Last year, I blogged about “Correlation and process in species distribution models: bridging a dichotomy”, a paper that we published in a recent special issue of the Journal of Biogeography.
Broadly speaking, the paper discusses properties and issues around different approaches to modeling species distributions, with a focus on the extent to which those models merely describe associations between species and their environment (correlative) as opposed to including explicit causal mechanisms (process-based). It is, among other things, the fact that we concentrate mostly on this particular aspect what I interpret as the main objection of a correspondence by Kritikos et al., which was just now published alongside with a response by us.
Both comments are fairly short, and I don’t want to repeat the points made in detail here (although I’d be happy to comment on them). Much of the discussion seemed to circle around words, classifications and focus. I can’t say that I was particularly persuaded to deviate from the angle taken in the original paper, but I think that’s fair enough, I usually find it really useful as a reader to also get a range of opinions on a topic, which a single paper simply can’t provide.
Some other aspects of the exchange, however, are maybe more among the things on which some agreement would actually be useful, although I wasn’t sure whether we reached it. One particular aspect I want to highlight is the often repeated claim that mechanistic models are in some sense intrinsically superior and better at extrapolation than correlative models due to their mechanistic nature. I think much could be said about that already (see e.g. here), but the additional question that pops up in the context of this paper is: what about calibrated mechanistic models? Kritikos et al. state that:
Fitted process-based models such as CLIMEX and STASH (Sykes et al., 1996; Sutherst et al., 2007) are able to draw on the strengths of both correlative and mechanistic modelling paradigms. They allow the modeller to inductively fit ecologically relevant range-limiting functions to species distribution data in a similar manner to many correlative methods.
Admittedly, we make a similar point with a more Bayesian twist in a recent paper on Bayesian calibration of process-based models, where we write in the conclusions:
The importance of prior knowledge about parameters, and also about model structure, however, will remain an area where DVMs differ significantly from correlative modelling approaches. We therefore think that inverse modelling methods will not, as one might fear, reduce DVMs to merely a ‘very complicated’ version of a correlative model that is blindly adjusted to data.
While the latter two statements do express what one would hope for as a process-based modeler (and from a Bayesian viewpoint, I maintain that this hope is, in principle, justified because mechanisms are simply another word for strong prior information, which should improve the inference), I think it is not unreasonable to take a more critical look at this question, which we do in the response to Kriticos et al.:
Fitted process-based models may create an illusion of predictive power by reference to their mechanistic underpinning, but if the process-based model structure and independent ecological knowledge do not sufficiently constrain potential outcomes, fitting the model parameters to observed species distributions may produce drawbacks in terms of transferability and extrapolation that are similar to those in purely correlative models. Therefore, we maintain that fitted process-based models lie somewhere in between completely correlative and completely forward process-based models.
In the end, it all boils down to structural rigidity and correctness as well as to model sensitivity. Do we have sufficient control about these in practical situations? Not sure, but I think it’s a point deserving discussion at a time where the statistical and the mechanistic camp are getting ever closer together through the possibility of more complicated statistical model structures on the one hand and the possibility to statistically fit mechanistic models on the other.