Hi Yoannis,

Wether or not it is correct all depends on your research question I would say. If you do have good reasons to think that the three species you are studying may differ from each other regarding their respective link between morphological distances and geographical distances, then it might be a good idea to test the species effect.

If I may suggest you something, another interesting way to analyze your data could be to run a Multiple Regression on distance Matrices (MRM) thus relating morphological distances (Y) against geographical distances (X). The slope parameter of the model Y~X will give you the distance decay in similarity between populations. Doing this separately for your three species and then testing if the slope parameters differ significantly among the three species might give you insights on the effect of dispersion/connectivity on the distance decay in between-populations similarity. To test the differences in the slope parameters between species you will need to use non-parametric approaches like bootstrap techniques so as to get a kind of confidence interval for each slope parameter.

Hope that helps.

Best,

Jonathan

Hello Jonathan,

I testing two thing:

1. if geographically isolated species or populations have differences regarding the rest (I already did other analyses: PCA, ANOVA).

2. the three species are very different in vegetative morphology but similars in flower morphology, in the other hand I've founded the same or close related insect in the flowers of the three species, so I would like to know if, appart the differences in vegetative morphology, they could share pollinators among species and populations since they are (some of them) geographically distant.

Thanks for your comment, off course that it is helpful

Best

Yoannis

Ok, I see, then your mantel test based on the correlation between morphological distances and geographical distances sounds correct, given your arguments for pooling all three species together.

Did you try Canonical Correspondence Analysis ? It might give some good insights also.

Hi D

an, I didn't do it but I could explore this option too, thanks for the suggestion.

Yoannis

It is dedicated to species location on the basis of distances and influencing parameters. Welcome

Hello everyone,

I am but a mere Master's student, but I suggest not using any methods that are derived from the mantel test, this includes MRMs or MRDMs whatever you want to call them. If I were you, I would look at Moran's Eigenvector maps (MEM), check out Chapter 14 in Numerical Ecology by Legendre, P. and Legendre, L, make sure it's the 3rd edition (2012). In this book they even warn you about mantel tests. The use of the mantel test is heavily debated, but thankfully there are many other methods, See "Comparison of the Mantel test and alternative approaches for detecting complex multivariate relationships in the spatial analysis of genetic data" Legendre & Fortin (2010). Also, I noticed that you cited a paper from 1970 for the mantel test. There was a paper published in 1967 "The detection of disease clustering and a generalized regression approach" by Mantel, I'm pretty sure this is the appropriate citation for the simple mantel test. If you would like a pdf or these papers or chpt 14 in numerical ecology I can send it to you, I have them on my laptop.

Thanks

Hi Jonathan and Yoannis,

Could you tell me how can I perform a Multiple Regression on distance Matrices? what program can I use? I have a similar problem, I want to know whether populations of different species (same genus) are more or less similar morfometrically if they are geographically closed.

I will appreciate any suggestion.

HIi Robby,

Thanks for your comments, I also have the paper published in 1967, but I would like to read the other you've mentioned [Comparison of the Mantel test and alternative approaches for detecting complex multivariate relationships in the spatial analysis of genetic data" Legendre & Fortin (2010)] and off course the chapter 14 in numerical Ecology.

Best

Y

Hi Cecilia,

I'm also exploring GLM (General Linear Models) in Systat.

GLM can estimate and test simple and multiple linear regression models (including multivariate models) using two matrix X and Y. In all multivariate models, Y is a matrix of continuous measures and the X matrix can be either continuous or categorical dummy variables, according to the type of model. Check it out in Systat or Mystat (this last is free).

Hope it helps

Y

Hi Yoannis,

As indicated by Jonathan, you can definitely do MRM, and as indicated by others you can do canonical ordination. Both are commonly-used approaches. There are also caveats with these approaches, though - particularly with MEM eigenvectors. Though the technique is commonly used, it is difficult to interpret what the complex signal actually means in ecological terms. See attached paper. Good luck - sounds like a cool project!

Thanks Joseph,

I think that your paper is very useful for a deepest insight of these methods by comparison

I asked Dr. Paul W. Mielke, Department of Statistics at Colorado State University. His response is follows: "Dear Howard: I am familiar with the Mantel-Valand test since I questioned it in a paper I wrote in 1978. The problem with the test in the 1970 paper which Mantel and Valand wrote are the following three features: (1) the asymptotic normal distribution for the statistic was wrong, (2) the distance function they used yielded results that were not invariant to rotation (they used a city-block metric for their distance function, and (3) the form of the statistic they used was not efficient for routine problems (while the paper contained unique ideas, it was also a mess). If you are talking about another paper (Mantel published numerous papers during that time), then more clarification such as a reference is needed. I refer to the 1970 paper and he also wrote up another result before he duplicated my results in roughly five papers a few years later. Paul"

I hope this is helpful. Following RA Fisher, we use permutation procedures that follow Euclidean distances and are thereby congruent to geographic parameters.

Hi Cecilia,

You can run MRMs in R using the "ecodist" package for instance (cf. Sarah Goslee and Dean Urban):

http://cran.r-project.org/web/packages/ecodist/ecodist.pdf

For running MRMs, I also highly recommend to read this reference from Jeremy Lichstein:

Lichstein J. (2007), Multiple regression on distance matrices: a multivariate spatial analysis tool, Plant Ecology, Vol 188, pp. 117-131

To add to the discussion regarding MRMs and Mantel tests, it is true that there is a heavy debate around those techniques. However, they can provide very insightful and valuable information on spatial patterns as soon as you understand how these work. At least, I found it very useful. As many suggested in this very inspiring discussion, these techniques require careful interpretations. Indeed, they are based on distance matrices suffering from the fact that data points (observations) are pair-wised comparisons (euclidean differences or dissimilarity indices for instance) and thus not independent from each other. Some of the pairs are sharing information. For this reason, you need to use permutations, by means of bootstrap approaches, to actually test relationships between the response and explanatory variables. The package "ecodist" does that very well for MRMs and Mantel tests. I have been using it several times and it works perfectly fine I think. For instance I used MRMs to look at distance decay in similarity among different group of organisms differing in dispersal abilities and it gave very interesting results. Robby's suggestion to use Moran's Eigenvector Maps is also an interesting approach though it is totally different to me. Spatial eigenvectors are very powerful and kind of trendy at the moment in Ecology in general. As far as I understand it, these may be very useful to capture spatial patterns that are not already captured by your explanatory variables. I think it is time for me to stop writing ;)

By the way, I totally agree with Joseph's comment, spatial eigenvectors in general are powerful but it is very tricky to interpret their ecological meaning, if they do have any ecological meaning...

Hi Yoannis!

I believe you are asking if geographical proximity can explain morphological similarity between two individual plants. This question makes sense only if you assume that geographical distance works as a surrogate for the strength of gene flow. Therefore, as an answer to your original question, you should analyse the three species separately in Mantel test. Different species do not change genes (naturally this is a slight oversimplification but probably acceptable here) and therefore you would get blurred results by combining the different species in your analysis.

About the general question of using Mantel test (or other statistical approaches to analyse the variance in pair-wise distance measures), please remember that it is a totally different thing if you are analysing distances or if you are analysing raw data. In the last line of the abstract in the Legendre & Fortin 2010 paper this is stated very nicely. Yet, unfortunately in the very same paper the authors make the mistake of comparing explanatory power of raw data analysis to that of distance analysis and concluding from this comparison that one method would be better than the other. This is not a justified conclusion because the two methods analyse different variances that are not necessarily correlated with each other even if they had been calculated from the very same data set. As a response to the interesting study by Gilbert & Bennett, you may be interested in checking also this: http://onlinelibrary.wiley.com/doi/10.1111/j.1600-0587.2012.07339.x/full

Thanks a lot Jonathan and Yoannis. Robby could you send me the chapter 14?

Dear Yoannis,

We did an analysis of the habitat fragmentation and genetic differences, for Moor frog. See the paper by Arens and myself. In a GIS environment we calculated (geographic) distances, but also the added effect of barriers. (article included in my profile).

From the same authors a paper on plant species, fragmentaton and genetical differentiation.

Regards,

Theo

You may try Cluster analysis (Ecludian) as well - Try it by MVSP software