Howdy!
First, let me apologize for drastically misunderstanding BIll Silvert's
background. My own pre-ecology background is similarly complicated:
thirty-plus years of "hard systems" engineering and a great deal of
modeling--including communications theory (per Shannon, et al.),
communications network theory (per nobody worth naming), and a few other
esoteric odds and sods.
I'm glad that Bill and a few others caught the intent of my comment
about Lotka-Volterra models. The quotation from MacArthur, "Every
mathematical model is a lie -- but one that hopefully allows us to
glimpse a bit of the truth." is something I should have included. And
the comments about models being "for insight, not prediction" are also
close to the point.
The reality is that we use models _both_ for insight and prediction,
with varying degrees of success for both purposes. This is nowhere more
evident (to me, at least) than in my own present research.
I also think Jane Shevtsov's comments and book recommendations are very
much on point. But I still believe, for a general program of
development of new ecologists in general and new post-baccalaureate
ecologists in particular, that we need to emphasize the maths (and
algorithms) of models--including I-calc, D-calc, diff-EQ, Markov methods
(alias Leslie methods), Monte Carlo methods and GOK what else.
Having a decent background in matrix math (generally) and
transition-probability (Markov, etc.) approaches (particularly), the
first time a population-ecology prof. talked about a Leslie age-stage
matrix, my only questions were about why we (apparently) didn't include
some of the "not strict sequence" possible transitions. This was while
very most of my classmates were struggling with the basic ideas of how
matrix math worked. Having a background in discrete-unit models I had
no problems with Gillespie-discrete models other than getting around
some of the limitations imposed by narrower terminolgy used by the
ecology professor. I could go on...
Our school of ecology offers a good number of courses which teach and
use maths-applied techniques for ecologists, including a very good one
aimed directly and almost solely at "population modeling"--yet few
students on M.S. or Ph.D. track take many of them, usually just one.
That is half the problem. The other half of the problem is that these
courses mostly do not teach the _math_ of the math that is being applied
so it can be very difficult (I have seen it being very difficult for my
classmates) to know how to transfer an underlying approach from the
"kind" of problem where it was learned to some other problem.
I do not know where a complete answer lies, if there is one, generally
or specifically, to Bill Silvert's original question, but I believe it
lies somewhere in the vicinity of teaching more breadth of "appliable
maths" at the front-end of graduate or undergraduate studies. I am sure
that this discussion has helped me bring some more thought to the subject.
Regardz,
Ken
--
Ken Leonard, Ph.D. Candidate
The University of Georgia
Odum School of Ecology (Bradford Lab)
517 Biological Sciences Bldg.
Athens, GA 30602 US
"Any man who afflicts the human race with ideas must be prepared to see
them misunderstood."
-- H. L. Mencken
[email protected], [email protected]
http://kleonard.myweb.uga.edu/
1+404.307.6425
