Hi,
I hope this is not a dumb question. I have set of sites which are discrete
and connected by a graph. On each site (vertex in graph theory
parlance) lives a population which is modeled as a discrete time ricker
model, n(t+1)=n(t)exp[r(1-n(t)/k) + e] - E + M, E is a proportion of the
population migrating out only along the edges of the graph and M is the
sum of migrants coming in for other vertices and e is a random error
term correlated in space but independent in time. Now I am interested in
the correlation cor(v_i, v_j) as a function of distance. I set the
migration to zero, so that after a sufficient amount of time all
populations hover around their equilibrium K. I have the correlation in
the random errors e specified as p^||s_i-s_j||, an isotropic covariance
that is a function of distance alone.
Now the question, if I calculate all pairwise correlations between
vertices and fit a smoother, I recover the specified corelation function
with very little bias (provided t is large enough), and this seems to work
for a relatively small sample of vertices. However if I caculate the
auto-correlation function using the standard estimators and average them
over time, or calculate the average of the standardized populations and
fit the auto-correlation function, the result is severely biased (under
estimates) the correlation as a function of distance, even for large v. I
have some hunches about this, but does anyone know where I can find
some more information on this?
Nicholas
CH3
|
N Nicholas Lewin-Koh
/ \ Dept of Statistics
N----C C==O Program in Ecology and Evolutionary Biology
|| || | Iowa State University
|| || | Ames, IA 50011
CH C N--CH3 http://www.public.iastate.edu/~nlewin
\ / \ / [EMAIL PROTECTED]
N C
| || Currently
CH3 O Graphics Lab
School of Computing
National University of Singapore
The Real Part of Coffee [EMAIL PROTECTED]
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