The only way to handle this is to know how the spatial correlation is distributed BEFORE setting up the sampling protocol to guarantee that observations will be more or less spatially independent. Spatial autocorrelation statistics measure and analyze the degree of dependency among observations in a geographic space. Classic spatial autocorrelation statistics include Moran's I, Geary's C, Getis's G and the standard deviational ellipse. These statistics require measuring a spatial weights matrix that reflects the intensity of the geographic relationship between observations in a neighborhood, e.g., the distances between neighbors, the lengths of shared border, or whether they fall into a specified directional class.The Mantel and partial Mantel tests can be flawed in the presence of spatial auto-correlation and return erroneously low p-values See e.g. Guillot and Rousset, 2013.

I expect you to sampling the different treatments at each location, right? 3 altitudes x 2 aspects x 3 locantions x N replicas. If you do that, everything is OK. I think you can try with GLM analysing altitude x aspect, and in the interactions analyze the influence of the location. Or, just try to made a multiple ANOVAs, and see if location influence or not. Another chance is to made multivariate analysis, many choices to do that!

Thank you for your answer, So, I don't need to be concerned for how close it the plots are?

Moises

Take a look at this:

Borcard D, Legendre P, Avois-Jacquet C, Tuomisto H (2004) Dissecting the spatial structure of ecological data at multiple scales. Ecology 85:1826–1832

In this other you will find an application of this method to a study in another mexican TDF:

Hernández-Stefanoni, J. L., & Dupuy, J. M. (2008). Effects of landscape patterns on species density and abundance of trees in a tropical subdeciduous forest of the Yucatan Peninsula. Forest Ecology and Management, 255(11), 3797-3805.

I hope it works

Pacho

Maybe you could explore a Mantel Test between the matrix of distance (the euclidian distance between the sites) and the matrix of the "ecological distance", this could be diversity distances, or trait distances... the idea is that closest places will be more similar, if the two matrices are indeed correlated in this way it suggest certain spatial autocorrelation, but if they are not correlated (whatever the distance between two points, differences between traits are variable), you are pretty sure there are no spatial structure in the distribution of your trait (easily to do in R, see last link).

http://userwww.sfsu.edu/efc/classes/biol710/spatial/spatial.htm

www.nbb.cornell.edu/wkoenig/k087ta_98.pdf

http://www.ats.ucla.edu/stat/r/faq/mantel_test.htm

Hi Moises,

I agree with Ian about using a Mantel Test. In fact, I used the Mantel test in R

Thank you so much to all. I really appreciate your help. I think that with all the comments send it I can handle my problem. Cheers

Dear Moises,

You can try Geary, Moran or Mantel tests (see Cliff and Ord 1973, spatial autocorrelation).

Best,

Guy

The only way to handle this is to know how the spatial correlation is distributed BEFORE setting up the sampling protocol to guarantee that observations will be more or less spatially independent. Spatial autocorrelation statistics measure and analyze the degree of dependency among observations in a geographic space. Classic spatial autocorrelation statistics include Moran's I, Geary's C, Getis's G and the standard deviational ellipse. These statistics require measuring a spatial weights matrix that reflects the intensity of the geographic relationship between observations in a neighborhood, e.g., the distances between neighbors, the lengths of shared border, or whether they fall into a specified directional class.The Mantel and partial Mantel tests can be flawed in the presence of spatial auto-correlation and return erroneously low p-values See e.g. Guillot and Rousset, 2013.

Dear Moises, please, take a look in the paper by Dormann et al. (2007) in Ecography (complete reference below). It can help you to deal with spatial autocorrelation in your data. This paper provide several methods to deal with this "problem". But remeber that all things are spatially autocorrelated depending on the scale. This can not a problem in all cases, but it can indicate that you can have problems with your hypothesis testing! I hope this reference will help you! Bests

http://onlinelibrary.wiley.com/doi/10.1111/j.2007.0906-7590.05171.x/full

Dear Moises, I suggest you to look at the book of Alain Zuur: Zuur, Alain F., Elena N. Ieno, Neil J. Walker, Anatoly A. Saveliev, and Graham M. Smith. Mixed Effects Models and Extensions in Ecology with R. 1st ed. Springer, 2009. Spatial autocorrelation can be overcame with mixed effect models

Hi, Ludovico, I will look at the book you recommend me

As somebody already noted, it depends on the spatial arrangemente and randomization of treatments. If the treatments have been properly arranged, you could just use a split-plot type analysis, either in an ANOVA framework or on a GzLM framework.

Of course, a more flexible and robust approach would be to use a linear mixed model or generalized mixed model with a spatial variance-covariance matrix to analyse the data. They allow to explain more properly the spatial variation, and hence should give a best fitt. But in turn they are much much more difficult to be applied.

Good luck.

           Asier

I am not sure that you need to avoid the auto-correlation if your data states spatially correlated. Yet I believe what you can do the distribution of your sample plot are related to each other on some condition so what I can do is take more other variable that similarly correlates the low mid and top slopes the hill may be see different degree of the slops differences, may be there appear insignificant difference so they appear auto-correlated. But a scientific result it put in away that can be justified though it come out off your expectation.