Path: utzoo!attcan!uunet!wuarchive!usc!ucsd!orion.oac.uci.edu!manderse
From: manderse@orion.oac.uci.edu (Mark Andersen)
Newsgroups: bionet.population-bio
Subject: Re: geneflow:asymmetry,equilibrium
Message-ID: <272321E7.18602@orion.oac.uci.edu>
Date: 22 Oct 90 16:44:23 GMT
References: <9010210525.AA06820@genbank.bio.net>
Reply-To: manderse@orion.oac.uci.edu (Mark Andersen)
Organization: University of California, Irvine
Lines: 48

In article <9010210525.AA06820@genbank.bio.net> AEBAKER%CSUGREEN@PUCC.PRINCETON.EDU (ann baker biology dept 303 491 5307) writes:
>
>Equilibrium seems to be what theoretical popgeneticists use as a
>stopping point for their simulations. It removes the influence of
>the initial starting conditions, but I have a problem with this:
>in house mice living in barns or homes, the habitat is often changing
>at the whim of the economics (price of corn, hay, eggs etc): the
>barn is cleaned out, the chickens or corn are sold etc: often these
>cleaning out periods occur every year (about 4 generations?) in house
>mice (Petras and Topping 1979? JMamm for example). Can equilibrium
>occur that quickly? No. Yet we run simulations for 200 generations
>or so until the equilibrium is reached. I don't know a way around
>this problem: the equilibrium is easily defined, the other stuff is
>not, though the other stuff may be a more realistic reflection of
>house mouse populations near human habitation.
>
>ann eileen miller baker
>biology department
>colorado state university
>fort collins 80523
>aebaker@csugreen


Ann, you've identified an important problem, namely the importance of transient
dynamics (i.e., what happens between the initial conditions and equilibrium)
in both demography and population genetics. The problem is recognized, I think,
by both theoretical ecologists and pop'n geneticists. Recognized, but 
underappreciated, or at least not given its due in studies by theorists.
This problem affects empiricists as well. Since they see little mention of
transient dynamics in (accessible) theoretical works, they fail to 
recognize what they observe in the field or lab as transient dynamics.
I try to look at transient dynamics in my own theoretical work, but the 
results one gets are seldom clear-cut. It's much simpler to find a fixed 
point for a system, and determine conditions for its stability; the techniques
for doing so are standard, even for very sophisticated mathematical models. 
For example, just this weekend I was using local linearization techniques to
look at the stability of systems of integrodifference equations; these are
some hairy mathematical beasts that can easily be tamed with simple analytical
methods.

I welcome discussion from anyone on how theorists can emphasize the importance
of transient dynamics in their work. Poor communication between theorists and
empiricists slows progress.


Mark Andersen                   manderse@orion.oac.uci.edu
Dept. of Ecology and Evolutionary Biology
UC Irvine, Irvine, CA, 92717