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Methodology in quantitative research
Bas KooijmanDept theoretical biology
Vrije Universiteit [email protected]
http://www.bio.vu.nl/thb
master course WTC methodsAmsterdam, 2005/10/31
University School
in the sense that you learn things that you must reproduce later
• Notice the philosophical positions taken in these lectures
• Listen carefully to the arguments on which they are based
• Work on your own philosophical position that you can defend with arguments
• A lot of nonsense finds its way to the printer: read critically!
• Science: fine art of the battle creativity critical evaluation
Presumptions Laws
LawsTheoriesHypothesesPresumptions
decrease in demonstrated supportamount of support is always limitedProofs only exist in mathematics
role of abstract concepts
0 large
“facts” “general theories”
no predictions possible predictions possible
Theories ModelsTheory: set of coherent and consistent assumptions from which models can be derived for particular situations
Models may or may not represent theories it depends on the assumptions on which they are based
If a model itself is the assumption, it is only a description if it is inconsistent with data, and must be rejected, you have nothingIf a model that represents a theory must be rejected, a systematic search can start to assumptions that need replacementUnrealistic models can be very useful in guiding research to improve assumptions (= insight)Many models don’t need to be tested against data because they fail more important consistency testsTestability of models/theories comes in gradations
Measurements typicallyinvolve interpretations, models
Given: “the air temperature in this room is 19 degrees Celsius” Used equipment: mercury thermometer
Assumption: the room has a temperature (spatially homogeneous)Actual measurement: height of mercury columnHeight of the mercury column temperature: model! How realistic is this model? What if the temperature is changing?
Task: make assumptions explicit and be aware of themQuestion: what is calibration?
Empirical cycle 1.2
Assumptions summarize insight
• task of research: make all assumptions explicit these should fully specify subsequent model formulations
• assumptions: interface between experimentalist theoretician
• discrepancy model predictions measurements: identify which assumption needs replacement
• models that give wrong predictions can be very useful to increase insight
• structure list of assumptions to replacebility (mind consistency!)
molecule
cell
individual
population
ecosystem
system earth
time
spac
e
Space-time scales 1.2.1
When changing the space-time scale, new processes will become important other will become less importantIndividuals are special because of straightforward energy/mass balances
Each process has its characteristic domain of space-time scales
Problematic research areas
Small time scale combined with large spatial scaleLarge time scale combined with small spatial scale
Reason: likely to involve models with large number of variables and parameters
Such models rarely contribute to new insight due to uncertainties in formulation and parameter values
Small scale More fundamental
“fundaments of biology can be found in molecular biology”
Molecular biology engineering research on optimization of motors of cars
Ecology managing of queuing problems in traffic control
Knowledge on motors of cars is of little help to solve queuing problems
Notice difference is space-time scales
Different models can fit equally well
Length, mmO2 c
onsu
mpt
ion,
μl/
h
Two curves fitted:
a L2 + b L3
with a = 0.0336 μl h-1 mm-2
b = 0.01845 μl h-1 mm-3
a Lb
with a = 0.0156 μl h-1 mm-2.437
b = 2.437
Verification falsification
Verification cannot work because different models can fit data equally well
Falsification cannot work because models are idealized simplifications of reality “All models are wrong, but some are useful”
Support works to some extend
Usefulness works but depends on context (aim of model) a model without context is meaningless
Biodegradation of compounds 1.2.4
n-th order model Monod modelnkXX
dt
d
1)1(10 )1()(
nn ktnXtX
ktXtXn
0
0
)( kXt /0
}exp{)( 0
1
ktXtXn
n
akXaXt
nn
1
1)(
111
00
XK
XkX
dt
d
ktXtXKXtX }/)(ln{)(0 00
ktXtXXK
0
0
)(
}/exp{)( 0
0
KktXtXXK
aKkakXaXt ln)1()( 1100
; ;
X : conc. of compound, X0 : X at time 0 t : time k : degradation rate n : order K : saturation constant
kXt /0
Biodegradation of compounds 1.2.4
n-th order model Monod model
scaled time scaled time
scal
ed c
onc.
scal
ed c
onc.
Stochastic vs deterministic models 1.2.4
Only stochastic models can be tested against experimental data
Standard way to extend deterministic model to stochastic one: regression model: y(x| a,b,..) = f(x|a,b,..) + e, with e N(0,2)Originates from physics, where e stands for measurement error
Problem: deviations from model are frequently not measurement errorsAlternatives:• deterministic systems with stochastic inputs• differences in parameter values between individualsProblem of alternatives: parameter estimation methods become very complex
Stochastic vs deterministic models 1.2.4
Tossing a die can be modeled in two ways• Stochastically: each possible outcome has the same probability• Deterministically: detailed modelling of take off and bounching, with initial conditions; many parametersImperfect control of process makes deterministic model unpractical
Producer/Consumer DynamicsDeterministic model
Stochastic model
in closed homogeneous system
Producer/Consumer Dynamics
0 2 4 6 8
0
10
20
con
sum
ers
nutrient
1.75 2.3 2.4
2.5
2.7
3.0
1.23
1.15
1.0
2.81.231.53
tang
ent
focu
s
Hop
f
Bifurcation diagram
isoclines
