Is Modelling Science, Mathematics, or Instinct?

Cientista Visitante

IPIMAR

William Silvert

Who is a Modeller?

• It is widely thought that only certain people are “modellers”, and to be a modeller requires mathematical and computer training.

• In fact, modelling is a universal activity. We are all modellers, not just those who are called “modellers”.

Consider this lovely young child, with his nice red teddy bear. What does he know about models?

Let’s see how he develops his modelling ...

He has some other nice things that are bright red, so that seems to be a good feature to use in predicting what will be fun to play with.

But some objects that are a nice pretty shade of red are not quite as nice to the touch,

How we Start to Develop Our Modelling Skills

And some are downright dangerous!

Model Testing and Validation

• The original model, that red objects make good toys, works for teddy bears and wagons, but not for pots, kettles, and matches.

• So even a young child experiences the frustration of constructing, testing, and ultimately falsifying a model.

Modelling is Like Breathing• We all breath,

and we all model.

• Some people breath better than others because they have learned special skills.

Need for Powerful Computers!

There are some researchers who are convinced that it has been the hardware limitations [of computers] that have obstructed progress and that advances in modelling are now possible because of larger computer capacity. There is no basis for this belief; bigger computers simply permit bigger mistakes.

D. H. Lee (1973)

Mathematical Modelling

• Modelling is science, not mathematics. It deals with reality. Good mathematics cannot save a model based on bad science.

• So one cannot be a modeller without also being a scientist. The modelling aspect of research should never be separated from the science.

A Little Math can be Dangerous!

• Would you call this linear? Of course not! (I hope.)

• If you test it for significance of linear regression, it qualifies!

0

1

2

3

4

5

0 1 2

x

y

Modelling Food Chains

Phytoplank ton

Zooplank ton

F ish Linear Model dZ/dt = aP - bZ

Lotka-Volterra Model dZ/dt = aPZ -bFZ

Do we need Models?• Can we do experiments without

using models? Pure data collection?• We had a post-doc studying the

growth efficiency of amphipods who didn’t see any need for modelling.

• At the end of the experiment he tried starving the animals.

• They continued to grow very well!

And when Models fail?

• If a model doesn’t fit the data, what does that tell us? What is wrong?

• Most people assume that if the model and the data don’t agree, the model must be wrong.

• But can the data be wrong? Here are some cases - you decide!

Uptake Kinetics

Many important processes in ecology can be modelled with the uptake-clearance equation

dC/dt = aX – bC

This is one of the most universal and reliable equations we have.

Aliasing

Catches of Carapau

0

1

2

1984

1986

1988

1990

1992

1994

1996

1998

Landings of Trachurus japonicus in millions of tonnes

(incomplete data, see next slide)

Fish Catches, China & Others

0

1

2China

Others

Landings of Trachurus japonicus in millions of tonnes

Two Major Points

• Modelling is a universal activity. We are all modellers, not just those who are good at mathematics and play with equations and computers.

• Modelling is science, not mathematics. It deals with reality. Good mathematics cannot save a model based on bad science.