Modelling for Empirical Scientists Introduction: Our ‘functional’ world

By Justin Wan

“You couldn’t really do ecology if you didn’t know how to construct even the most basic mathematical model — even a simple regression is a model (the non-random relationship of some variable to another).” — CJA Bradshaw

NOTE: If you’ve come from a modelling background or already use modelling (are of the initiated) — this is probably not for you, however, do feel free to look on through or give suggestions!

Every scientist will have to deal with models at some point — whether we want to do a statistical analysis (e.g. ANOVAs), or when we happen across one of those dreaded “squiggly-line” theoretical papers (perhaps not the modelling catwalk type). My PhD dealt with the evolutionary ecology of plant populations and involved doing lots of experimental-empirical stuff — many hours in the glasshouse, growing and measuring plants as well as data synthesis. Early on, I had some background/foundation modelling papers saved up in a secluded file somewhere on my cluttered desktop, however, they never really left my mind. Not only do these kinds of papers explain experimental results, but they can also open doors to new ideas and ways thinking, as well as provide answers to explain experimental results.

“Maths is not for me; it is scary” — “I don’t come from a theoretical or mathematical background, therefore I couldn’t possibly understand it”. You might be right. But, if you did maths all those years back in high school — or have mathematics anywhere in your genes, then you most likely already have it in you. You will be able to utilise modelling in your research or use it to gain a new perspective on your subject. It also lets you understand and tweak the code in statistical packages to your liking (e.g. R).

Simply plonk the equations from those modelling papers into a program to understand how things are related to each other. Change the values of one variable, and watch the others change with it, or not change. Simply doing this could provide an answer to your question, or some insight into an idea.

^ this is also known as implementing a model.

As you may already be aware, our world is made up of Functions SO much that some argue that the world is a simulation or projection from some other dimension..God may actually be a programmer.What is a function? Functions are basically our attempt to predict stuff we observe. For instance, Joe walks at a speed of 4 kph. He walks from his lab back home which is 8 km away. We can make a function to describe how long it takes for him to walk a certain distance. Something which is predictive for a range of different values, not just one.

Time it takes for Joe to walk certain distance (hr) = Distance(km) / Joe’s speed (kph)

There we go, we have a function — which is also a model. Of course, this model is not perfect or completely accurate, and neither are any models. Joe needs to sleep, he will stop for food, terrain slows him down — so there are limitations to the model. Some models are extremely, extremely accurate — and they need to be. For instance the models needed to get a rocket to the moon and back need to be very accurate, otherwise, there will be very few astronauts. While others maybe not quite so accurate — for instance, daily weather forecasts. Indeed, functions and models are what runs modern society (how to make an airplane fly ← the Lift equation), so it is important we get it reasonably right.

Any understanding of mathematics is important in any environment or setting. In ecology and evolution, it is no different.

If you’ve clicked on the link above on what lets us fly safely to our desired destinations (e.g. scientific conferences), you may have noticed this function doesn’t look that scary after all — looks something like “A is equal to B times C divided by D squared”. You’d be happy to know that often it isn’t too complex! Even if the model you are examining looks heaps more squiggly, the idea is still the same. There are some great tools for jotting down and playing with the relationships between A and B,C, D; for this we can use R and/or Matlab.

“What if I want to try different values for A?” — Simply plonk the equations from those modelling papers into a program to understand how things are related to each other — change the values of one variable, and watch others change with it, or not change. Simply doing this can directly provide an answer to your idea.

In these sections, we will be learning how to work with R and Matlab. We will also go through the basic building blocks of models that you’ll likely run across in ecology and evolution. Some of the more complex building blocks will be covered as well.

With these tools in hand, mathematics will never be nearly as scary anymore.

Making a model is like building a Lego model — a castle, a battleship! Each component Lego block plays its own role in the overall model — a model is composed of many functions (Lego blocks).


Acknowledgements

Thanks to Susan Rutherford for the inspiration. I also thank my thesis-adviser for making this possible.—Disclaimer: This publication deals with opening up possibilities from modelling for empirical scientists. The contents of this publication wholly come from the own skills and experience gained through work in my PhD as an empiricist.

Advertisements