##### New Member
Hi!, :wave:
I want to use Adonis in R (non-parametric permutation MANOVA) to test for relationships between bray-curtis distances (dissimilarities I guess) for species data and various site characteristics that are continuous variables. I was able to get R to run this no problem (see output below), but I have no idea how this works, and was wondering if anyone could shed some light? The only info I can find on Permanova is for a ANOVA type of design where you are comparing groups, but my variables are continuous. Does it take the dissimilarity coefficients and regress them against the variables? The output looks exactly the same as would for the same test with categorical variables.

Any thoughts would be much appreciated. Thanks!
Brandi

P.S. I'm a biology student, not a stats person, so forgive me if this sounds like I have no idea what I'm talking about...

R output:

Call:
adonis(formula = crpsplog.dat ~ Forbs + Richness + Age + Litter + Shrubs + Grasses, data = crpveglog.dat, permutations = 4999, method = "bray")

Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
Forbs 1 0.34302 0.34302 8.3190 0.32977 0.0002 ***
Richness 1 0.15779 0.15779 3.8268 0.15169 0.0154 *
Age 1 0.11212 0.11212 2.7191 0.10779 0.0422 *
Litter 1 0.00600 0.00600 0.1454 0.00577 0.9872
Shrubs 1 0.04832 0.04832 1.1720 0.04646 0.3328
Grasses 1 0.04307 0.04307 1.0445 0.04140 0.3768
Residuals 8 0.32986 0.04123 0.31712
Total 14 1.04018 1.00000

#### bugman

##### Super Moderator
I have attach a little background on this to get you started.

1st. How have you quantified shrubs and grasses? Are these really continuous?

2nd. You have noted an important point. PERMANOVA is design for categorical designs and is a permutational analogue of ANOVA; however you are modelling species data (BC similarity) on continuous environmental variables, which can be thought of as multivariate multiple regression (or Redundancy analysis - redundancy can be thought of as "explained variance") or better still (because RDA is on Euclidean distance) dbRDA or distance based redundancy analysis.

dbRDA is found in VEGAN and should allow you to perform stepwise modelling of your species data (using ANY distance measure) in much the same way as you would in a multiple regression.

PERMANOVA is not what you want here, but note for later use, that you can include 1 or more continuous co-variates into this design.

##### New Member
Hi! Thanks for the response Bugman.

Variables - Well, I guess Field Age and Species Richness are not continuous, but rather discrete quantitative variables, e.g. 8, 10, 19... Litter, Forbs, Shrubs and Grasses are % cover estimates that are averaged over many replicates and so I think would be considered continuous, e.g. 10.2, 7.6, 30.3

The field age could really be grouped into a categorical variable, young vs. old. (8-10 yrs) vs. (19-20 y rs). I first did non-metric multi-dimensional scaling (NMDS) to see if differences in age were reflected as differences in the spider communities. I went with NMDS because the freedom from assumptions - the data are right skewed, with lots of zeros. So, to test the relationship with age PerMANOVA seemed like a good option since it is non-parametric, and also sample independence is not an issue (I have multiple years of data from the same 8 locations). But because the observed clusters appeared to be more based on vegetation characteristics (looked at correlations with NMDS axes) I decided it would be cool to be able to test for significant associations with these variables and see which are most important.

Perhaps I should just stick with testing age as a categorical variable and relate to veg. variables with spearmans correlation coefficients, and a Mantel's test (with Euclidian dist. for veg. data) for overall relation with NMDS? This doesn't allow me to determine which variables are "significant", so I'm open to other options.

I will look into distance based RDA - I'm not familiar with it, so I am unsure of assumptions and fit to less-than-ideal ecological data. :yup:

Thanks Again,
Brandi

#### bugman

##### Super Moderator
(looked at correlations with NMDS axes)
Brandi
Since NMDS axes have no scale, I am not sure this is the correct approach, unless you have overlaid vectors or bubbles to give you an idea.

I will look into distance based RDA - I'm not familiar with it, so I am unsure of assumptions and fit to less-than-ideal ecological data.
Let me assure you that dbRDA is the correct approach for continuous environmental variables modelled on species abundance data. Since it is based on any distance measure for your species data, the assumptions on the x variables are more relaxed. Furthermore, the fact that the method was developed for exactly this type of design, and given most ecological data sets are less than ideal, this will work perfectly fine.

:yup:

##### New Member
Partial Mantel's Tests on multiple predictor variables...

Hi. It's me again.
So I've been doing some reading on dbRDA (Mcardle and Anderson 2001, Legendre and Anderson 1999). It seems really complicated
In my defense, I have heard that NMDS is better than Principle Coordinate Analysis in compressing the distance relationships among objects into two or three dimensions - which is important, because I'm not attempting to interpret something on 5 axes... (for the NMDS I set it two use only 2 axes).

Which reminds me, I need to ask - anyone know which Kruskal's stress formula is default in R isoMDS? my stress value was 11.06, which if that is for formula 1 is really super high right? That can't be right!?

OK, so back to hypothesis testing. I used the Mantel's test for an overall correlation between species data and environmental data, and that was highly significant, but like we discussed before, I want to know which environmental variables are most important and if they are "significant."

As a last resort before having to try to figure out how to do dbRDA in R, of which my knowledge is very much in it's infancy, (I know, I'm whining) what do you think about doing partial Mantel's tests? I've never heard of them, but I was searching the web on this topic in general and found this tutorial thing about spatial analysis in ecology (see quote below). I would give proper citation, but I can't figure out where it came from other than an author name at the bottom. Anyways, this sounds like it could work if I maybe just chose a few of the variables that are likely to be of ecological importance? But what of multiple comparisons? Would that even matter with a permutation test?

This procedure is detailed in Smouse, Long and Sokal 1986 - Multiple regression and correlation extensions of the Mantel Test of matrix correspondence... But alas it too is very technical. A dumbed down version would be ideal.

OH, so many questions! Sorry to take up your time, but if you have it, I sure do appreciate it!

"Case 6. Partial Mantel’s on Multiple Predictor Variables. Often, knowing that the environment has some relationship with the dependent variable of interest is not sufficiently satisfying: we wish to know which variables are actually related to the dependent variable. The logical extension of Mantel’s test is to multiple regression, in which the predictor variables are entered into the analysis as individual distance matrices (Smouse et al. 1986, Manly 1986). As a partial regression technique, Mantel’s test provides not only an overall test for the relationships among distance matrices, but also tests the contribution of each predictor variable for its pure partial effect on the dependent variable." -D.L. Urban

#### bugman

##### Super Moderator
Re: Partial Mantel's Tests on multiple predictor variables...

Hi. It's me again.
I have heard that NMDS is better than Principle Coordinate Analysis in compressing the distance relationships among objects into two or three dimensions - which is important, because I'm not attempting to interpret something on 5 axes... (for the NMDS I set it two use only 2 axes).
Which reminds me, I need to ask - anyone know which Kruskal's stress formula is default in R isoMDS? my stress value was 11.06, which if that is for formula 1 is really super high right? That can't be right!?
mmmm, debatable. They often give very similar results, though NMDS is more robust to outliers. Your choice of transformation or distance measure will often be much more influential than deciding between PCO and NMDS. I would not advise choosing only two axes. Often the default is five, which can be informative to see how much additional info is in the extra axes.

I think R uses Kruskals percentages from his original paper (I dont know what formula 1 is), while other software use the proportion (which I am more familiar with). 11.06% (0.11) is a bit high, but is a fair representation of the data cloud in 2d space. If you are unsure, compare a cluster analysis dendrogram to see if the same groups are represented.

As a last resort before having to try to figure out how to do dbRDA in R, of which my knowledge is very much in it's infancy, (I know, I'm whining) what do you think about doing partial Mantel's tests?
As far as I know, this method suffers from the same or similar problems as doing multiple t-tests on multiple groups instead of an ANOVA. There are papers on this, I just don't have them on hand - watch this space, I'll try and get hold of it.

One last thing.

You say that dbRDA looks difficult in R, but let me say that given you have the confidence and know how, how to run a permanoa model, the dbRDA will be a piece of cake.