# Ecology and Physics

*November 3, 2011*

Suppose you are interested in the rate at which some population (bees, bacteria, people, whatever) changes as time goes by. What makes the population increase, or decrease, or stay the same, or oscillate about some value?

One way ecologists study this is to make mathematical models. A typical model looks something like this:

The rate at which the population increases is proportional to the population itself (makes sense: the more mothers there are, the more babies will be born per year),

but also:

The rate at which the population

decreasesis related to the population itself (the more people there are, the more waste there is and the less food there is to go around, which could lead tofewerbabies per year).

What actually happens depends on which of these two effects is stronger for a particular situation. Realistic models will be much more complicated, with additional terms to account for various details, but most of them are built on this simple starting point.

What all such models have in common is that they attempt to answer the question:

What does the rate of change of the population depend on?

What I have become interested in is whether or not they should, instead, attempt to answer the question:

What does the rate of change

of the rate of changeof the population depend on?

I first learned about this issue in a wonderful book by Lev Ginzburg (an ecologist at Stony Brook University) and Mark Colyvan (a philosopher of science at The University of Sydney) called Ecological Orbits: How Planets Move and Populations Grow. They make the following analogy with Newtonian physics (the study of the motion of things like a baseball, or a rocket, or the moon): In physics, we are interested in how the position of an object, say a baseball, changes as time goes by. It turns out that the model that works best is one which asks, not what does the position of the baseball depend on, not what does the velocity (the rate of change of position) of the baseball depend on, but:

What does the

acceleration(the rate of changeof the rate of changeof the position) of the baseball depend on?

Ginzburg and Colyvan ask the question: Should ecologists, in trying to understand how populations change with time, take a hint from the physicists and ask about the rate of change of the rate of change of the population (the “acceleration” of the population, if you will), instead of the the rate of change of the population (the “velocity” of the population). Newton’s Laws wouldn’t have been discovered if Newton had not looked at *acceleration*. Perhaps ecologists need to look at the “acceleration” of populations if they want to get a handle on the laws of ecology, whatever they may be. Being a physicist, I am, of course, a sucker for their argument!

There are two big questions which arise. One is: How might you determine, experimentally, whether or not a population model should be based on the “acceleration” of the population (as opposed to the “velocity” of the population)? The other question is, if it turns out that the “acceleration” point of view is more realistic, what biological mechanisms give rise to such an effect? After all, populations are not baseballs, so there is no reason why they should obey the same laws!

I will say more about how my research is attempting to address the first question in later entries, but for now I will mention that, for those interested in the more mathematical details of all this (two semesters of calculus is all you need), I have a tutorial on this subject that I use with my students. You can find it at : http://www2.truman.edu/~prolnick/EPM/EPM_Tutorial.html.