The table below lists the goals of mathematical modelling as described in three books and one journal article with respect to my list.* For each reference, when an item from my list is mentioned, I provide the page number, section, or chapter where the mention is made.
Levin 
Caswell 
Hilborn 
Haefner 
Otto 

1. Quantitative prediction 
p424@ 
p34 
Ch 4 
1.3.3 

2. Qualitative prediction 
p424 
p34 
Ch 3 

3. Bridge between different scales  
4. Parameter estimation 
1.2 (2.) 
1.3.2; 1.3.4 

5. Clarify logic behind a relationship 
p424 
p34 
1.3.1 

6. Test hypothetical scenarios 
p424 
p34 
1.2 (4.) 
1.3.3 

7. Motivate test/experiment 
p424 
(6) p38 
1.3.1 

8. Disentangle multiple causation  
9. Make an idea precise, integrate thinking 
p424 
(4) p38 
1.2 (3.) 

10. Inform data needs 
1.2 (1.) 

11. Highlight sensitivities to parameters or assumptions 
(3) p38 

12. Determine the necessary requirements for a given relationship 
(2) p38 

13. Characterize all theoretically possible outcomes 
(1) p38


14. Identify common elements from seemingly disparate situations 
p424 
(2) p38 

15. Detect hidden symmetries and patterns 
p424 
References
Levin (1980), Mathematics, ecology and ornithology. Auk 74: 422425.**
Caswell (1988), Theory and models in ecology: a different perspective. Ecological Modelling 43: 3344.***
Hilborn and Mangel (1997), The Ecological Detective. Princeton Monographs.
Haefner (1996), Modeling biological systems: principles and applicaitons. Chapman and Hall.
Otto and Day (2006), A biologist’s guide to mathematical modeling in ecology and evolution. Princeton University Press.
Footnotes
*Please feel welcome to suggest references to be added or to disagree with the placement of items in the table.
References suggested by **lowendtheory and ***Pablo Almaraz during comments on the ‘Crowdsourcing’ post at the Oikos blog.
@Although Levin advocates for the derivation of qualitative models as these rest on firmer axioms.
Very cool idea…would also be neat to see how mathematical biology is represented in some of the common Ecology textbooks. E.g. Krebs, Smith & Smith, Molles, etc.. Might be a good thing to do in order to stimulate greater coverage of the topic in introductory materials.
Thanks. I think it’s interesting to, even among the mathematical biology books, how the philosophy side of it is tackled. Haefner is quite daring in this regard, Otto & Day mix it up, and Theoretical Ecology by May and Maclean don’t really talk about it at all. I’m not sure of the answer to the intro ecology textbook question, but it would be worth a look. My favourite is Begon, Harper, Townsend, but that’s because there’s a lot of theory in there!
Excellent summary.
In your ‘list’ post, you mentioned putting together a Venn diagram. I’d like to suggest piecing both that list and this table together with a mapping program like VUE (from Tufts University). You can easily link references, categorize, and connect your modelingmotivations with it.
Thanks, that sounds like a fun idea. I’m planning to revise the table once more (after looking at some more books) and then I’ll have a go at the diagram after that.
Pingback: Why do mathematical modeling? « Oikos Blog
It seems that #3 could fall into the same trap described by Helen (comment: Jan 4 2012 post) e.g. “…brush over things vaguely in a verbal description”. I think she was highlighting the need to make assumptions explicit. Don’t get me wrong, I think it makes sense to formulate a model to gain insight into an adjacent scale, but one would need to be cautious about the model application if it does not include assumptions at the scale of inference. I would argue the assumptions could be different for different spatial scales (as usual, it depends). It seems that the path of formulating modeling goals, objectives, and avoiding pitfalls can be circular… or at least each entry on the list can be intertwined with another. Oops, this is off the path of ‘just simple enough’
Thanks Rich. I can see your point regarding assumptions possibly not holding across different spatial scales. The point of contention seems to be not whether it is possible to construct multiscale models, but is it reasonable to think the assumptions hold across spatial scales. I am thinking more broadly than just spatial scales, though, in my example my scales are the individual and the population.
I told Joan Strassman she needs to read this post!
Striking that even a very smart empiricallymindedbuttheoreticallyinformed biologist like Joan has a rather limited view of what theory is for:
http://sociobiology.wordpress.com/2012/06/19/thetroublewiththeory/
Pingback: False models are useful BECAUSE they’re false  Dynamic Ecology
Pingback: What are simple models for? Two mustread views from economics  Dynamic Ecology
Pingback: On progress in ecology  Dynamic Ecology