[R-sig-eco] Mantel test with skew-symmetric matrices?

[Jari Oksanen]

Steve,

My answer concerning the vegan part is so short that I top-post (my
apologies for those who are sensitive about this): No, you cannot use
non-symmetric matrices in mantel() functions in vegan. The functions use the
standard R distance objects which are regarded as symmetric. If you supply a
non-symmetric matrix, only its lower triangle will be used. Changing this
would require redesign of the functions. Contributions are welcome and will
be credited in the vegan manual pages to their authors.

Best wishes, Jari Oksanen


On 1/10/09 20:20 PM, "Steve Arnott" <ArnottS at dnr.sc.gov> wrote:

> Hello All,
> 
> I'm interested in using the mantel()and mantel.partial() functions in the
> 'vegan' R package to examine fish morphology in several lakes with respect to
> distance between lakes, lake elevation (above sea level) and various habitat
> measures. For example, several authors have postulated that jaw length varies
> with habitat conditions, but jaw length, lake distance, elevation and the
> habitat measures co-vary. Applying a partial Mantel to control for elevation
> or lake distance seems like a good way of attacking the problem.
> 
> Typically, Mantel tests are performed using symmetrical distance matrices
> based upon absolute distances. For example, a symmetrical matrix of distances
> between 3 lakes might look like this:
> 
> 0 7 3
> 7 0 4
> 3 4 0
> 
> This makes sense with distance data (miles, km, etc), but information is lost
> on the direction of effect between lakes with data such as jaw length or
> elevation. Instead, a so-called skew-symmetric matrix can be generated, which
> would instead look something like this:
> 
>  0  7  3
> -7  0 -4
> -3  4  0
> 
> I have two questions:
> 
> 1) Is it wrong to use skew-symmetric matrices - i.e. should I just forget
> about the skew data and use absolute values to make all my matrices symmetric?
> The original Mantel paper (1967, Cancer Research, 2: 209-220) does talk about
> skew-symmetric matrices, but the published applications I've come across only
> seem to use symmetric matrices.
> 
>  2) If it is ok to use skew-symmetric matrices, do the mantel() and
> mantel.partial() functions in 'vegan' (or related functions in other packages,
> such as 'ecodist') handle them correctly? I've found that it is possible to
> process skew data and generate results using these functions, but I'm
> uncertain from the documentation whether the results are meaningful (i.e. is
> the coding designed to handle such cases appropriately?)
> 
> With thanks, Steve
> 
> ------------------------------------------------------------------------------
> Stephen A. Arnott, PhD
> Associate Marine Scientist
> Marine Resources Research Institute
> South Carolina Department of Natural Resources
> P.O. Box 12559
> Charleston
> SC 29422-2559
> 
> Phone: (1)-843-953-9794
> Fax: (1)-843-953-9820
> E-mail: arnotts at dnr.sc.gov<mailto:arnotts at dnr.sc.gov>
> ------------------------------------------------------------------------------
> 
> 
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