Posted by
Russell Standish on
URL: http://friam.383.s1.nabble.com/Diversity-and-Stability-in-Food-Webs-tp520801p520811.html
On Thu, Nov 10, 2005 at 09:04:06AM -0800, Tom Carter wrote:
>
> But also, back to the original prompting email, I've just been
> reading a fun little book -- "Ecological Orbits - How Planets Move
> and Populations Grow" . . . I recommend it (although I don't
> necessarily agree with all of it). The authors (Lev Ginzburg and
> Mark Colyvan) are pushing for a transition beyond the Lotka-Volterra
> regime of population modeling (their current fave is something they
> refer to as "maternal effects"). They argue that it's time for a
> "Newtonion revolution" in population modeling, largely in the sense
> that they think we should start using second order difference /
> differential systems in our (analytic) models. For example,
> classical Lotka Volterra, while nonlinear (with "quadratic" terms) is
> still a first order system. They argue that we should be looking
> more at the second derivative of population (i.e., rate of change of
> population growth rate) . . .
>
> Anyway, it's a fun, quick read . . .
>
> tom
But any second order differential equation is just a 1st order
differential equation in a higher dimension. If Ginzburg and Colyvan
are really arguing for an increase in the order of differential
equation, then they're arguing for a case of fetid dingoes kidneys.
OTOH, of course there are extensions to LV that need to be followed up
- the functional response terms Roger mentions in the next post -
as well as a hell of a lot about LV we don't know about.
Cheers
--
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