Post on 28-Mar-2015
A philosophical approach to model complexity
Jim Smith
Some types of environmental model
• Mechanistic
• Empirical
• Statistical/Stochastic
• Deterministic
• Bayesian
• Behaviour-based
• Dynamic
• Process-based
• Analytical
• Numerical
• Kinetic
• Matrix
• Predictive
• Neural network
How do we judge “good science”?
• Publications
• High impact journals
• Citations
• Reputation
“Mechanistic” or “reductionist” approach to studying complex systems.
• New processes
• New insight/understanding
• Complex models
• Detailed experiments
Chernobyl
Radioactive pollution of lakes
Aquatic food webs
Cs concentration in fish
K concentration
Retention rate in lake water
Excretion fishBiouptake fish
~
Emp water
Volume
Fish weight
Age of plant
Outflow areas
Decay rate for Cs
Modified runoff rate
Outflow areas
Month of fallout
Total Cs in water
Cs in lake water
Max depth
Decay rate for Cs
Direct fallout
~
Fallout of Cs
Lake area
Input from OALake outflow
Altitude
Latitude Precipitation
Biomagnification factor
VolumeCatchment area
Catchment area
Cs in OA
Cs in IA
Mean depth
Retention rate in lake water
Seasonal moderator for Q
DTA
Dcrit
Mean depth
Theoretical water ret time
Monthly water discharge
Default runoff rate
Biological halflife
Default fall velocity for Cs
Precipitation
Cs in A
Diffusion
BET
Sed A
To passive sediments
Age of active sediments
Sed rate of Cs
Mean depth
E and T bottom areas
Decay from ET
All prod moderator
Lake area
Age of ET sediments
Susp matter
Diffusion rate
Latitude
Volume
Hypo temp
Mean annual temp
~
Seasonal variability norm for temp
Seasonal variability in epitemp
Epilimnic temp
Longitude
Hypolimnic temp
BET
EpiT to HypoT
Epi temp
Hyp
Hypo
Altitude
Fish weight
Particulate phase
Dissolved conc
Biouptake delay factor
Volume
Water discharge
Age of active sediments
Depth of active sed
Susp matter
Deposition on OA
Deposition on IA Input from IA
Decay from OA
Decay from IA
habitat
Lake Kd
Biomagnification factor
Gross sed rate
bioavail conc
Form factor
Cs in A
Steady state
Epi temp
K mod
Cs in ET
Soil permeability factor
Lake area
Factor for sediments
Form factor
Adv to water
Form factor
Rel depth
Aut prod moderator
Cs in ET
Form factor
TotalP
Lake pH
TotalP
Rel depth
K concentration
Gross sed rate
Active vol
Sed ET
Adv to A
Age of ET sediments
From IA to OA
Active vol
Epi areaForm factor
Max depth
Lake area
Epi vol
Distribution coeff
Epi depth
Hypo temp
Bioturbation factor
Dissolved fraction
Dissolved fraction
~
Seas norm Latmax~
Seas norm Latmin
~
Seas norm Altmax
~
Seas norm Altmin
~
Seas norm Qmax~
Seas norm Qmin
Seasonal moderator for Q
Mean annual Q
Emp mean annual Q
Cs concentration in plants
Biouptake plants Excretion plants
Biomagnification factor for plants
Dynamic ratio
Stratification limit
Dynamic ratio
Dynamic ratio
Interaction of Cs-137 with lake sediments
Cs+
Burial ofsediment
Aqueous Solid phases
Lake water
eibefeed
eo
e CsCkCkrCxsK
C
xD
xt
C
)(
iefibii sCCksCk
x
rsC
t
Cs
)(
0
5
10
15
20
25
30
35
40
1 10 100 1000
Total solids Cs-137 (Bq/Kg)D
epth
(cm
)
Chernobyl
Weapons
0
5
10
15
20
25
30
35
40
0 500 1000 1500
NH4 & K Concentration (uM)
Dep
th (
cm)
CF
BMF
Biological halfilfe (BHL)
WF
MA MET
Fish sub-model
Fish weight (WF)
Biouptake delay factor (BUD)
Epi temperature (MMET)
Steady state (SS)
Biomagnification factor (BMF)
Physical decay rate (Rd)
Outflow areas (OA)
All prod moderator (YAL)
Diss fraction (Ddiss)
Part coeff (Kd)
Tot conc in water (Cwa)
Lake volume (Vol) Amount in
A-sedimentsAmount in ET-sediments
K conc (CK) K moderator (YK)
TP conc (CTP)
Aut prod moderator (YAU)
Susp part matter conc (SPM)
Conc in diss phase (Cdiss)
Biouptake in fish (FIF)
Fish excretion (FFO)
Conc in fish
Feed habit (HA)
Conc in part phase (CparT)
= Distribution coefficient = Driving variables
Fish sub-model
Caesium-potassium model
Cs conc in biota
In (= UR*CCs)
Uptake rate (UR)
Max uptake rate (Vmax = 46560 µmol/g dw*d)
KsCs (= 27.5 µM)
CK (µM, range 25-4000)
KsK (= 23.2 µM)
CCs (µM, default 0.001)
Out (= 0.693*Cp/Tp)
CFMM
Kmoderator (YK)
Halflife for Cs in biota (Tp = 0.55 d)
Michaelis-Menten kinetics
Nernst equation (equlibrium assumption)
Universal gas constant (Ro = 8.31 J/mol*degree)
Faraday const. (F = 96.5 J/mol*mV)
CFN
Temp (default = 20°C)
Diffusion potential for K (Eo = 105 mV)
Emp constant (Const = 0.73)
CF
Deficiency (< 0.1 mM)
Sufficiency (> 0.1 mM)
C
CFnorm (= 40)
CF/CFnorm
Caesium-potassium model
Empirical caesium-potassium model
Vanderploeg et al. 1975
Water
Fish
kf kb
• Any given set of empirical observations may be explained (fitted) by an infinite number of possible models (hypotheses).
Historical explanation (curve fitting) is relatively easy.
• How do we decide which is the best model/explanation?
Two key criteria:
- Simplicity
- Predictive power.
Equifinality Ludwig von Bertalanffy (1901--1972)
“It is vain to do with more what can be done with less”.
- William of Ockham
Ockham’s razor
“If the consequences are the same it is always better to assume the more
limited antecedent”
- Aristotle, Physics.
“We are to admit no more causes of natural things than such as are both true
and sufficient to explain their appearances”
- Newton, Principia.
“Everything should be made as simple as possible, but not simpler."
- Einstein, Autobiographical notes.
Complexity and predictive power
0
0.2
0.4
0.6
0.8
1
0 Model complexity
Goo
dnes
s of
fit,
R2
1
10
100
1000
10000
100000
0 Model complexityO
bser
vatio
ns re
quire
d
Conjecture and refutation
Conjecture and RefutationKarl Popper
• Form a hypothesis (by any means you like)
• Test the hypothesis against empirical evidence
• The best theory is the simplest one which stands up to the most critical tests.
Some types of environmental model
• Mechanistic
• Empirical
• Statistical/Stochastic
• Deterministic
• Bayesian
• Behaviour-based
• Dynamic
• Process-based
• Analytical
• Numerical
• Kinetic
• Matrix
• Predictive
• Neural network
Does ecology work like this?- Very rarely (Peters)
• Vague and/or untestable general theories
– Density dependent relationships and population models– Evolutionary ecology– “Ad-hockery” and historical explanation
• Quantified but trivial mini-hypotheses
– Detailed studies of “model” systems– “Tractable mini-questions”
• How many “blind” tests of predictive models do we see?• How many failures?
2
122222
1
211111
)(
)(
K
bNNKNr
dt
dN
K
aNNKNr
dt
dN
0
10
20
30
40
50
60
70
1 15 29 43 57 71 85 99 113 127 141 155 169 183 197
Time
Po
pu
lati
on
Prey
Predator
Physics is simpler than environmental science
Some characteristics of useful predictive environmental models
• Simple in structure
• Few driving variables
• Ignore many processes
• Strong empirical basis
• Applied to many systems
• Well tested
Some predictive models in ecology
• Phosphorus in lakes – Wollenweider model
LakePhosphorus inflow
Phosphorus sedimentation
Phosphorus outflow
Some predictive models in ecology
• Radiocaesium in rivers and lakes
LakeCs-137 inflow
Cs-137 sedimentation
Cs-137 outflow
Fish
Dnieper
1
10
100
1000
10000
100000
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Time after the accident (y)
137 С
s (d
isso
lve
d)
Bq
m-3
Predicted
Measured
Besed
1
10
100
1000
10000
100000
1000000
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Time after the accident (y)
137 С
s (d
isso
lve
d)
Bq
m-3
Predicted
Measured
0.01
0.1
1
10
100
1000
10000
100000
0 5 10 15 20 25
Time (years)
137 C
s in
wat
er (
Bq
l-1
) an
d f
ish
(B
q k
g-1
)
Model w ater
Model, small f ish
Model, large pred f ish(pike)Water measurements
Pike measurements
Measurements, smallCyprinidae
Conclusion
The central purpose of environmental science is not to “understand” or simulate complex ecosystems, but to provide practical solutions to real environmental problems.
"All models are wrong, but some are useful."
- George Box