Like politics, science is the art of the possible. Ideally, we’d collectively focus a lot of research effort on the biggest, most important, most interesting topics.* But some topics are more difficult to address than others, for all sorts of reasons.** Hence my question: what are the biggest understudied topics in ecology? The topics that are studied the least, relative to how big, interesting, and important they are?
Here’s my answer: non-stationarity. As far as I know, Peter Chesson is the only ecologist working on this. Which, if you’re just going to have one person working on this, is probably the right person! But really, I think it would be better if he had some help. 🙂
Warning: extended digression on non-stationarity coming up. Just skip to the end if you don’t care, and in the comments suggest your own big understudied topic.
To understand what non-stationarity is and why it’s important, you first have to understand stationarity. Stationarity has various technical definitions, but the gist is that a stationary system has some typical distribution of behavior in the long run. The mean, variance, and other statistical moments don’t change. A stationary system necessarily has some sort of return tendency–some process, analogous to negative density dependence, that keeps it from moving away from that stationary distribution of states.
Note that stationarity is a much broader concept than stable equilibrium. For instance, a population of jackalopes can be stationary even if it never reaches equilibrium (or even if it fluctuates irregularly or chaotically rather than in some regular cyclic fashion.) I’m totally unbothered that the world is non-equilibrial, because that doesn’t present any particularly difficult conceptual or practical obstacles. Plus, it raises various fun possibilities that wouldn’t exist in an equilibrial world. But non-stationarity–that worries me.
Stationarity matters because there’s a very large and well-developed toolbox of theoretical and empirical methods for studying the dynamics of stationary systems. For instance, Ziebarth et al. 2010 (a paper I love, so I keep linking to it) estimated the strength of population regulation for many different populations. That is, they assumed the populations were stationary, and used time series analysis techniques to estimate rates of return to stationarity. In general, it’s much easier to study something, theoretically and empirically, if it has some typical distribution of states or behavior. Roughly speaking, stationary systems are those that can be said to have typical behavior. A non-stationary system is one that doesn’t have any typical behavior.
Note that worrying about non-stationarity is not the same thing as worrying that short-term dynamics might be atypical or might differ from long-term dynamics. Every field ecology grad student’s worry that their first field season will be a “weird” year weather-wise is not a worry about non-stationarity. Worrying that this year your study system will be in a state that’s out in one tail of its stationary distribution (i.e. a state it’s rarely in) is not the same as worrying that your system has no stationary distribution. Nor is worrying that you’re observing transient dynamics rather than long-term dynamics the same thing as worrying about non-stationarity. Stationary systems can have transient dynamics that aren’t representative of the long-term stationary distribution. Nor is worrying that your system might exhibit different behaviors on different timescales the same thing as worrying about non-stationarity. Stationary systems can fluctuate differently on different timescales (e.g., daily vs. seasonal vs. year-to-year).***
I worry about non-stationarity because in a non-stationary world because many of our usual methods don’t apply. For starters, as far as I know most of our theoretical models, and the mathematical concepts and techniques used to analyze the long-term behavior of those models, go out the window. It’s not just that they don’t apply exactly, it’s that they don’t apply even approximately, or at all. Indeed, in a non-stationary world, many of the questions we ordinarily ask as ecologists don’t even make sense. For instance, what sense does it make to ask about coexistence in a non-stationary world? You can’t ask why species coexist if they’re not coexisting, merely co-occurring for some period of time. You can’t ask what their long-term average rates of increase when rare are if they have no long-term average rates. Or actually, you can ask some of those questions, but there’s no point to doing so, because the answers are going to change. You can perfectly well calculate the mean, variance, and other statistical moments of some finite realization of a non-stationary time series. But those numbers won’t tell you anything about what the series was like in the past or what it will be like in the future. In a non-stationary world, every period of time is unique, and so history becomes just one damned thing after another. You can do science about a unique series of one-off events, but it’s a totally different sort of science from the sort that many ecologists do. Conversely, in a non-stationary world other questions that we don’t often ask take on greater interest and importance. Brian suggests asking why non-stationary systems often seem to persist for such long periods of time, despite their non-stationarity. For instance, if species have non-stationary dynamics, how is it that the average species manages to persist for millions of years?
But don’t despair. There are various research strategies for a non-stationary world. Unfortunately, most of them involve working around non-stationarity than actually studying it.
- Describe non-stationarity. Long-term monitoring is obviously an essential component of any research program on non-stationarity. But on its own it’s not very satisfying.
- Focus on short-term dynamics. Think for instance of population viability analysis, key goals of which are to estimate the current rate of increase or decrease of some population we want to conserve, and predict the near-term effects of management interventions on population growth rate. This is much easier than trying to make long-term predictions about the population’s stationary dynamics, because you can safely assume that many things affecting the population growth rate (such as population structure) won’t change in the short term, at least not too much. (Aside: if you’re going to go this route, for the love of your deity of choice do it right. There are many weak studies of short-term dynamics in ecology.)
- Study variables that have stationary dynamics. Think island biogeography theory: individual species come and go and might well have non-stationary dynamics, but species richness is stationary.
- Find a spatial scale on which the dynamics are approximately stationary. For instance, in some metacommunity models you might well have non-stationary dynamics of individual species, and constant turnover of species composition within patches. But thanks to movement among patches, species richness, composition, and species abundances might be stationary at the larger spatial scale of the entire metacommunity.
- Find a time scale on which the dynamics are approximately stationary. Stationary processes can look non-stationary if you don’t watch them for long enough. For instance, the famous 10-year cycle of Canadian lynx and snowshoe hares is stationary. But if you only had 5 years worth of lynx abundance data starting from the cycle nadir, it would look like a non-stationary increasing trend. Conversely, consider a system that is non-stationary only because it’s being exogenously forced by some non-stationary variable that changes very slowly relative to the other processes that affect the value of whatever variable you’re studying. You can consider that system to be stationary on time scales substantially faster than those of the exogenous driving variable.
- Study variables and questions for which stationarity doesn’t matter. For instance, species abundance distributions have roughly the same predicted shape (lognormal or lognormal-ish) whether the underlying dynamics are dominated by drift or not. Pure drift is non-stationary. More broadly, there are many topics in ecology that have nothing to do with whether the world is non-stationary.
- Treat a long-term trend as what’s “typical”. If the non-stationarity takes the form of a long-term trend in the mean, one can treat this trend line as what’s “typical”, and so ask questions about how long it will take the system to return to the long-term trend line following a perturbation, etc. That’s what macroeconomists do. For instance, US real per-capita GDP has grown at a long-term annual rate of 1.87% since at least the 1870s (figure), and so macroeconomists focus on perturbations away from, and recoveries to, that long-term trend line. I rarely see this done in ecology. Perhaps because there aren’t many ecological variables for which non-stationarity takes the form of long-term growth or decline?
Ok, that was a very long digression about non-stationarity. To wrap up, I want to return to the question I asked at the beginning: what are the biggest understudied topics in ecology? There was a time when “the microbiome” might’ve been a good answer, but not anymore. Same for “positive species interactions”. So, what’s your answer? Looking forward to your comments.
*Or, you know, not.
**Although the difficulty of addressing a question is not a fixed constant. Technological advances, creative insights, model systems, big grants, etc. can all make
easy tractable what otherwise would’ve been intractable.
***One big practical challenge for studying a non-stationary world is figuring out whether you’re in one or not. Technically, stationarity is a property of the process that generated your data. Your data are merely a (finite) realization of that process, and it can be difficult or impossible to estimate the properties of that process from your finite data. Simple illustration: if you flip a coin four times and it comes up heads every time, you can’t infer from that whether the coin is fair or not; it’s not enough data to go on. Disagreement about whether we’re in a non-stationary world crops up often in ecology and evolution. For instance, it’s the crux of the debate about whether there are ecological limits to continental-scale species richness. I leave it to you to argue about what, if anything, the practical difficulty of distinguishing stationary from non-stationary processes implies for whether or how much we should worry about non-stationarity. I could see arguing this in at least three ways…