interpreting ecological distance approaches (Bray Curtis after various data transformation)

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.

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 keltez?ssel, Tim Richter-Heitmann ?rta:

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.