I'm not quite comfortable with Ken's comments. First of all, I of course
agree that a good background in mathematics is really important. I have a
PhD in theoretical physics and my math skills were a great help in moving
into theoretical ecology. However a good background in science was more
important, and this is often lacking in mathematicians, with the result that
what they teach is not necessarily what the field requires. For many
mathematicians a good background for scientists means just calculus and
differential equations. Unfortunately this is not all there is to ecological
modelling, and in fact most models that use DEs use just one, the
uptake-clearance equation. This leaves the putative modeller with too much
knowledge about one approach and little flexibility.
The same is true of statisticians. Try to get one to teach your students
non-linear stats. For that matter, try to get them to teach propagation of
error.
Other disciplines have the same problem. When I was teaching physics I tried
to get the math department to offer a course in applied group theory, but
they refused and insisted that physicists only need calculus. I ended up
teaching the subject myself, and perhaps this would work best in ecology
too, have the "math" taught by a mathematically skilled ecologist rather
than a mathematician.
As for the statement that "the state of practice of eco-modeling beyond
simplistic (and wrong) Lotka-Volterra-like things is somewhat of a nasty
business" is partly true - the field is a mess. But the LV equations are
greatly underrated. Although they are a poor representation of most systems
from a purely quantitative point of view, most continuous models are
generalisations of LV systems and they are great for developing a
qualitative understanding of ecosystem dynamics. Ignoring LV theory can lead
to really stupid mistakes. For example, quite a few fisheries scientists
have tried to prove that mulispecies fisheries models are unnecessary
because the correlations between predators and prey are small. But that is
exactly what a LV model shows, and it demonstrates that only lagged
correlations are meaningful.
Of course LV models have to be understood. A lot of nonsense about
stability-complexity theory was written by mathematicians who used LV
networks without understanding their limitations. A little knowledge of
ecology is all you need to spot their errors.
Bill Silvert
----- Original Message -----
From: "Ken Leonard" <[email protected]>
To: <[email protected]>
Sent: Wednesday, January 21, 2009 6:28 AM
Subject: Re: [ECOLOG-L] Ecology Research Modeling Re: [ECOLOG-L] ecologcal
modeling
OK, another two pence worth!
I'm not sure I would use the word "uniform" in this context, honestly.
There are, depending on how one chooses to count (lumping or splitting)
somewhere between two and maybe a dozen significantly different
"species" of mathematical models applicable to systems of things,
including ecological systems (in the mathematical sense, not
ecosystems). There are also, of course, subspecies and strains and
lineages and variants beyond counting.
Each model species has unique characteristics and particular differences
and similarities when compared to the others. So each species has
certain correspondences and discordances when compared to the functions,
relationships and parameters of a particular system of
interest--ecological or otherwise.
Other than a focused text or course on "pop" or "ecosys" or "l-scape"
modeling from some author or professor with his/her own axe to grind,
own biases (pro and con), own pet paradigms, and own voids of knowledge,
I'm not sure you're going to find any "how to do" eco-modeling.
Ideally, you could find a good, broad modeling maths course in your
local maths department.
You might be better served by surveying the eco-theoretical literature,
then the microbial (really!) organismal-bio-theoretical lit, then the
general organismal-bio-theoretical lit to see what kinds of models have
been used to deal with problems mathematically similar to what you are
dealing with. Then go to your local maths department and your favorite
publishers for tutorials or texts dealing with the model approaches you
might want to use.
You might also check the user forums for your favorite (or
not-so-favorite) maths software such as Mathematica or MathCad or
whatever.
And, of course, when you get down to a small set of focused questions,
you can always post to this forum asking for anyone who is doing similar
work.
In spite of the fact that ecology is a theoretical, integrative,
meta-science, where all of us should be basically clompetent modelers,
the state of practice of eco-modeling beyond simplistic (and wrong)
Lotka-Volterra-like things is somewhat of a nasty business, really, and
(in my obviously not-so-humble opinion) is best approached by stepping
aside to learn the maths first, then returning to the eco-stuff.
Regardz,
Ken
