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] -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org