How critical is calculus...

[Bryan Hamilton]

...to a population biologist?

I have some calculus background, but absolutely no ability to apply it. As I move down the wormhole into population biology, is re-learning calculus a useful way to spend my time? Reading through some of the big textbooks, I notice that there is a lot of calculus. Can I skip really understanding those portions, and still make useful inferences about wildlife demography?

[cooch]

...to a population biologist?

I have some calculus background, but absolutely no ability to apply it. As I move down the wormhole into population biology, is re-learning calculus a useful way to spend my time? Reading through some of the big textbooks, I notice that there is a lot of calculus. Can I skip really understanding those portions, and still make useful inferences about wildlife demography?

I tell all my students the same thing: minimally, one course in calculus, one course in linear algebra, one course in probability theory, and one course in programming at something higher than the level of an Excel macro. Virtually all of my undergraduate advisees (official or otherwise) have gone this route, and most I think would report that it has served them well (here at Cornell, in the 'concentration' where I teach 4 courses, most of the students take 2-4 of these courses, supplemented with the math classes at least. A few manage to squeeze in the programming, with somewhat fewer than that the probability theory).

You can always 'make inferences' without understanding the underlying 'technical bits' (which often have a basis in math and statistical theory), but you'll often make better, wiser inferences if you understand what's going on 'under the hood'. This is why the better books show you the math, and provide near-complete explanations of 'why things work', not simply 'here is what you do' -- which in part is what motivated inclusion of same in the MARK book (see for example, the appendix on the Delta method). Whether or not the MARK book has been successful in meeting that intent I'll leave for others to decide.

It is worth noting, though, that 'population biology' -- in the literature -- can be completely devoid of the issue of 'parameter estimation' -- have a look at any issue of 'Theoretical Population Biology' for good examples of this. It is also not hard to find papers in other journals where the who focus is parameter estimation, with little connection of the end result of those efforts to any sort of prospective dynamical modelling exercise. I would argue that to have any support to the claim of being a 'population biologist', you need some of both.

My 2 cents.

[gwhite]

If you can't understand the necessary assumptions that are being made, then you are unable to objectively assess the reliability of the inferences.

So I echo Evan -- don't assume a black box is legitimate. Understand the mathematics, or you'll get out on a limb that will be sawed off.

Gary

[bacollier]

Just jumping in with a thought here (and I am by no means a true statistician/mathematician like many on the board are), but in addition to what Evan/Gary said, I would add that the 'best' class that I ever took that helps me almost daily (doing whatever it is I do ) was a graduate level Categorical Data Analysis class, one that does the theory not just the program based analysis. Cause, although you get the math/methods in the earlier classes they mentioned, that class covered in detail (in my case at Arkansas) all the link functions in the exponential family and the associated MLE theory that goes along with how they all work. I did not make the link back then (no pun intended), but I see regularly now how CDA I learned is extremely related to what we do in parameter estimation now.

my $0.02/2 thought.

\bret

[Bryan Hamilton]

Thanks for the replies. I greatly appreciate the advice.

Understand the mathematics, or you'll get out on a limb that will be sawed off.

Ouch. First step for me is to drop the saw.