remain in the early
experimental stages.
“Shell” Models
Models of various types collected and
run together on a single platform
Example:
Across Trophic Levels System Simulation (ATLSS)
Florida Everglades
<http://atlss.org/>
(ODE, Leslie, IBM)
“Shell” Models
Shell models are still in
the developmental stages.
Coupled Process Models
B
C
A
D
dA
  k1 AB  k 2 AC  k3 AD
dt
dB
 k1 AB  k 4 BC
dt
dC
 k 2 AC  k 4 BC  k5 DC
dt
dD
 k3 AD  k5 DC
dt
Coupled Process Models
• Prone to pathological behaviors
• Do not calibrate or verify easily.
• Poor prediction ability.
Platt, T., K.H. Mann, and R.E. Ulanowicz. 1981. Mathematical
Models in Biological Oceanography. UNESCO Press, Paris
Natura cum Machina?
Given the very limited successes of multispecies simulations, we are justified in
asking whether the entire paradigm of
“nature as a clockwork” is appropriate or
even counter-productive in the long run?
We need to examine the very
foundations of our scientific enterprise to
see whether alternative postulates might
lead us in more effective directions.
Natura cum Machina?
We note in particular how everything
that can transpire in a mechanical
conception of the universe is already
built into the model one that one
employs.
There can be no truly emergent
surprises!
The Newtonian Metaphysic

Causally closed

Deterministic

Reversible

Atomistic

Universal
(Depew and Weber 1995)
Causally Closed
Only mechanical or material causes are legitimate.
No final or “top-down” causality.
Influence of Newton’s Principia.
Atomistic
Decomposable into stable least units.
Reassembly.
Reductionism.
Reversible
Behavior same in both temporal directions.
= Conservative (Noether.)
Novelty cannot arise.
Deterministic
Predictable with arbitrary precision.
Divining Angel/Demon (Laplace.)
Universal
Laws apply everywhere,
over all time and space.
No “gaps” or “wiggle room”
Sola Lex?
Is everything we see around us determined
by physical laws? (The four force laws of
physics and the two laws of
thermodynamics)
Walter Elsasser (1981): Laws in the
nature of those pertaining to physics are
inapplicable to heterogeneous
situations, such as characterize biology.
Continuum 
Operations on Homogeneous Sets
2
X
2
2
4
2
2
4
=
4
4
8
4
8
8
8
Whitehead and Russell
Principia Mathematica 1913
8
Operations on Heterogeneous Groupings
Elsasser 1981
3
1
2
4
5
X
5
4
2
3
1
=
6
4
5
8
15
Corollary:
There are no mechanisms
in ecology!
(Ulanowicz)
Probability theory and statistics
are inadequate to describe events
most relevant to change in biology.
(Elsasser 1969)
No. of Simple Events in the Universe
(After Elsasser)
~1085 Elementary particles in Universe
and
~1025 Nanoseconds since Big Bang.
Therefore,
~1085 x 1025 = 10110 Possible simple events.
Note, however, that
80! ≈ 10116 >> 10110
Heterogeneity and combinatorics
overwhelm law.
(Elsasser 1969, 1981)
6! = 720
35! = 1040
Massive degeneracy!
Give Chance a Chance
I. The operation of any system is
vulnerable to disruption by unique chance
events.
What type of agency accounts
for the order we observe in
biological systems?
Process:
The interaction of random events
upon a configuration of constraints
that results in a non-random, but
indeterminate outcome.
(Ulanowicz, 2009)
Polya’s Urn
Required:
One opaque urn
Many red balls
Many blue balls
Place one red and one blue ball into urn.
Make a blind draw.
If “red”, then replace two red balls.
If “blue”, then replace two blue balls.
Continue for many drawings.
Polya’s Urn
Question 1:
After many draws, does the ratio
red:blue become non-random?
Red:Blue  0.54591
Polya’s Urn
Question 2:
If the balls are separated and the
series restarted, will the ratio red:blue
converge to the same limit?
(Is the limit determinate?)
Red:Blue  0.19561
Process
• Involves chance
• Involves self-reference
• Conditioned by history
Nature Unshackled
In order to understand living systems
emphasis should shift away from fixed laws
and towards the description of process.
What type of natural agency
accounts for the order we
observe in biological systems?
Auto-Metaballos
II. A process, via mediation by other processes,
may be capable of influencing itself.
(“In principle, then, a causal circuit will generate a
non random response to a random event…”
Gregory Bateson 1972)
Autocatalysis
Utricularia ssp.
Indirect Mutualism
Selection
History as Destiny?
III. Systems differ from one another according
to their history, some of which is recorded in
their material configurations.
“Every living thing is a sort of imperialist,
seeking to transform as much as possible
of its environment into itself and its seed....
We may regard the whole of evolution as
flowing from this "chemical imperialism"
of living matter.” (Emphasis mine)
Bertrand Russell
An Outline of Philosophy 1960
Duality in Nature?
1.The dynamics of nature are the result of two
opposing tendencies:
On one hand, order is constantly being eroded by the
consequences of unique chance events. On the other, the
centripetal nature of autocatalysis is constantly building
order.
This natural agonism ameliorates at higher levels, because
autocatalytic drive requires novel perturbations to evolve,
while autocatalytic structures necessarily create greater
dissipation.
A Hegelian dialectic?
Beneficence is ontologically
prior to competition.
Competition is impossible without
mutuality at some lower level.
Autocatalysis induces Competition
Exeunt Epiphenomena
2. Pertinent agency in living systems resides
more with configurations of propensities
than with explicit physical forces or their
attendant objects.
Tiezzi’s Dead Deer
Same mass
Same bound energy
Same molecular structure
Same morphology (almost)
So what is missing?
Ans: Configuration of processes!!
Newtonian Postulates
1. Causally closed.
2. Atomistic.
3. Reversible.
4. Deterministic.
5. Universal.
“Inversions”
• Components are organically imbedded in
configurations of processes
• History is destiny
• Chance is crucial
• Influence is often top - down
• Processes are circumscribed
“Process Ecology”
I Chance
II. Self-Influence
III. History
1.Dual Agonism in Nature
2.Agency in Configurations of Processes
Network Analysis
Identification and parsing only.
No “modelling”
1.Who eats whom?
2.By how much?
Network Analysis
Trophic Analysis
Cycle Analysis
Ascendency


 TijT 
A   Tij log 

T
T


i, j
pj
iq 

q
p

How effectively resources are processed
(System Performance)
Phenomenological Principle
In the absence of major perturbations,
ecosystems have a tendency over time to
take on configurations of greater ascendency.
9
5
2
4
9
4
4
1
9
2
4
9
4
4
4
5
10
3
4
10
10
5
4
4
4
9
1
9
3
10
10
5
4
5
10
10
4
4
9
9
5
2
A ≈ 43
30
30
5
A ≈ 86
(a)
(b)
1
3
30
30
4
A ≈ 240
(c)
5
10
Sensitivities of Ascendency
A
B prst

 T..... 1  Tp.rst T. prst  

 2
2


B
B
B


....
prst
prst 




2

Tpqrst B.... 
A

 log
Tpqrst
 B prst Bqrst T..... 
identify the controlling elements and arcs in the system.
Schematic of nutrient controls in Chesapeake mesohaline system
Ascendency is only half of the story!
System Capacity, C
 Tij 
C    Tij log  
i, j
T 
C≥A≥0
F=C–A
F is called “overhead”.
Let
a = A/C
represent the degree of order in the system.
Notice that
0<a<1
Now, define the robustness, R,
of the system as:
R=


   Tij a  log a 
 i, j 
Sustainability
1
Robustness
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
Degree of Order
0.8
1
Sensitivity of Robustness
(Vectors to Sustainability)
R
F
 F  T..
Tij
Tij
R
a
 F  T..F '
Tij
Tij
2





T
T
T
R
T..F ' 

ij ..
ij
F
log

a
log



 
Tij
C 
T
T
T
T
 i. . j  
  i. . j 

where
 loga  
F '  e
 1
 log(e) 
Marginal Contribution of Tij
R
is the marginal contribution of Tij
Tij
to the robustness of the system. That
is, it is the amount that each unit of Tij
contributes toward the robustness. It is
equal to unity for all i and j when R is
maximal (at a = [1/e]).
10.44
41.47
0.51
Filter
Feeders
1
15.79
Predators
0.05
5
.
.
0.33
14.72
0.30
0.17
0.64
Deposited
Detritus
6
8.17
.
6.16
Deposit
Feeders
4
1.91
.
4.24
0.43
7.27
0.66
1.21
Microbiota
2
.
5.76
1.21
Meiofauna
3
.
3.58
Oyster Reef Network, Dames & Patten 1981
(Flows in kcal/m2/d)
(1.03)
41.47
(1.08)
15.76
(1.00)
0.51
(0.879)
Filter
Feeders
1
Predators
0.05
(0.675)
5
.
.
0.33
(0.885)
14.76
(0.949)
0.30
(0.829)
0.17
(1.05)
0.64
(0.831)
Deposited
Detritus
6
8.17
(1.09)
.
6.16
(0.885)
Deposit
Feeders
4
1.91
(1.01)
.
4.24
(0.985)
7.27
(1.07)
0.43
(0.726)
0.66
(0.955)
1.21
(1.06)
Microbiota
2
.
1.21
(0.906)
Meiofauna
3
.
3.58
(0.917)
5.76
(0.997)
Oyster Reef Network, Marginal contributions in parentheses.
a = 0.436
(1.14)
141.47
(-0.49)
115.76
(-0.28)
0.05
0.51
(3.46)
Filter
Feeders
1
Predators
5
.
.
0.33
(4.18)
14.76
(4.27)
0.30
(4.49)
0.17
(-0.35)
0.64
(4.75)
Deposited
Detritus
6
108.17
(-0.55)
.
6.16
(5.93)
Deposit
Feeders
4
1.91
(2.39)
.
4.24
(2.54)
7.27
(1.37)
0.43
(5.71)
0.66
(0.594)
1.21
(3.19)
Microbiota
2
.
105.76
(-0.39)
1.21
(5.05)
Meiofauna
3
.
3.58
(3.01)
Hypothetically Eutrophic Oyster Reef
a = 0.683
Software Availability
EcoNETWRK (NOAA)
<http://www.glerl.noaa.gov/EcoNetwrk/>
WAND (Allesina)
<http://www.dsa.unipr.it/netanalysis/?Software>
NETWRK4 (Ulanowicz)
<http://www.cbl.umces.edu/~ulan/ntwk/netwrk.zip>
(for DOS only)
Templeton Foundation Press, 2009