From hstevens at muohio.edu  Mon Feb  8 19:30:05 2010
From: hstevens at muohio.edu (Hank Stevens)
Date: Mon, 8 Feb 2010 18:30:05 +0000 (UTC)
Subject: [Rd] Canberra distance
References: <4B6D8D33.2070108@u-paris10.fr> <4B6D945F.2030709@stats.uwo.ca>
	<4B6D9956.3030708@u-paris10.fr>, <4B6DA028.8080902@stats.uwo.ca>
	<1BDAE2969943D540934EE8B4EF68F95FB262394F37@EXNSW-MBX03.nexus.csiro.au>
Message-ID: <loom.20100208T192330-917@post.gmane.org>

 <Bill.Venables <at> csiro.au> writes:

> 
> That is interesting.  The first of these, namely
> 
> sum(|x_i - y_i|) / sum(x_i + y_i)
> 
> is now better known in ecology as the Bray-Curtis distance.  Even more
interesting is the typo in Henry &
> Stevens "A Primer of Ecology in R" where the Bray Curtis distance formula is
actually the Canberra
> distance  (Eq. 10.2 p. 289).  There seems to be a certain slipperiness of
definition in this field.

Thank you for bringing to my attention the similarity of the Canberra and
Bray-Curtis quantitative indices. Bray-Curtis dissimilarity can also, of course,
be defined as 

1 - 2w/(a+b) 

where w is sum of the minimum of each relevant pair of values, and a and b are
the totals for sites a and b, respectively. These definitions appear to yield
similar results, and to better reflect the original work by Bray and Curtis, I
should probably define their distance as they did!

Cheers,

Martin Henry Hoffman Stevens (a.k.a. Hank)

> 
> What surprises me most is why ecologists still cling to this way of doing
things,  It is one of the few places I
> know of where the analysis is justified purely heuristically and not from any
kind of explicit model for
> the ecological processes under study.
> 
> Bill Venables.
> 
> 
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> 
>



[Rd] Canberra distance
Hank Stevens