…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.

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.

Via Twitter:

Dynamic Ecology: Writing your lectures for you since…well, just now, as far as I know. 🙂

Via Twitter:

Aside: I said a year or two ago that we weren’t seeing much sign that people were commenting on our posts on Twitter instead of here. But now we’re seeing it. Which is a bummer. And a pain; it’s annoying to have to keep copying tweets into our threads so that we have a record of the discussion about our posts.

Maybe there is some kind of WordPress widget that could display not only Dynamic Ecology’s twitter feed but the comments associated with direct replies/retweets? e.g. https://dev.twitter.com/web/embedded-timelines/search

That would be handy! Not sure if there’s anything out there we could use. We’re hosted for very cheap on WordPress.com (not WordPress.org), so we can’t fully customize the blog and have access to only a limited number of widgets. I’ll look into it, thanks for the suggestion.

Ah, right, the hosting fees would be a constraint. But if it’s of interest, here’s a perfect example of what I meant (found while winding through the recent internet kerfuffle about the top 100 ecology papers article/gender bias in ecology, etc). There’s a “tweets referencing this article” section at the bottom: https://www.biorxiv.org/content/early/2017/11/16/219824

Not sure if it would do much to address the issue of merging conversational flow between the twitter and blogging interfaces though!

That kerfuffle is also an illustration of why I’m not sure I *want* to automatically bring all twitter conversation about our posts onto the blog! I think blogs and the associated moderated comment threads are just better for productive discussion of hot button issues than Twitter or other social media. Twitter and other social media are designed to eliminate (or at least not reward) nuance and elaboration. And they make it hard/impossible to filter out personal attacks or dial down the temperature when a discussion starts to get heated. Finally, people who don’t want to get into shouting matches tend to self-select out of participating in social media arguments, leaving the field to be dominated by the most aggressive, passionate people. I haven’t dug much into the social media kerfuffle over that ‘top 100 papers” paper, and I’m sure a lot of it is fine, but what little I’ve seen linked to on blogs hasn’t encouraged me to dig further. I’ve seen groundless criticism of the authors’ presumed motives, for instance.

Where do you place the “Metabolic Theory of Ecology”?

It certainly does fit regressions [ body size]…but many folks put these regressions into dynamical models, Indeed Rob Peters original arguement was that the body size regressions were useful in that way.

Fishery mgt models are dynamical , but most involve regressions; estimates of mortality are the biggest, but so are body size growth functions.

All of behavioral ecology is based on normalizing selection, which forces us to focus on the tradeoffs; it also assumes population stability[ implicit].

I am having trouble getting my head around your distinction as fundamental.

ric

Good question.

I think the answer depends on which bit of the MTE you mean. There are bits I’d definitely classify as regression models. The bits that basically just show that some allometries can be predicted from other allometries (or other allometries plus some auxiliary assumptions).

But the original WBE optimality model of branching circulatory systems to explain the metabolic rate-body size allometry isn’t really classifiable in my framework. Lots of optimality models aren’t. Ditto for, say, biomechanical models (e.g., of gait).

Re: fisheries model, yes, I’d call them dynamical, but if you wanted to say they straddle the fence because they have regressions as a key component, I wouldn’t argue with you.

Re: not seeing my distinction as fundamental, fair enough. I freely admit I can’t provide a lot of evidence that it’s fundamental; just my own admittedly-anecdotal gut feeling. Possibly, it’s just one cross-cutting distinction among many that one could draw among ecologists, and no more important than several others.

I share your gut feeling, and do indeed think it useful to distinguish dynamical thinking from… other. But they are so,so entangled.

Consider life history theory. Does one assume directional natural selection, using the machinery of quantitative genetics, to build/test an evolutionary dynamics…or does one assume normalizing selection, captured by a fitness optimization model where one focuses on the constrains. And always lurking behind even the optimization is …what does one assume about the population dynamics? And does it matter for the predicted outcome? The predictions of ‘optimal life history’ are usually very different for non-growing pops vs growing [ or maybe fluctuating?].

Of course, my hobby horse, sex ratio theory has it all; and in the 90s there were several studies of the evolutionary dynamics of sex ratio. Under natural selection acting on initial biased population sex ratios…. well within a few generations the pop sex ratio moved to 1:1, as predicted by theory. Most of us assume normalizing selection from the get go, and use the ESS approach to study sex ratio, including situations where population have fancy dynamics; sometimes it matters, sometimes it does not.

I think some fisheries models of density dependence are a good illustration of the distinction. Fisheries folks often do statistical analyses of density dependence using models where the response and predictor are both states (stock and recruitment, abundance now and abundance in the future). Lots of other population ecology folks do statistical analyses of density dependence using models where the response variable is a rate (r). Of course, they’d often both be using regression for these kinds of analyses, so maybe they’re both straddling the fence?

Via Twitter:

Provocative thesis! I’ve two main comments which I will split. And yes – I voted “both” so I am definitely a fence straddler.

Comment #1 (related to above comment on metabolic scaling and Ric’s comment on fisheries management). Where do you put people who have a rate (dN/dt) as the y-variable in a regression but then are very regression oriented – throwing in multiple explanatory variables and seeing how much they can explain. Some of my favorite studies in population ecology come out of England (Lawton, Beddington, Sibly, the entire edited volume by Sibly on Wildlife Population Growth Rates) and are of exactly this form. Metabolic rate as the dependent variable is another example. Various ecosystem work (rates of decay of leaf litter as a regression).

Treating dN/dt (or some other rate of change in some other variable) as the dependent variable in a multiple regression is regression thinking to my mind.

Comment #2 – “It’s not a distinction between theorists and empiricists.”

I think this is nothing more than a distinction between theorists and empiricists. As you can note one can be a field ecologist motivated by theory or a theorist motivated by data and hence a blend. But these are the essence of the two approaches. Theorists build abstract models decoupled from data. Empiricists go out to see what nature has to tell them.

This distinction is ancient (and maybe even more general than the theorist/empiricist distinction). It goes back to Plato vs Aristotle, Descartes and the continent vs the British Empiricists (Bacon, Locke, Hume). Induction vs. deduction. Sharon Kingsland’s history of ecology traces this as the fundamental tension throughout the 100+ year history of ecology.

So I think what I’m saying is the distinction is not novel, and does align with an existing faultline (albeit there are always straddlers – many by the appearances of the poll), but I actually like the way you phrase it a lot. You have operationalized the distinction very effectively and productively as I think many of the comments and tweets show.

I disagree that the distinction I’m drawing maps neatly onto a distinction between people who are decoupled from data vs. people for whom the data comes first. But yes, the two distinctions may have some positive covariance.

I agree with you that Jeremy’s categories seem to map fairly well on to an empiricist-theorist divide, but not perfectly. For example, consider Gremer and Venable’s Mercer Award-winning paper on delayed germination as a bet-hedging strategy — they used tons of field data to parameterize a model of the dependence of long-term fitness on delayed germination in the context of other aspects of life history and competitive ability. In the end, they had to run regressions to test their hypothesis, but my feeling is that paper is much more grounded in understanding the dynamical processes that make it useful to delay germination. But it’s not a theoretical paper.

Jeremy’s comment reminded me of what my economist friends talk about when they describe reduced form vs. structural models. In a reduced-form context, you may often use statistics to estimate effects of things without necessarily putting an interpretation on what is the true process underlying that effect. When using a structural model, you want to parameterize a model that you do think underlies the process. Either way, you will probably want to use some empirical data (unless you’re an old-school DSGE modeler…) and will probably do some statistics, but the structural model doesn’t emphasize the centrality of the statistics in the same way. Of course, structural models require some theory-building, but I also don’t necessarily think this distinction maps cleanly onto an empiricist-theorist divide.

Yes, Gremer & Venable is a great example of an empirical paper based on dynamical thinking.

The example of reduced form vs. structural models is a very interesting one in this context. Not sure if/how that distinction fits into my schema. My first instinct is to say it’s a different thing (to do with different approaches to causal inference) that doesn’t really have to do with my schema.

@Jeremy — fair enough. I think I’d kind of lost sight of what the essence of the dynamical approach (rates of change in state variables over time) — but perhaps the reduced form vs. structural dichotomy, like the theoretical vs. empirical dichotomy, covaries strongly (along with maybe things like mostly inductive vs. mostly deductive reasoning, and perhaps some of the things you list as not *identical* to the distinction you make). It would be interesting to know whether there really is a strong correlation among these different variables, as I would expect, or not.

+1 theorists vs.empiricists. And of course, theorists need data and empiricists need models.

Nice post! I always refer to these two kinds as process- and pattern-oriented scientists. I definitely share Jeremy’s card-carrying membership of the dynamical modeling school, but what has always struck me in conversations with ecologists that are more of the regression school (the pattern-oriented one’s) is that they may start with presenting to me an interesting regression relationship that they have detected, but then go on and ask me whether I can formulate a model that explains the relationship. My guess is that most of us realise that patterns in the end emerge because of the underlying processes. The post effectively conveys the distinction between the two schools, but in my opinion they are also connected with each other.

Thanks Andre. And yes, the hope is that the two ways of thinking are complementary.

Via Twitter. I was waiting for someone to say this:

I hope that Don (and/or others who feel as he does) will stop by and comment to elaborate. I’d be very interested to hear more from them and I’m sure I’d learn a lot.

Via Twitter:

For the record, I never said that. In fact, I’ve said the opposite. For instance, quoting myself from this post (https://dynamicecology.wordpress.com/2014/02/17/on-progress-in-ecology/):

“I think ecologists have gotten better over time at linking models and data–that’s an area in which ecology has progressed.”

Anyone who wants to know what I think about the current status and rate of change in “quantitative” ecology vs. natural history/field biology/call-it-what-you-will is encouraged to read the following posts:

https://dynamicecology.wordpress.com/2014/01/28/stats-vs-scouts-polls-vs-pundits-and-ecology-vs-natural-history/

https://dynamicecology.wordpress.com/2017/09/13/ask-us-anything-the-demand-for-field-biologists/

Without wanting to pick on David or Don specifically, this is a small illustration of why I don’t tweet (except occasionally to joke with friends). A tweet-length summary pretty much inevitably distorts anybody’s views on any matter interesting enough to be worth having a conversation about.

I have to say I share your irritation about the drive by tweeters, and that’s just as a reader. Looks like it’s getting worse and worse. Do you guys tweet your blogs when you write them?

The Twitter account associated with this blog mostly just automatically tweets the titles and first few words of each post when the post is published. I occasionally also tweet myself from the account, mostly to joke with friends. It’s hard for me to imagine ever switching to discussing our posts on Twitter, though I experimented with it a little bit with this post.

I emphasize that I’m not annoyed at all with people who prefer to discuss our posts on Twitter. Everybody’s going to discuss our posts in the venue they prefer, and that’s fine. I wish everybody preferred to discuss our posts in the same venue I prefer, namely our comment threads. But if someday all discussion of our posts moves onto Twitter, well, that’s just life.

Ok, I take back everything I said earlier about how it’s a bummer that people are using Twitter to comment on our posts:

Feel free to call my posts “shockingly insightful” all you want, tweeps! 🙂

(In seriousness, it’s very nice to get such positive feedback, thanks so much!)

Via Twitter:

I think of machine learning as regression, and I don’t know what “data fusion” is. But as I said in the post, I also think it’s a mistake to confuse the techniques people use with their ways of thinking. I wouldn’t say that anyone who uses machine learning in their work must therefore think in terms of regressions. Just like how I’m definitely a dynamical model thinker even though my papers have more regressions of one variable on another than differential equations.

It’s useful to distinguish types of ecologists (including types that are ends of a continuum, as I said in the post) for the same reason it’s useful to classify anything. It helps summarize and make comprehensible the otherwise-incomprehensible variation around us. That all classifications (and other summaries) inevitably throw away at least a bit of information, and inevitably are at least slightly distorting in other ways, is true and important but is not an argument against using classifications (and other summaries).

I’ve spent some time digging into this, here for example is a paper looking at the inferences that species’ distribution models (i.e. machine learning ish methods) make when presented with data from a process oriented model of species interactions. Based on what i’d found i tend to think that machine learning methods are often interpreted as informing process but lean much more towards pattern. http://onlinelibrary.wiley.com/doi/10.1111/j.1600-0587.2011.07103.x/full

Another point of connection between these perspectives: bifurcation diagrams plot the equilibrium values of different ecological variables vs. environmental parameters — for example, biomass in different trophic levels vs. nutrient supply. In this case, the predicted Y* vs X results from the balance of dynamic processes and feedbacks, not just a simple assumed relationship.

Yeah, I see what you mean. But rather than that being a point of crossover I think of it more as an illustration of what distinguishes the dynamical modeler mindset from the regression modeler mindset. It’s just as you say: instead of hypothesizing or assuming an X-Y relationship based on some verbal model (or on relationships observed in previous empirical data, or whatever), a dynamical modeler derives the X-Y relationship from an underlying dynamical model.

Jeremy, I think this is a good post for new graduate students to think about. The basic point being is that a regression model is rarely the same as a process model.

(By the way, are you talking about differential equation models in general, or more particularly differential equations models over time?)

Ideally I’d want to model processes (over time), but more and more I am skeptical that we can scale lower level process models up to the ecosystem and community level (i.e. show me a dynamical ‘mechanistic’ (or quasi-mechanistic) resource competition model that can successfully predict the abundance and coexistence of all the plant species in a real-world community). We might need a different approach.

Is there a third option? What about models that are static in nature but that are clearly not regressions. I’m thinking of exotic constraints based approaches. What about this recent paper using sphere packing to successful model distribution of tree sizes in a forest? Perhaps this is a kind of regression but definitely not of the usual kind.

Taubert, F., M. W. Jahn, H.-J. Dobner, T. Wiegand, and A. Huth. 2015. The structure of tropical forests and sphere packings. Proceedings of the National Academy of Sciences 112:15125–15129.

I’m thinking of models that describe changes in state variables over time. A category that in my mind includes not just differential equation models, but difference equations, partial differential equations (e.g., for describing how a population spreads across a landscape over time), individual-based simulations, etc.

“i.e. show me a dynamical ‘mechanistic’ (or quasi-mechanistic) resource competition model that can successfully predict the abundance and coexistence of all the plant species in a real-world community”

https://www.nature.com/articles/nature24038.pdf. That was too easy. C’mon, gimme a hard one! 🙂

Good question where constraint-based approaches like MaxEnt fit (or not) in my schema. I’m not sure.

Jeremy the Usinowicz paper is great and definitely rate-based thinking. I agree it got “coexistence” in the sense of coexistence mechanisms. But abundance, I don’t think so that I could find.

You nicely highlighted some of the limits of the regression approach. But to me this is the main limit of the rates approach. Its really good at predicting rates and change. But precisely because it is so good at nonlinear feedbacks its really bad predicting what box-and-arrow diagram people call the stocks or levels. Its got the flows (rates), but the levels are determined by a combination of flows that are themselves nonlinear functions of the levels. That’s not super tractable.

As the commentor noted, I’ve never seen a model that predicts the abundances of multiple species in a community just from rates. They all somehow have to sneak in an empirically derived, circular parameter (K or rate of density dependence which is estimated by where the rate crosses zero which is still pretty circular). The forest models like SORTIE get a little more mechanistic by using light competition instead of density itself and having that drive growth rates instead of dN/dt directly. But these are still empirical curves that are more or less sneaking in the abundances (as does any empirically estimated rates of density dependence). IE rates of density dependence or closely related concepts are always empirically fit in a way that leaves the observed abundances more of a parameter than a prediction.

Joan Rougharden gave a philosophy talk once about how physicists were smart enough to only talk about changes (rates) and not make predictions about levels/stocks which is a doomed program. I don’t think its a doomed program – it just requires a regression approach. But I don’t think a rate approach is ever going to be able to be deeply informative about stocks or levels in a complex system (e.g. again predicting equilibrium abundances of multiple species in a community) without sneaking in a lot of information in a circular fashion.

@ Brian:

“But abundance, I don’t think so that I could find.”

Ok, how about Harpole & Tilman 2006: http://www.cedarcreek.umn.edu/biblio/fulltext/t1928.pdf. Although as an aside, it’s actually kind of surprising that R* can predict abundances, for reasons outlined here: https://dynamicecology.wordpress.com/2011/05/19/when-should-species-traits-predict-species-abundances/

Brian said most of what I wanted to say. Usinowicz is great and we need more papers that connect coexistence to the physical environment. But as Brian said I don’t know of many attempts using dynamical models to predict the abundances of all the species in a community, let alone how those abundances will change in response to a perturbation such as N addition, global warming, or CO2 enrichment. Look at all the data Tilman has collected at Cedar Creek and yet there are very few attempts even with that data to go from basic resource availability to predicting the abundances of all the species in the system. Without such a model how else are we to predict how communities will respond to environmental change? Aren’t predictions for these state variables exactly what society expects our science to be able to deliver? We might as well use a collection of single species population models with density dependence, in which case, what is community ecology?

I’m concerned we aren’t going to get much farther towards my objective using dynamical models parameterized population by population for the reasons Brian states. To avoid the circularity Brian mentions requires a ton of data about the environment and species’ physiological responses to the environment. This may be more data than we can hope to measure accurately for more than a few species per community. I think we dynamical ecologists (I count myself as one) need to be more open minded towards regression and statistical mechanics types of approaches for modeling state variables in complex ecosystems. Towards that end here’s a paper that I would argue deserves more attention:

Bertram, J., and R. C. Dewar. 2015. Combining mechanism and drift in community ecology: a novel statistical mechanics approach. Theoretical Ecology 8:419–435.

http://rdcu.be/yDil

Jeremy your post on Harpole and Tilman proves Brian’s point: From their paper “In these N-limited habitats, species abundance ranks correlated with their predicted competitive ranks [R*s]” The operative word their being “correlated”. From my scan of that paper, they did not use the dynamical model to predict the abundances directly. That would require knowing the per capita competition coefficients for all the species in the community. Or knowing all the resources they compete for and knowing their R*’s as well as their resource uptake rates. As you know the dynamical model Tilman uses would predict that both Cedar Creek and Konza would be dominated by only one species if you only considered R* for Nitrogen as the only difference between species.

Ok, now I’m clear on exactly what you’re looking for.

In that case, Tilman 1977’s prediction of the relative abundances of 2 Lake Michigan diatom spp. based on lab-measured chemostat model parameters is the sort of thing you’re looking for. Though that’s just two species and its a prediction of relative rather than absolute abundances so I guess you probably wouldn’t count that either?

The Usinowicz model may not have been used to predict abundances, but I’m pretty sure it could’ve been (going by memory, would have to go back and check).

And there’s Adler et al. 2006, which parameterizes a model for the dominant 4 species of perennial grasses in a community and uses it to understand coexistence. The same model could be used to predict species abundances–you just simulate the model.

Yes – I had exactly the same reaction as akleinhessel to Harpole & Tilman. Again a great paper. But on the question of predicting abundance, they got correlations of magnitude 0.3 (i.e. r2=0.09) on an arithmetic abundance scale (abundance predictions across species really need to be tested on a log scale). Which looking at the graphs basically means their top 1/3 predicted species had 2 or 3 species that were the dominant species. Its not a really strong prediction of abundance.

I’ll give you Tilman’s diatoms. But in my mind that is the all time perfect storm for R*. It is based on silicon which is a really unusual and fully non-substitutable resource and it was only two species that were pretty different.

Yes I had that the same thought that Usinowicz (and Adler 2006) could have predicted abudnance but they didn’t. Maybe they just didn’t. But I suspect if it was great at doing that, they would have published that. Papers that predict abundance well have a habit of getting into Science or Nature because its a hard problem.

But really all of this is kind of avoiding the point. I’ll even stipulate you could throw out 3 or 4 more papers. But that is a drip in all of the papers in the world. Way, way below Type I error rates although the analogy there is not perfect.

So that’s not really a strong disproof of our point. Predicting abundances (or pools or stocks) in dY/dt models is very hard to do precisely because they involve lots of nonlinear feedback loops. It is not a strength of those models and never will be in my opinion.

And it goes beyond ecology. Hydrologists are much happier looking at flows into and out of a lake then they are at being asked to predict the level of the lake. They can project those flows in and out forward into change in levels from the current state (which is a big give to provide the current state) a little bit into the future, but it eventually goes wonky pretty quickly and they have much more long term accuracy on the flows in (flows out depend a lot on the levels). Its exactly the same as population dynamics doing well on predicting abundance a few years into the future from the current point, but not doing well far into the future. And not really having a theory of N* or Naverage beyond making it a parameter in the model.

Its not a knock on the dynamical approach. No method is perfect after all. There are certainly limits to a regression approach and you highlighted those rather niftily. I just think this is the main limit to the dynamic approach

This is a great post that is making me think a lot. So far it seems to me that categories that might not fit this axis are:

– physiology models (e.g. blood flow via Pouiselle’s law (sp?), leaf stomatal dynamics, etc)

– optimization models

– natural history

These are interesting exceptions. Should the dN/dt school be expanded to include physiology and optimization models and the regression end be expanded to include natural history? Or does that break it and decrease the value? I tend to think the models could be added to dN/dt without destroying the value. But I think natural history (a valuable and worthwhile pursuit) does not fit into the spectrum (e.g. just add to regression) without breaking it. Maybe this is a spectrum of quantitative ecology?

Another thought experiment what parts of ecosystem ecology go where? Much of ecosystem ecology is rate thinking but it often boils down to: a) flow box-and-arrow diagrams, b) putting numbers on those boxes and arrows (56.3 gt/C/year), or c) regression of various factors explaining the rates. I know you put dN/dt~x1+x2+x3 in regression, but I think it straddles and it seems to me a lot of ecosystem ecology is in this straddling category too.

Yes, there are large areas of work that don’t fit on my spectrum. I think you’ve identified several of the big ones.

I’m tempted to say that ecosystem flow diagrams are more towards the dynamical modeling end. I hesitate only because I know that some of my fellow dynamical modeling types don’t like that stuff. The Silwood mob are paradigmatic “dynamical model thinkers”, and they were no fans of the Odum school of ecosystem ecology (The Silwood Circle is good on this: https://dynamicecology.wordpress.com/2014/02/20/book-review-the-silwood-circle/). I guess that just means that some people who think in terms of dynamical models would define “thinking in terms of dynamical models” differently than I did in the post.

Worth mentioning that both approaches are examples of plotting lines on graphs, and many of us are uncomfortable with how to do this (i.e. what y=mx+b represents). I’d argue that we can make the two camps merge a bit more clearly by getting comfortable with this the connections between the regression models an dynamic models. I for one was blown away when someone explained to me that you can represent logistic growth as a straight line on a plot of per-capita growth versus density (as in Jeremy’s r-K selection post), and that more complex ecological models are often modifications of this (thanks Dominique Gravel). I was originally taught the regression version but this type of plot made it natural to move to the dynamic version.

Just to keep jeremy from having to self cite 🙂 https://oikosjournal.wordpress.com/2011/06/29/zombie-ideas-in-ecology-r-and-k-selection/

That’s interesting. Has me thinking back to an old comment of Brian’s in which he characterized MacArthur and Wilson’s classic island biogeography model as a regression model. Which to my mind it isn’t at all–it’s a picture of a dynamical model (which is still a dynamical model to my mind). dS/dt=cP(1-S/P)-eS is perhaps the simplest version of the dynamical model that MacArthur & Wilson’s famous crossing-lines diagram illustrates. (that dynamical model would be illustrated by straight lines rather than curved ones, because it makes both the colonization and extinction rates linear functions of island species richness S. But the difference between straight vs. curved lines doesn’t affect the model behavior in any important way.)

Ted Case’s Illustrated Guide to Theoretical Ecology is a *fantastic* textbook for teaching basic mathematical modeling with pictures of the math, like the logistic growth example you refer to. I teach from it and *highly* recommend it.

Still working my way through Case :). I can see the confusion about what counts as a regression model. To me what is going on is that dynamic and regression models just both happen to be math, and some of the simplest math that we can intuit rigorously is straight lines. Once we are comfortable there we can tweak as needed.

Great post, a couple of thoughts:

– I would not necessarily put together what you call simulation models (and what others call process-based models) with dynamical equations models. Simulation models allow the development of (potentially complex) algorithm while I have the feeling that with dynamical models, the modelers try to end up with closed-form solution to more easily explore, well, dynamic. I have little experience in this being a pure regression guy, but I have the feeling that simulation models are more flexible and require a different set of skills than dynamical models (basically computing skills vs mathematical ones).

– Another thought is in model lifetime, regression models are especially short-lived basically every single study will use a different model, dynamical models are long-lived all sharing some common theme like Lotka-Voltera elements. I would put simulation models somewhere in-between with some elements that might be pretty standard like the modelling of growth rate and with variability in what is modelled, what is assumed constant, what is ignored ….

– in terms of which questions are best approached by the different modelling methods, I would approach it from a data-angle. If the data have a complex structure and/or limited temporal resolution then a regression approach is the way to go. If the data come from planned experiments with careful design ensuring little structure and good temporal resolution then dynamical models are the best. Even if one could imagine fitting structure to dynamical models using Stan these days … So the data shape the appropriate approach and questions.

– The dynamics you mentioned were implicitly over time, what about purely spatial dynamical models or spatio-temporal dynamical models, are there any recent studies using or developing these models with ecological data?

” the modelers try to end up with closed-form solution”

Nah. Almost no dynamical model worth thinking about has a closed-form analytical solution. But I think there’s something to your broader point. People who prefer algorithmic simulations and people who prefer equations are distinct subspecies of dynamical thinkers.

An interesting open question for me is whether the increasing ease with which people can simulate stuff will make more people into dynamical thinkers. Can you become a dynamical thinker by learning programming instead of math? I’m not sure. Mark Vellend is one ecologist who thinks so, but I’m not convinced (see discussion here: https://dynamicecology.wordpress.com/2016/12/19/book-review-the-theory-of-ecological-communities-by-mark-vellend/)

Re: fitting dynamical models to data, yes, we’ve been able to do that for years now (since before Stan and other Bayesian software environments). A lot of the ecologists I most admire were pioneers of this (see here: https://dynamicecology.wordpress.com/2012/01/30/statisticians-meet-ecologists/) I’d like to see more of it because I think it’s a tremendously powerful approach. So I’d like to see it made easier so that more people would do it. The R packages for doing it (like pomp) are infamously hard to use. I used to use a *great* C++ package that Simon Wood wrote, that required no programming skill to use, but it’s long since defunct, I think.

Yes, I absolutely think of spatiotemporal dynamical models as dynamical models, sorry if that wasn’t clear. Like, e.g., partial differential equations describing the spread of a species over a landscape. There’s a *lot* of theoretical and empirical work on spatiotemporal dynamics in ecology. Not sure what you mean by “purely spatial dynamical” models, though. Do you just mean a model that describes, predicts, or summarizes spatial data from a single moment in time? Because I wouldn’t call that “dynamical”. I think of that as either regression thinking, or as falling outside the framework of this post.

I am also not so sure if ease of simulating dynamics will bring simulation-orientated ecologists towards dynamical-orientated models. After all why bother learning the maths if you can run 10000 of iterations and get what you want. Not to say that dynamical models won’t be as necessary and useful, just that math and computing skills are really distinct and that putting more emphasis on computing in study curricula will not bring a new generation of dynamical thinkers.

On fitting dynamical models to data maybe this is something for you then: https://github.com/stan-dev/example-models/blob/master/knitr/lotka-volterra/lotka-volterra-predator-prey.Rmd

On the purely spatial dynamical models I would still call this dynamical because we are describing the rate of changes of some ecological stuff among dimensions that are say the GPS coordinates. So I would put these dN / dxdy in the same categories as dN / dt.

@grumble10 — I think the key thing about the dynamical modeling approach isn’t the heavy-duty math, but rather the emphasis on rates of change over time (and the processes driving them). Many simulations over (simulated) time seem like a good example of that, because you have a series of steps that are executed from one time-step to the next.

I wouldn’t think of an Integral Projection Model as that related to regression. It’s just a dynamic model where the functional forms (or splines) are fit to data [regression]. It’s no more a regression than fitting time series data to a Lotka-Volterra model (which one can do via many different methods, some also involving splines, https://projecteuclid.org/euclid.aoas/1437397110). I guess we can call both straddling but I probably wouldn’t call either straddling.

An interesting question via Twitter:

I have no idea, so I’ll punt to our commenters. My first instinct is that the distinction I’m drawing is too advanced and technical to be all that relevant to scicomm. But I really have no idea.

I think that this distinction is echoed in economics. I hear economics commentators use the phrase “rates not levels” in the same way that we might use “correlation not causation”. In rates corresponds more or less to dynamic approaches and levels corresponds more or less to regression approaches.

With 141 survey respondents so far, I’m unsurprised that the most common response is “regressions”, followed by “both”, then “dynamical models”.

I confess I’m proud that only a few people picked “not sure” and only one picked “neither”. I am choosing to take the former as a sign that I wrote the post clearly, and the latter as a sign that the post picks out a real distinction that applies to ecologists quite generally though not universally. Do not burst my bubble. 🙂

I confess I don’t understand this tweet, because I didn’t realize that “disease ecology” and “epidemiology” were considered two very different things. Meghan, can you help?

I can’t comment on the differences here, but I always enjoy hearing about these distinctions between subfields which, to an outsider, sound like the same thing. Epi & disease ecology. Microbial ecology & environmental micro. Ethology & behavioral ecology. Are there others?

I think I know the difference between ethology and behavioral ecology. But the others, not so much.

Epidemiology uses a different set of default statistical models than infectious disease ecology. The mindset is entirely different too. Epi uses linear and regression-based models and is heavily concerned with appropriate handling of confounders and causal inference. Infectious disease ecology is grounded in nonlinear dynamics and can be a little more casual about causality.

I’m surprised so many ecologists would place themselves in the regression camp. Ecology is processes—that’s how I teach it, anyway. Our understanding of nonlinear dynamics and the frailty of correlation-based analyses is essential to progress and (and I’m totally smug here, I admit) makes our models way cooler than the defaults in epi and econ. I use regressions frequently, but I’m always thinking about when they might lead me astray.

I also don’t know anyone who prefers simulation to math. Usually we simulate when it’s more efficient given the number of state variables.

Thanks!

I think both apply, depending on context. Interestingly, I think in terms of dynamical models, but largely used regression approaches at beginning of my career because of lack of skills/training/collaborators. Also fyi – after I voted, the poll reverted to voting format when I visited the page for the second time…hope no unscrupulous voters are gaming the system!

Hmm, not sure what happened with the poll, it’s not giving me the opportunity to vote more than once.

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