These past few days, I have been re-reading a paper that stimulated me a lot during my PhD. And I found myself wanting to dig in a little bit deeper into the mechanisms of one particular result. Since this paper was published in the 1990s, I never even attempted to look for the code, and started re-writing my own implementation. It made me realize a few things along the way.
There is a very important family of models in ecology based around describing the flows and fluxes of quantity across “boxes”. This can be biomass across species, alleles across spatial patches, population size, individuals across age classes, etc. Almost all of these models are based on ordinary differential equations, and they use parameters to express ecological processes. And the more quantities you want to model, the more parameters you need to link them together. As a result, complexity of the models often increase in a non-linear way with regard to the size of the problem.
I remember the first time I have been surprised by a model. I was working on the conditions under which a mutualist can protect its host from a pathogen, and in particular whether the mutualist can persist or will be displaced by the pathogen (unless there are multiple populations connected by dispersal, the answer is no). What surprised me was how, in the end, the answer to this question depended on the relative value of three parameters. Of course, nothing in modeling should be surprising, because the model encompasses the entirety of its own rules, and so of course the answer is in here, waiting to be found. But where do the models come from?