Dear Sebastian and Julian, and others,

the full reference of the paper Sebastian referred to is:
Hawkins BA, Diniz-Filho JAF, Bini LM, De Marco P, Blackburn TM (2007) Red herrings revisited: spatial autocorrelation and parameter estimation in geographical ecology. Ecography 30:375-384

It is part of an ongoing debate about the importance of spatial effects on regression estimates, started by
Lennon JJ (2000) Red-shifts and red herrings in geographical ecology. Ecography 23:101-113

Returning to the main problem of estimating effect size (or partial R2) for effects in spatial models:
1. I regard the Hawkins et al. paper as inconclusive. Although the space sampling points far apart, they do not show that spatial autocorrelation was hence removed. In my review (Dormann CF (2007) Effects of incorporating spatial autocorrelation into the analysis of species distribution data. Global Ecology & Biogeography 16:129-138) I found spatial autocorrelation at all scales, and resampling to coarser grain may or may not remove underlying spatial autocorrelation. It could hence be that the supposedly autocorrelation-free models are still spatially autocorrelated.
2. The easiest way to compare effects for their importance in a spatial model would be to compare their standardised coefficient estimates. Thus, scale the variables before the analysis, then the (absolute) estimates are direct measures of their importance.
Which leaves the question, how important is the spatial effect compared to the non-spatial effect? The key problem is that we cannot fit a spatial-effect-only model and compare that to the full model, because the spatial effect will then take over some of the effects attributable to our environmental variables.
When you check the help for predict.sarlm (package spdep), you will find that the fit can be decomposed into two elements, "trend" (i.e. the non-spatial part) and "signal" (the spatial part). 
If you run the first example in spautolm (spdep), then I think it is correct to use: cor(nydata$Z, attr(predict(esar0), "trend"))^2 to extract the partial R2 for the non-spatial bit, and
cor(nydata$Z, attr(predict(esar0), "signal"))^2 for the spatial component. trend and signal sum to the total fit values. In the case of this example, the majority of the combined effect of 0.216 (calculated using cor(nydata$Z, predict(esar0))^2) is attributable to the non-spatial part (0.1904) and less to the spatial component (0.0557).
(For the sake of completeness: When predicting to unobserved sites, the signal is set to 0, and all prediction is made from the non-spatial part of the model: see ?predict.sarlm.)
I did not check if this works similarly for the other spatial model types (e.g. the various gls implementations). If you use spatial eigenvector mapping (ME in spdep), which I personally like very much, then the spatial effect is an ordinary part of the LM and the partial R2 can be directly calculated as in any OLS model.

Best wishes,

Carsten



 -- 
Dr. Carsten F. Dormann
Department of Applied Landscape Ecology
UFZ Centre of Environmental Research
Permoserstr. 15
04318 Leipzig
Germany

Tel: ++49(0)341 2353946
Fax: ++49(0)341 2353939
Email: carsten.dormann@ufz.de
internet: http://www.ufz.de/index.php?de=4205





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