Charles Paxton wrote:
> [...] I
> have a curve of cumulative number of species over time (i.e. time, years in
> fact on x). For theoretical reasons I want to fit a two parameter
> rectangular hyperbola of the form Y=(A*X)/(B+X) where A and B are
> constants. [...]
> The problem is that as I see it is that my Y variables are not independent
> of each other as obviously cumulative scores build on each other.
Do I understand correctly that the *observed* number of species
(presumably a random variable) in each year (i = 1, 2, ... N) is s1, s2,
... sN. You add them up to form Yi = s1 + s2 + ... si. Now, according
to some theory, the *cummulative* number of species Yi (i = 1, 2, ... N)
increases with time according to the rectangular hyperbola, Y = f(X, {A,
B}). Correct?
If I understand this correctly, then why not avoid the problem (i.e.,
lack of independence among the *cummulative* data items) by fitting the
*observed* number of species to the derivative function, Y = df(X, {A,
B})/dX ? It should be just another rational polynomial:
Y' = A B / (B + X)^2
BTW, it's kind of interesting that the *integral* of some dynamic
process should end up looking like a rectangular hyperbola. It isn't
clear to me what would the physical meaning of A and B in the
differential model.
Are you sure you don't want one of the conventional growth models? I am
thinking about Chapter 4 and 5, dealing with growth models, in the
"Introduction to the Mathematics of Biology" by Yeargers et al. (1996),
Birkhauser, Boston, pp. 98-153.
HTH,
-- Petr
_____________________________________________________________________
P e t r K u z m i c, Ph.D. mailto:[EMAIL PROTECTED]
BioKin Ltd. * Software and Consulting http://www.biokin.com
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