I’ve been attending a workshop on modelling cyclic population dynamics this week. Sadly, I can’t stay for the full workshop; teaching duties call. It’s been very interesting; here are some random, off-the-cuff thoughts. I emphasize that these are purely personal; I’m not speaking for anyone else at the workshop and no one else bears any responsibility for anything I say.
- Understanding cyclic population dynamics is one of those tantalizing problems that’s tractable enough to keep people (including both modelers and empiricists) working on it, but not so tractable that a solution seems like it’s just around the corner. For instance, one of the bodies of work I admire most in ecology is mechanistic modeling of cyclic population dynamics. I had thought that, for a few species at least, we had more or less nailed down what was going on. And perhaps that is true, for some value of “nailed down”. But for me, one takeaway from this workshop is that for even the best studied cycling species there are important details of the dynamics that we still don’t understand, at least not mechanistically. For instance, theorists keep thinking of plausible new biological mechanisms or combinations of mechanisms to explain many natural observations that I thought had already been well-explained. For instance, latitudinal gradients in vole cycle period might not be due to latitudinal gradients in generalist predation per se, but rather due to the interplay of generalist predation and breeding season length. As another example, to fully-understand many predator-prey cycles we apparently need a better understanding of adaptive behavioral changes of predators in response to changes in prey density (e.g., adding different prey to their diets). We may even need to understand things like individual-level variation, phenotypic plasticity, and maternal effects. And in many systems, apparently we don’t even know enough to make partially-specified (aka “semi-parametric” or “semi-mechanistic”) models an option (see Simon Wood’s work for background on partially-specified models).
- Figuring out the apparent collapse of cycles in many species over the last 10-15 years or so is the big issue on the empirical side right now. Many populations that used to cycle have suddenly stopped doing so. Lots of questions here. Are the cycles even collapsing? (i.e. Is the ecology of the system truly changing, or are apparent collapses just some sort of transient, or maybe a stochastic flip to an alternate attractor?) If they are collapsing, why? Is it for the same basic reason in different species or in different areas? And what will the consequences be? For instance, apparent collapse of cycles seems to be accompanied by collapse in mean density, so species are now consistently rare rather than cycling between being rare and being abundant. So one consequence might be increased risk of local extinctions (?) Lots of opportunities for theoretical and empirical work here. On the empirical side, one problem is lack of good long-term data from North America; most of what we think we know about collapse of cycles comes from Europe.
- On the mathematical side, the big question is the interplay of stochastic and deterministic processes, with lots of interest in phenomena like stochastic flipping between alternate attractors, and how you study those phenomena analytically. Also lots of interest in modeling stochasticity appropriately. There are lots of mathematical subtleties here, you can’t just stick a diffusion term somewhere in your model and be confident that it makes any sense, biologically.
- At the interface of models and data, the big question is whether there are reliable, generally-applicable diagnostics that you can use to check whether different dynamical mechanisms contributed to generating your time series. Lots of ideas bandied about, some of them totally new (at least to me), but no firm answer. Certainly nothing like a general “workflow” or “checklist” that you could follow to diagnose the processes that generated your data (even assuming you had sufficient data, which we often don’t). Looking at power spectra seems promising, as there’s often an interpretable mapping between peaks in the power spectrum of a time series and the processes that generated it. Of course, one limitation here is that you can’t have a short and/or non-stationary time series (e.g., recent collapse of cycles). My clever (?) idea was whether you could turn the approach of Ives et al. 2008 into a general strategy. They demonstrated the existence and importance of alternate attractors in part by showing that a mechanistic model including alternate attractors could fit the time series data, while more flexible phenomenological models lacking alternate attractors could not. Can you use that as a general approach? To demonstrate the importance of factor X, build a really flexible phenomenological model that is capable of fitting just about anything–except that it lacks factor X and so can’t fit data generated by a system in which factor X is present. For this to work, factor X has to be the sort of thing that a system, or a model of that system, either has or doesn’t. Perhaps this could work for time lags? Or for exogenous forcing? I dunno, I’m totally just tossing out ideas here.
- The general trend in statistics towards explicitly modeling all of your sources of variation in a complex hierarchical model (which sometimes is essential, but sometimes just amounts to statistical machismo). It seems like there’s a similar trend in theoretical modeling, towards more complicated nonlinear stochastic models that have to be analyzed numerically rather than analytically. On the one hand, that should please empiricists, because a big motivation for building such complex models is that real biology seems to demand it. On the other hand, if you as an empiricist find it hard to understand linear deterministic models, you’re really going to find nonlinear stochastic models rough sledding!
- One gap in the workshop is that nobody here is working on stage-structured cycles, sometimes called “generation cycles” because they have a period of one or two generations of the species concerned. That’s not a complaint; no 20-person workshop can cover everything. You have to have a focus.
- While people like Lindenmayer & Likens are worrying about “real” ecology getting replaced by mathematics and meta-analysis, and people like E. O. Wilson are treating math as a routine technical exercise that you can always find somebody to perform for you, the rest of us are getting on with the job of doing science using all the tools available to us. This workshop was a mix of mathematicians, ecological theoreticians (not the same thing as “mathematician”!), and people who do various mixes of data collection and modeling. Everyone is interested in the same big questions, understands and appreciates where everyone else is coming from, is having productive conversations that hopefully will lead to a review paper, etc. It’s funny, we talk a lot on this blog about whether ecology consists of opposing “camps”, often backed up by the anecdotes everyone has about getting bad reviews from people who don’t see any value in their approach. But you never actually meet anybody like that–at least I don’t! I mean, when I go to conferences or workshops or give visiting seminars or whatever, I meet all sorts of people doing all sorts of work. And I never meet anyone who questions the value of mathematics, or microcosms, or field experiments, or natural history knowledge, or meta-analysis, or whatever. Even when I disagree with people on some matters, and even when those with whom I disagree do totally different science than I do, there’s almost always a lot we agree on, so that we can have a perfectly productive and professional discussion about our disagreements. So I dunno, maybe the perception of ecology as consisting of opposing “camps” arises from people naturally tending to remember their rare negative interactions with someone from a different camp, and forgetting about all the positive interactions they’ve had with people from different camps?
- Totally random, navel-gazing thought which you may want to skip: it occurred to me that I have no outstanding skills or technical knowledge. Here I am, at a workshop in mathematical biology, despite knowing very little math, at least compared to most people here. I mean, I got the gist of every single talk, and in some cases was at least passingly familiar with mathematical concepts (like Ornstein-Uhlenbeck processes) that were unfamiliar to at least some of the mathematical types in the audience. But getting the gist is a looong way from actually being able to do math yourself. And on the empirical side, I don’t know a massive amount about any natural system. I just grow bugs in jars. Don’t get me wrong, there’s a lot of value, and at least a bit of technical cleverness and “feel for the organism”, that goes into growing bugs in jars. But it is still just bugs in jars, which is the whole reason I work in the system–it’s more tractable than, say, lynx and hares. And while it didn’t come up in this workshop, I’m not really a statistical expert. And I’m a crap natural historian. My biggest skills would seem to be either fairly nebulous things like “ability to ask good questions” or “ability to draw analogies“, or else things that aren’t really “skills” at all, like “willingness to work in a tractable model system” .* I’ve had this thought before. Perhaps “knowing a bit about lots of different things” counts as a “skill”?**
*I leave it to you to decide if “blogging” counts as one my biggest skills. 🙂
**Yes, I did just ask whether “dilettante” counts as a “skill”. 🙂 Also, I emphasize that these remarks about my skills are purely self-directed. I am not implying that others at the workshop only have technical skills or technical knowledge! Nor am I at all downplaying the value or importance of the skills that I personally lack! Everybody has their own strengths and limitations. I’m just commenting on what seem to me to be my own strengths and limitations, and how I find it easier to articulate my own limitations than my own strengths.