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

[Ben Bolker]

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On 10-10-31 07:08 PM, Karen Kotschy wrote:

> 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.

  OK, although if you have a measure of sampling effort you may be able
to use offsets to adjust for it.

> 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.

  Sounds fine.

> 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?
> 
  I don't know exactly where that rule of thumb comes from ...
  'model II beta regression' would correspond in my mind to fitting a
bivariate probability distribution with Beta marginal distributions -- I
know that this can be done using an object/approach called 'copulas' but
this is a whole new can of worms which I have not opened myself ...

   Ben Bolker
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