Methodology in quantitative research Bas Kooijman Dept theoretical

Methodology in quantitative research Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam Bas@bio. vu. nl http: //www. bio. vu. nl/thb master course WTC methods Amsterdam, 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 Theories Hypotheses Presumptions decrease in demonstrated support amount of support is always limited Proofs only exist in mathematics role of abstract concepts 0 “facts” no predictions possible large “general theories” predictions possible

Theories Models Theory: 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 nothing If a model that represents a theory must be rejected, a systematic search can start to assumptions that need replacement Unrealistic 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 tests Testability of models/theories comes in gradations

Measurements typically involve 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 column Height 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 them Question: 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!)

Space-time scales 1. 2. 1 Each process has its characteristic domain of space-time scales space system earth ecosystem population individual cell molecule When changing the space-time scale, new processes will become important other will become less important Individuals are special because of straightforward energy/mass balances time

Problematic research areas Small time scale combined with large spatial scale Large 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 O 2 consumption, μl/h Two curves fitted: a L 2 + b L 3 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 Length, mm

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 n-th order model ; 1. 2. 4 Monod model ; X : conc. of compound, t : time n : order X 0 : X at time 0 k : degradation rate K : saturation constant

Biodegradation of compounds Monod model scaled conc. n-th order model 1. 2. 4 scaled time

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 errors Alternatives: • deterministic systems with stochastic inputs • differences in parameter values between individuals Problem 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 parameters Imperfect control of process makes deterministic model unpractical

Producer/Consumer Dynamics Deterministic model Stochastic model in closed homogeneous system

10 3. 0 Bifurcation diagram Hopf 20 tangent focus 1. 0 consumers Producer/Consumer Dynamics 1. 15 2. 7 0 1. 23 0 1. 53 1. 23 1. 75 2 2. 8 4 6 2. 3 nutrient 8 2. 5 2. 4 isoclines