Dear Lucas

Choosing the right multivariate analysis can be a bit painstaking. In general, it all depends on the preference of the investigator to choose their ordination analysis. Some use weight of the parameters and others eigenvalue. Having said that, not all ordination analyses can be used for every data. There are ways that you can figure out what ordination analysis best suit your data.

If you have CANOCO software then your life can be a bit easier. Fear not if you don’t. Simply use the open source program PAST which contain all the ordinations and many more multivariate analyses. It also has non-metric multidimensional scaling which some prefer over PCA if values are not linear.  

First thing first you need to figure out whether your data (i.e biological) are linear or unimodal or somewhere between. Best test to do this is to run a Detrended Correspondence Analysis (DCA) and look at axis 1 gradient length of ordinated species data. If this number is lower than 2 [SD] units, your data is linear. In this case the best ordination to compare your biological data with environmental data is a linear analysis, such as RDA (Redundancy analysis). If it is higher than 4 [SD] then you have a unimodal data and analyses such as CCA are the best fit for your data. If it is between 2 and 4 standard deviation [SD] units it is not clear whether a unimodal or linear response model best fit the data. In this case run two separate ordinations, both linear approaches RDA and unimodal approaches CCA. Whichever, method gives you higher variation on community data that methods best represent your data (i.e. correlation with environmental variables).

Make sure to perform Stepwise backwards elimination to find what environmental variable are best correlated with benthos community composition.

Hope this helps.

PCA is an unconstrained analysis, therefore you cannot correlate changes in env variable with biotic diversity. You could use some sort of multivariate analysis of variance (MANOVA) OR you can do a constrained ordination, such as redundancy analysis (RDA) to look at how the environmental data co-vary with the community (species abundance-site data). Best to use vegan package in R or PRIMER software.

Chris

I advice you to use CCA analyse or co-inertia to link environemental parameters with species composition!

As such, nothing wrong in using PCA, rather depends how you will do it. If applied to the environmental variables only, it can be help reduce their number and produce a few composite variables which unites correlated variables. These correlations can indicate which factor is “principal” and more important, how much variation in data is explained, etc. Then yo can plot biodiversity data (estimated species richness based on rarefactions and Simpson’s index would be the best, but you can use other indices such as H’ too for comparing to old data sets). In this way you can get an idea as to which variable(s) mostly drives diversity in your system.

The CCA, NMDS etc. are very good too and you can show how species distribute along environmental gradients.

May be you change a bit your approach, I would use all the species as dependent variables instead of synthesizing them into a diversity index. Then you can apply the classic PERMANOVA to evealulate each factor (pH etc..) against changes on the comunity. Visualization of cluster can done using typical PCA, K-means or any other algorithm.

If you want to carry on with you approach you should then use a multiple regrssion approach: Diversity ~ Ph + etc....In this sense PCA is not so helpful for your visualizations.

If you need some help with the code just let me know. I run everything in R environment.

Cheers

PCA assumes linear response, while the univariate equivalent (CA) assumes a unimodal response. The latter is usually used for species data, not indices like diversity. If you are interested in doing a constrained ordination, I would suggest doing redundancy analysis (like PCA this method assumes a linear response). Other options are running a PCA on your environmental data and then simply using correlation to study relations between the biotic indices and a a few environmental gradients (e.g. the first and/or second PCA axes scores; the PC axes are orthogonal, i.e not correlated, so this a pretty robust method for doing gradient analyses). Or as others have suggested, constrained ordination (CCA or RDA) of the species abundance data and environmental variables, alt CA or NMDS axes scores correlated with PCA axes scores. The choice of method should be based on what type of questions you are asking and the size of the data set, i.e. the easiest approach is often the best.

Dear Lucas

Choosing the right multivariate analysis can be a bit painstaking. In general, it all depends on the preference of the investigator to choose their ordination analysis. Some use weight of the parameters and others eigenvalue. Having said that, not all ordination analyses can be used for every data. There are ways that you can figure out what ordination analysis best suit your data.

If you have CANOCO software then your life can be a bit easier. Fear not if you don’t. Simply use the open source program PAST which contain all the ordinations and many more multivariate analyses. It also has non-metric multidimensional scaling which some prefer over PCA if values are not linear.  

First thing first you need to figure out whether your data (i.e biological) are linear or unimodal or somewhere between. Best test to do this is to run a Detrended Correspondence Analysis (DCA) and look at axis 1 gradient length of ordinated species data. If this number is lower than 2 [SD] units, your data is linear. In this case the best ordination to compare your biological data with environmental data is a linear analysis, such as RDA (Redundancy analysis). If it is higher than 4 [SD] then you have a unimodal data and analyses such as CCA are the best fit for your data. If it is between 2 and 4 standard deviation [SD] units it is not clear whether a unimodal or linear response model best fit the data. In this case run two separate ordinations, both linear approaches RDA and unimodal approaches CCA. Whichever, method gives you higher variation on community data that methods best represent your data (i.e. correlation with environmental variables).

Make sure to perform Stepwise backwards elimination to find what environmental variable are best correlated with benthos community composition.

Hope this helps.

I suggest best method for Canonical correspondence analysis CCA, Redundancy Analysis and Multiple regression analysis for your study. Now XL stat software and Past software free version available for making CCA and RDC analysis.

Dear Armin,

You explanation is really useful and helpful, especially testing whether the data is linear or unimodal or somewhere between by using DCA. Could you please share with me the report or book that I can read about this topic (testing data whether or not it is linear)?

Many thanks,