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