[R-sig-eco] interpreting ecological distance approaches (Bray Curtis after various data transformation)

[Botta-Dukát Zoltán]

Dear Tim,

You are right: Bray-Curtis distance will be non-zero if two communities 
differ in size (sum of abundances), even if the relative abundances is 
the same. If you have number of individuals data, rarefying is the best 
solution. If you cannot apply it (e.g. because only cover data are 
available), you can calculate distance from relative abundance, and yes, 
this case BC is equivalent to Manhattan. Note that using relative 
abundances don't remove fully the effect of different sampling effort, 
because rare species could missing from the smaller sample.

I don't recommend calculating BC-distance from Hellinger-transformed 
data, because sum of transformed abundances are meaningless.

Best regards,

Zoltan

2019. 04. 02. 17:15 keltezéssel, Tim Richter-Heitmann írta:
> Dear list,
>
> i am not an ecologist by training, so please bear with me.
>
> It is my understanding that Bray Curtis distances seem to be sensitive 
> to different community sizes. Thus, they seem to deliver inadequate 
> results when the different community sizes are the result of technical 
> artifacts rather than biology (see e.g. Weiss et al, 2017 on 
> microbiome data).
>
> Therefore, i often see BC distances made on relative data (which seems 
> to be equivalent to the Manhattan distance) or on data which has been 
> subsampled to even sizes (e.g. rarefying). Sometimes i also see Bray 
> Curtis distances calculated on Hellinger-transformed data,
>
> which is the square root of relative data. This again makes sample 
> sizes unequal (but only to a small degree), so i wondered if this is a 
> valid approach, especially considering that the "natural" distance 
> choice for Hellinger transformed data is Euclidean (to obtain, well, 
> the Hellinger distance).
>
> Another question is what different sizes (i.e. the sums) of Hellinger 
> transformed  communities represent? I tested some datasets, and 
> couldnt find a correlation between original sample sizes and their 
> hellinger transformed counterparts.
>
> Any advice is very much welcome. Thank you.
>