[R-sig-eco] Reducing spatial autocorrelation

Thu Oct 15 10:58:37 CEST 2009

My apologies to Carsten for misspelling his name, 
but I still see its paper appropriate in the multivariate case.

I was thinking on  something like computing your 
favourite ordination or NMDS on the species or 
environmental or both (i.e RDA), and then compute 
a correlogram on your ordination scores. This 
would let you select the minimum distance between 
sites to minimize autocorrelation (this could 
also be obtained from a multivariate Mantel correlogram).
And /or you could also generate autocovariates 
from your ordination score(s) and include them as 
predictors in that "some statistical analyses" to 
account for the autocorrelation.

Marcelino

At 15:41 14/10/2009, Matthew Landis wrote:
>That's a really great paper, but if memory 
>serves, it focuses on univariate regression 
>models.  Useful in this context for exploring 
>the responses of a single species at a time, 
>instead of a multivariate approach considering multiple species simultaneously.
>
>By the way, I have the author as Dormann.
>
>M
>
>Marcelino de la Cruz wrote:
>>I would recomend the paper of  Dortman et al. 
>>(Ecography 30: 609628, 2007). This 
>>reviews  many available spatial statistical 
>>methods to take spatial autocorrelation into 
>>account in tests of statistical significance. From their abstract:
>>
>>"Here, we describe six different statistical 
>>approaches to infer correlates of species’ 
>>distributions, for both presence/absence
>>(binary response) and species abundance data 
>>(poisson or normally distributed response), while accounting for
>>spatial autocorrelation in model residuals: 
>>autocovariate regression; spatial eigenvector mapping; generalised
>>least squares; (conditional and simultaneous) 
>>autoregressive models and generalised estimating equations."
>>
>>The suplementary material includes R scripts to run all the methods.
>>
>>HTH
>>
>>Marcelino
>>
>>
>>
>>
>>
>>At 14:49 14/10/2009, Martin Alejandro Piazzon de Haro wrote:
>>
>>>Content-Type: text/plain
>>>Content-Disposition: inline
>>>Content-length: 3518
>>>
>>>Dear friends,
>>>
>>>I found this thread very useful, so I wanted to apport something, Corrado,
>>>you asked for some references about PCNM, here is what i found:
>>>
>>>Borcard, D. and Legendre, P. 2002. All-scale spatial analysis of
>>>ecological data by means of principal coordinates of neighbour
>>>matrices. Ecological Modelling 153: 51-68.
>>>
>>>Borcard, D., P. Legendre, Avois-Jacquet, C. & Tuomisto, H. 2004.
>>>Dissecting the spatial structures of ecologial data at all scales.
>>>Ecology 85(7): 1826-1832.
>>>
>>>I hope will help you.
>>>
>>>2009/10/14 Corrado <ct529 at york.ac.uk>
>>>
>>>
>>>>Dear Matthew,
>>>>
>>>>thanks for your kind answer!
>>>>
>>>>The first approach you describe is the one I have been looking at until
>>>>now.
>>>>
>>>>I am puzzled about the second one: I do not really understand it. What
>>>>model
>>>>are you talking about, when you say "incorporate the spatial variation in
>>>>the
>>>>model"? At the moment I have no model, just the data and I am trying to
>>>>reduce
>>>>autocorrelation before analysing the data.
>>>>
>>>>Do you have any good reference (articles or books) about the approach you
>>>>mention?
>>>>
>>>>Thanks in advance
>>>>
>>>>
>>>>On Wednesday 14 October 2009 13:11:04 Matthew Landis wrote:
>>>>
>>>>>Corrado:
>>>>>
>>>>>The simplest way would be to take a subset of sites to maximize the
>>>>>distance between them.  Say, choose 400 sites evenly spread over the
>>>>>study area.  That would minimize autocorrelation to the greatest extent
>>>>>possible, but you would be throwing away data.
>>>>>
>>>>>The second thing you could try would be to incorporate the spatial
>>>>>variation in the model to control for it.  This way you can also study
>>>>>the autocorrelation, see what spatial scales it is operating and what it
>>>>>looks like and try to learn something from it.  Legendre, Borcard, Dray
>>>>>and colleagues have developed some really interesting ways of dealing
>>>>>with multivariate data and decomposing the variance into spatial
>>>>>component vs. explanatory variables.  I believe it is called PCNM and
>>>>>can be found in the spacemakeR package (don't think it is on CRAN - have
>>>>>to do a google search).
>>>>>
>>>>>Good luck!
>>>>>
>>>>>Matthew Landis
>>>>>
>>>>>Corrado wrote:
>>>>>
>>>>>>Dear friends,
>>>>>>
>>>>>>I have a large matrix of species (first 1100 columns) and environmental
>>>>>>variables (last 36 columns) for approx 2000 sites.
>>>>>>
>>>>>>The distance between sites varies. Some sites are near to each other,
>>>>>>others are far.
>>>>>>
>>>>>>I would like to select a subset of N sites (for example: 400 sites)
>>>>>>
>>>>with
>>>>
>>>>>>the minimum spatial autocorrelation. The aim is to obtain a significant
>>>>>>number of sites to carry out some statistical analysis, but with
>>>>>>
>>>>spatial
>>>>
>>>>>>autocorrelation significantly reduced.
>>>>>>
>>>>>>Is there a procedure to do so in R? How would you approach the problem?
>>>>>>
>>>>>>The aim of the "reduction" is to then work on dissimilarities between
>>>>>>sites that have the lowest possible spatial autocorrelation.
>>>>>>
>>>>>>Thanks
>>>>>>
>>>>
>>>>--
>>>>Corrado Topi
>>>>
>>>>Global Climate Change & Biodiversity Indicators
>>>>Area 18,Department of Biology
>>>>University of York, York, YO10 5YW, UK
>>>>Phone: + 44 (0) 1904 328645, E-mail: ct529 at york.ac.uk
>>>>
>>>>_______________________________________________
>>>>R-sig-ecology mailing list
>>>>R-sig-ecology at r-project.org
>>>>https://stat.ethz.ch/mailman/listinfo/r-sig-ecology
>>>>
>>>>
>>>
>>>--
>>>Martín Alejandro Piazzon de Haro
>>>PhD Student
>>>
>>>IMEDEA (CSIC)
>>>C/Miquel Marques, 21
>>>(07190) Esporles
>>>Mallorca, Illes balears.
>>>Spain.
>>>Tlf: (+34) 971611807
>>>
>>>         [[alternative HTML version deleted]]
>>>
>>>
>>>_______________________________________________
>>>R-sig-ecology mailing list
>>>R-sig-ecology at r-project.org
>>>https://stat.ethz.ch/mailman/listinfo/r-sig-ecology
>>>
>>
>>         [[alternative HTML version deleted]]
>>
>>
>
>________________________________
>
>Marcelino de la Cruz Rot
>
>Departamento de  Biología Vegetal
>E.U.T.I. Agrícola
>Universidad Politécnica de Madrid
>28040-Madrid
>Tel.: 91 336 54 35
>Fax: 91 336 56 56
>marcelino.delacruz at upm.es
>_________________________________ 