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

[Tim Richter-Heitmann]

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.

-- 
Dr. Tim Richter-Heitmann

University of Bremen
Microbial Ecophysiology Group (AG Friedrich)
FB02 - Biologie/Chemie
Leobener Straße (NW2 A2130)
D-28359 Bremen
Tel.: 0049(0)421 218-63062
Fax: 0049(0)421 218-63069