[R-sig-eco] adonis to test difference in sums of squares partitioning across treatments?

[Gavin Simpson]

On Thu, 2010-12-16 at 19:28 -0700, Andy Rominger wrote:
> Dear Etienne,
> 
> Thanks for your response, and yes I see clearly now the nested structure.
> However, I think this is not getting at our question.  I believe this method
> would address the question of "how different are communities given different
> land use treatments (and given that fact that treatments are nested within
> regions)?"
> 
> We are not interested in describing the community itself, but rather changes
> in the community composition, and the independent variable we are interested
> in is indeed *region* (we are interested in beta diversity).  We'd
> specifically like to know, in a sense, how beta diversity partitions
> differently to within and between regions, given treatment.  Here's a little
> more information:
> 
> There are four regions.  Within each region, three different land use
> "treatments" (say A, B, C) were replicated between 3 and 4 times.  When we
> plot these data in an ordination space, we see that for treatment C the
> regions for diffuse clouds that overlap, but their centroids are still far
> apart.  For the other two treatments, the regions form tight clouds, also
> with well spaced centroids.  We'd basically like to be able to say whether
> the relative "diffuseness" of these region clouds are different across
> treatments, and whether the relative distance between the region centroids
> is different across treatments.

adonis works on the centroids for the groupings - think of it like ANOVA
but with multivariate responses and any dissimilarity. You can use it to
see whether groups have statistically different centroids.

"diffuseness" is variance, the spread of the observations about the
grouping means/centroids. This can be analysed using Marti Anderson's
PERMDISP procedure. Some of this functionality is available in
betadisper() in vegan.

G

> I get the sense that perhaps we want region nested within treatment, but I
> feel like we also need an interaction term?
> 
> Thanks for your help--
> Andy
> 
> 
> On Thu, Dec 16, 2010 at 5:28 PM, Etienne Laliberte <
> etiennelaliberte at gmail.com> wrote:
> 
> > Dear Andy,
> >
> > For testing the null hypothesis of no land use effect, what you suggest
> > does
> > not take into account the nested structure of your design (with land use
> > nested in location).
> >
> > In ?adonis:
> >
> > "If the experimental design has nestedness, then use strata to test
> > hypotheses. For instance, imagine we are testing the whether a plant
> > community is influenced by nitrate amendments, and we have two replicate
> > plots at each of two levels of nitrate (0, 10 ppm). We have replicated the
> > experiment in three fields with (perhaps) different average productivity.
> > In
> > this design, we would need to specify strata = field so that randomizations
> > occur only within each field and not across all fields . See example
> > below."
> >
> > Which in your case translates to
> >
> > adonis(bird.com  ~ land.use, strata = site.data$region, data = site.data)
> >
> > Hope that helps,
> >
> > Etienne
> >
> >
> > -----Original Message-----
> > From: r-sig-ecology-bounces at r-project.org
> > [mailto:r-sig-ecology-bounces at r-project.org] On Behalf Of Andy Rominger
> > Sent: Friday, 17 December 2010 5:17 AM
> > To: r-sig-ecology at r-project.org
> > Subject: [R-sig-eco] adonis to test difference in sums of squares
> > partitioning across treatments?
> >
> > Dear list,
> >
> > We are working with a dataset of bird community composition across four
> > regions, each of which contain three land use treatments.  We are
> > interesting in understanding if the community dissimilarity within regions
> > and between regions differs according to land use treatment.  I understand
> > that multivariate analysis of variance (as implemented in adonis{vegan})
> > can
> > partition sums of squares between main effects and residuals, which I
> > understand would, for example, test the ratio (F-statistic) of between
> > versus within region dissimilarity.
> >
> > What we'd like to know is effectively if this partitioning of sums of
> > squares within (residual) and between (main effects) regions changes
> > significantly under the different land use treatments.  So would the
> > following model to the trick?
> >
> > adonis(bird.com~region*land.
> > use,data=site.data)
> >
> > where...
> > bird.com is a sites by species matrix, and
> > site.data is a data.frame containing columns that indicate to which region
> > (column 'region') and land use (column 'land.use') each site belongs.
> >
> > I appoligize for this simple question (and probably wrong model) I'm very
> > naive about these multivariate analyses.  We assumed that this approach was
> > probably wrong and so we are also working on a bootstrap method, which I
> > could post for your consideration if this use of adonis is incorrect, or if
> > no perMANOVA-based method would answer our question.
> >
> > Thanks in advance for your help--
> > Andy Rominger
> >
> >         [[alternative HTML version deleted]]
> >
> > _______________________________________________
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> >
> >
> 
> 	[[alternative HTML version deleted]]
> 
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