kurtze@plains.NoDak.edu (Douglas Kurtze) (10/31/90)
Does anybody out there know about (or know where I can find out about)
CONTINUUM Lotka-Volterra population models? By "continuum", I mean that
you take the usual many-species model,
dP_i/dt = P_i Sum c_ij P_j
and let the species indices i and j be continuous variables (so the sum
over j becomes an integral with a dj). I can interpret this by letting
the indices label slightly different phenotypes, with P(j)dj being the
number of individuals whose types are within dj of j. The variables
i and j can be multidimensional.
I encountered the continuum version of this equation a few years ago in
a completely different context -- studying the shape of flames (chemical
ones, not the ones you get here ;-) ) -- and realized that the results I
got could have some application to population dynamics.
Respond by e-mail or post; I do read this newsgroup. References would be
much appreciated!
Doug Kurtze kurtze@plains.NoDak.edu
Physics, North Dakota State
"Patience is its own reward" -- Flann O'Brienkurtze@plains.NoDak.edu (Douglas Kurtze) (11/01/90)
Gaffe!
In message <6514@plains.NoDak.edu>, in the heat of the moment and the
spirit of late October campaigning, I wrote the Lotka-Volterra equation as
* dP_i/dt = P_i Sum c_ij P_j
Of course, it should be
dP_i/dt = r_i P_i - P_i Sum c_ij P_j
Apologies to anybody who will have gotten confused and/or corrected me
before getting this message. With this correction, the rest of my
previous post is correct.
Doug Kurtze kurtze@plains.NoDak.edu
Physics, North Dakota State
"Patience is its own reward" -- Flann O'Brien