[R-sig-eco] spatial autocorrelation present and varies over time

[Penelope_Pooler at nps.gov]

Hi all,

I have both a how-to question and I would appreciate opinions from other
quantitative ecologists.  I'm working on a grant project to examine trends
in water quality for three metrics (Chlorophyll a, Dissolved Oxygen, and Kd
(light attenuation)).  For these particular data, there are 30 permanent
adjacent hexagons the comprise the estuary of interest.  During each
sampling year, a random location is identified within each hexagon and the
metrics of interest are measured there.

I developed a straightforward linear model (using lme() in the nlme
package) for each metric with year as a categorical variable.  There are
only four years of data at this point, and my collaborators want to compare
year to year.  I also included a random effect for each hexagon, using the
continuous form of the year variable.  Lastly, I verified that there was no
discernible temporal autocorrelation in the data.

My problem is that within each year, the data show substantial spatial
autocorrelation, but the spatial autocorrelation differs substantially from
year to year in both the shape and magnitude of the variogram.
Consequently, to account for that, I think I have to input my own V-CV
matrix into the model to account for the different  spatial
autocorrelations each year.  This is not something I have done before AND
seems overly complicated for the task at hand.  However, if it is
necessary, I would like to find away to do it effieciently, and more
importantly help other ecologist to do so as well.  This grant project has
a substantial outreach component.  Any good guidance on how to do this
would be appreciated.

The goal of the project is to detect trends over time in these metrics.
The spatial aspects of the metrics are examined within each year, but they
are not of interest from a trend point of view.  Another goal of this
project is develop models and guidance that can be used by NPS and other
users for their similar data, so I am hesitant to develop models that are
overly complicated and can't be reproduced.

My other thought was to randomly sample from the data until the spatial
autocorrelation was negligible, but the sample size was selected to
maximize the power to detect changes over time.

I appreciate any opinions, guidance, or references people can provide.
I've been looking through the liturature, but haven't found anything that
directly addreses this issue yet.

Thanks,
Penelope



===========================================
Penelope S. Pooler, Ph.D.

Quantitative Ecologist, National Park Service I&M
Northeast Coastal and Barrier Network
NPS email: Penelope_Pooler at nps.gov

Adjunct Professor, Dept. of Natural Resources Science
URI Coastal Institute in Kingston
URI email: ppooler at mail.uri.edu

1 Greenhouse Rd., Rm 105
Kingston, RI 02881
Ph.: (401) 874-7060
Cell: (540) 250-1096