…are those who think in terms of dynamical models (dY/dt = F(Y,X)), and those who think in terms of regressions models (Y=F(X)).

By a dynamical model, I mean any stochastic or deterministic mathematical model specified in terms of the rates of change in the values of its state variables (discrete time or continuous time), or any simulation model that could in principle be expressed that way (e.g., individual-based forest simulators). A state variable is just an amount of something that can change over time–population density, the species richness of an island, the number of juvenile individuals infected with a disease, total tree biomass, the frequency of an allele, whatever. The model describes the rates at which events occur that raise and lower the values of the state variables. For instance, for a model of population size the events might be births, deaths, immigration, and emigration. Dynamical modeling is all about specifying the rates at which those events occur–those rates typically will depend on various factors, vary in all sorts of ways for all sorts of reasons, etc. From those rates (and other information such as the initial conditions), you can figure out the values of your state variables at any time point. Dynamical models are colloquially called “bucket models” because a state variable is like the amount of water in a bucket. It’s an amount of “stuff” that is determined by rates of inputs and outputs: the rate at which stuff is added to the bucket and the rate at which it’s taken away.

By a regression model, I mean “regression” in a very broad sense: any model that statistically relates the value of one or more dependent variables to one or more independent variables. So not just regression sensu stricto, but ANOVA, GLMs, GAMs, MANOVA, and much more. Think for instance of “environmental niche models” that use data on species presence/absence at various sites, plus data on environmental conditions at those sites (mean annual temperature, mean annual precipitation, etc.), to describe and predict probability of presence/absence as a function of local environmental conditions. Even many neural network models and other machine learning models count as “regression” models for purposes of this post.

The key difference is that people who think in terms of dynamical models don’t ordinarily try to directly relate the variables that they ultimately care about–the state variables–to one another, or to other variables, the way people who think in terms of regressions do. Rather, people who think in terms of dynamical models think of the (past and current) values of the states variables and other variables as affecting the (current and future) values of the state variables only indirectly, via their direct effects on the (past, current, and future) rates of change in the state variables.

The distinction I’m drawing is a subtle one, in that it doesn’t map neatly onto more obvious ways of classifying ecologists:

It’s not a distinction between subfields of ecology, though it’s often mistaken for one. For instance, yes, plenty of population ecologists (and population geneticists) think in terms of dY/dt–but some don’t. Conversely, plenty of macroecologists and macroevolutionists think in terms of Y=F(X), but plenty think in terms of dY/dt too. For instance, if you think about phylogenies as arising from a “birth-death” (i.e. speciation-extinction) process, you’re thinking in terms of a dynamical model. Your state variables and rate parameters aren’t the same ones population ecologists tend to think about. But nevertheless you’re thinking in terms of state variables and rate parameters.

It’s not a distinction between ecologists who care about “causality” or “mechanisms” and those who care about statistical prediction. The parameters of a dynamical model needn’t be mechanistic. Indeed they can always be thought of as phenomenological “high level summaries” of unspecified “lower level” mechanisms. Conversely, structural equation modeling is a tool for inferring causality from observational data using interconnected set of regression models.*

It’s not a distinction between theorists and empiricists. Plenty of empirical ecologists think in terms of dynamical models without actually being modelers themselves. (Theorists who think in terms of regressions are rare, though, which is telling.)

It’s not a distinction between those doing hypothesis-testing work vs. those doing descriptive work.

It’s not a distinction between those doing fundamental work vs. those doing applied work. Plenty of people doing fundamental work think in terms of dY/dt–but so do plenty of people doing applied work in, say, fisheries and wildlife management. And people who think in terms of regressions do both fundamental work and applied work.

My distinction doesn’t tell you anything about the technical tools ecologists use in their day-to-day work. For instance, I think in terms of dY/dt, but you’ll find ANOVAs and regressions in many of my papers and differential equations in only a few of my papers. And I only have one paper in which I try to estimate the parameters of a dynamical model. Knowing that I think in terms of dynamical models doesn’t tell you much of anything about how I go about testing those models.

Many people straddle my distinction. Brian thinks of himself as a regression person, for instance, but I think he’s secretly a fence-straddler. 😉

There are research approaches that straddle my distinction. In particular, partially-specified models (Wood 2001) and integral projection models (Merow et al. 2014) are dynamical modeling approaches based partially or entirely on regression. Rather than making possibly-false assumptions about the shapes of the relationships between your rate parameters and your state variables, you instead “let the data do the talking” and describe the observed relationships with flexible nonparametric regressions such as cubic splines.

Nevertheless, I think my subtle distinction is real. Without meaning to invoke proof by authority, I note that I’m far from the only one who senses the distinction. For instance, Brian and various commenters on this old post identified two main “schools of thought” in ecology: what Brian called the “population process school” and…the other school, which commenters on that old thread (including me) found harder to pin down. I now think the members of Brian’s “population process school” are the people who think in terms of dynamical models (and they’re not all population ecologists, so “population process school” isn’t a great name for them). I now think the other school is the regression school.

I think my distinction is important because it shapes the sorts of questions we ask, and determines what we’re prepared to count as an answer. As a card-carrying member of the dynamical modeling school**, I obviously prefer the sorts of questions members of my school tend to ask, and the answers we tend to provide. I think members of the other school are at greater risk of making mistakes when they’re generating hypotheses about how their dependent variables will vary with their independent variables. In particular, I think feedback loops are basically impossible to think about or study without the aid of dynamical models, especially when nonlinearities and stochasticity also are involved.

But of course, as a member of the dynamical modeling school I’m sure I’m particularly alert to the failings of the regression school, and particularly blind to the failings of my own school. Perhaps there are certain sorts of questions that are best attacked by people who think in terms of dynamical models, and other sorts of questions that are best attacked by people who think in terms of regressions?

So which kind of ecologist are you?

*I actually do think that people who think in terms of dynamical models and people who think in terms of regressions tend to think about “causality” quite differently. But I’ve tried and failed to articulate this in old posts and just confused readers. So I’m not going to go there again.

**Here’s our business card. 🙂

UPDATE: To forestall a possible misunderstanding, no, I don’t actually think that literally every ecologist thinks in one of these two ways, or even in some mix of these two ways. And I certainly don’t think that thinking in either of these two ways (or some mix of the two) is a litmus test for being an ecologist! As I’ve said before, there is no essential attribute that defines “ecology” or distinguishes ecologists from non-ecologists. The purpose of this post is merely to identify one major axis along with I believe many (not all) ecologists’ ways of thinking can be usefully arranged. I recognize that the post title omits those nuances and so could be considered a bit provocative. For better or worse, a non-trivial fraction of people decide what posts to read based on their titles. The hope with any post title is that it’s brief, clear, and engaging enough to convey something of what the post is about and encourage people to read it, without being actively misleading about the post content. I think the title of this post was fine on that score. The alternative titles I could think of seemed either less engaging or too wordy, without actually being more informative about the post content (e.g., “A key axis along with the thinking styles of many but not all ecologists vary”, “On ecologists’ thinking styles”). But I welcome feedback on the post title.