[R-sig-eco] Relating species abundance and cover

[Karen Kotschy]

To Philip, Carsten, Etienne, Ben and Chris

I really want to thank all of you for the time and effort you put into 
answering my question. You guys rock!! It gives me such faith in the power 
of open-source communities like this, and makes me want to contribute in 
turn where possible!

Thanks, Philip, for your insightful questions and helping me to think 
about the data more clearly. I was being stupid with the zeroes: yes, they 
do result from aggregating the data, and they do represent cases where a 
species did not occur in a particular sampling unit (so no cover or 
abundance recorded). All records of abundance for a species have matching 
records of cover. Since I am mainly interested in how strongly correlated 
the 2 measures are, I think I can happily leave out the zeroes, since 
I am only interested in abundance vs cover where these were recorded. You 
have reminded me to think carefully about what the aggregation of my data 
means for the analysis, though. Ben, my cover data is not in the form of 
point counts so that is not an option. Also, I can't use raw counts for 
abundance because of unequal sampling effort/area.

I have decided that correlation coefficients are probably fine for my 
purposes. I have calculated Spearman and Kendall correlations, and used 
Pearson correlations and model II regression on log-transformed data (as 
you did, Etienne), as well as on ranked data. These all indicate a strong 
positive correlation, and a linear relationship with transformed data, and 
give a consistent picture.

Beta regression looks like a really useful tool that, even if I don't use 
it here, I may well use for some other aspects of my project. Thanks Ben 
for pointing me to it. 

Carsten: did you imply that beta regression is necesarily model I 
regression (no variance in predictor variable)?? I'd be interested to hear 
anyone's thoughts on how much of a limitation this is for situations where 
both y and x are random variables. Is it the same as for OLS regression, 
where OLS is acceptable if the error variance in x is less than a third of 
that in y?

Thanks again!

Cheers
Karen



On Wed 27Oct10, Philip Dixon wrote:
>  Karen,
> 
> I suggest you step back and ask two questions:
> 1) what are you trying to do? (i.e. what is the real goal?)
> 2) what do you do it to?  (i.e. what's the appropriate data?)
> 
> Do you want to construct a model or estimate correlations?  Your 
> detailed questions suggest that your real interest is the correlations.  
> If so, you don't need an explicit model.  Just estimate the 
> correlation.  You get to choose how to define correlation.  The four 
> most common choices are Pearson correlation on the original scale, 
> Pearson correlation on some transformed scale, Spearman (rank) 
> correlation, or Kendall's (tau) correlation.
> 
> I presume the 0's arise from species that are absent from a site, i.e. a 
> (0,0) pair of (abundance, cover).  Is it appropriate to include these?  
> You could define correlation in three ways:
> 1) conditional on a species present at a site.  That eliminates all the 
> (0,0).
> 2) conditional on a species present in the regional species pool.  This 
> MAY be the same as conditional on a species present in your data set.  
> You clearly have the second.  The BIG issue is whether 'in your data' is 
> an adequate representation of 'in the regional species pool'.
> 3) conditional on all extant species in your taxonomic group.  That adds 
> additional (0,0) pairs for all species present in other regions.
> If you really want to model the relationship, this issue is still important.
> 
> Best wishes,
> Philip Dixon
> 
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