# Interpretation of Mantel r correlations

I am using mantel() in R package ecodist to perform a series of partial Mantel tests.

I am examining the correlation between a species composition (Bray-Curtis dissimilarity) matrix and a series of environmental and spatial (UTM) variables (as separate Euclidean distance matrices).

The structure of the mantel equation is:

mantel(spp.dist ~ x.dist + a.dist + b.dist + .... + geo.dist, nperm=10000, nboot=500)


where spp.dist = the species dissimilarity matrix; x.dist is an environmental variable of interest; a.dist & b.dist and ... are all other environmental variables; and geo.dist = dissimilarity matrix of UTMN & UTME. x.dist cycles between all other env variables to determine its contribution to the pattern of correlation. nperm and nboot set number of permutations and iterations for bootstrapping to use, respectively.

Here is an example of output (modified slightly from actual data):

            plot        Year          position      pH
mantelr     0.03960184  0.000806223   -0.02970148   -0.009351586
pval1       0.0001      0.4534         0.9977        0.6981
pval2       1           0.5467         0.0024        0.302
pval3       0.0001      0.9407         0.0144        0.5925
llim.2.5%   0.03393448 -0.007369118   -0.03699412   -0.019564176
ulim.97.5%  0.04652775  0.008779442   -0.02203297    0.001134167


mantelr = Mantel coefficient.
pval1 = one-tailed p-value (null hypothesis: r <= 0).
pval2 = one-tailed p-value (null hypothesis: r >= 0).
pval3 = two-tailed p-value (null hypothesis: r = 0).
llim  = lower confidence limit.
ulim  =  upper confidence limit.


So I understand that the mantel r is essentially the correlation between the spp.dist matrix and each variable after having controlled for all other variables. But 2 questions I'm unsure about:

1. How do I interpret negative mantel r values?

2. Do I pay more attention to the one or two tail p-value? Which should I report?

1. How to interpret negative Mantel r values:

Mantel r values can fall within a range between -1 to 1. An r value of -1 suggests a strong negative correlation, 0 suggests no relationship at all and 1 suggests a strong positive relationship.

If, for example, we were interested in the relationship between wet/dry locations and presence of plants: an r of 1 would suggest that plants grow in wet locations (i.e. as water levels increase then plant abundance also increases). An r of -1 suggests that plants grow in dry locations (i.e. as water levels increase then plant abundance decreases). Finally, an r of 0 would suggest that there is no spatial relationship between water and plant presence.

2. Interpreting and reporting one or two tail p-values: It depends on your null hypothesis. In the R package ecodist you can choose between three null hypotheses.

The null hypothesis for "pval1" is that the Mantel r statistic will be equal to or smaller than zero (i.e. that there is a negative spatial correlation between variables).

Conversely, the null hypothesis for "pval2" is that the Mantel r statistic is equal to or greater than zero (i.e. that there is a positive spatial correlation between variables).

The null hypothesis for "pval3" is that the Mantel r statistic is equal to 0 (i.e. that there is no spatial correlation between variables). In other words, if one is interested in rejecting the null hypothesis that there is no spatial relationship between variables (either a positive or negative relationship) then pval3 is the reasonable choice.