Martin,
You're perfectly right, this is was an oversight from my part and David
gave a more general definition of my point of view (including flow of
material).
Now, if I go back on Katharine question, this is important to understand
that traits are just a kind of proxy to evaluate ecosystems functions and
more particularly ecosystems functions realized by estuarine fishes.
Consequently, in traits studies we are quite far from a pure evaluation
of functional diversity. My PhD thesis was on freshwater invertebrates
traits and some people said to me that I wasn't measuring a "functional
diversity" because there was no direct link with nutrient or energy. This
is true of course. But this is the reason why I wrote in my first message
that functional diversity measures "the different way to manage energy"
(or material). As traits highlight organisms strategies to maximize their
success in ecosystems, we can consider them as a good way to quantify one
part of the possible ways to transport energy and material.
Mathematically speaking, I'm not sure that beta diversity derived from
Rao's index can be considered as a real distance (ie with all properties
of a distance) and so included in a cluster analysis. This is a quite
complicated index giving a disproportionate weight to abundant species.
Consequently, by using Rao's index, you consider that species with high
counts are more important for ecosystems functions. Quite simply, a prey
(generally abundant) is more abundant than a predator to ensure flows of
energy and material. In addition, Rao's index express the mean
(functional, biological...) distance of two individual taken at random in
the community. As a mean, this index tend to stabilize as the number of
species increase (at a rate depending on the distance matrix used and so
on the chosen traits) leading to the conclusion that the more species you
have the more functionally redundant they are.
I could say many things on Rao's index but the most important is that we
must be very careful about our biological hypotheses on functional
diversity to check if indices are able to really illustrate them.
HTH again
Nicolas
Le Fri, 28 Sep 2012 18:41:02 +0200, Martin Meiss <[email protected]> a
écrit:
Nicolas,
Why would you restrict your interest to the flow of energy, and
not
include the flow of material, such as a nutrient like fixed nitrogen, or
potassium?
Martin M. Meiss
2012/9/27 Katharine Miller <[email protected]>
Hi,
I wanted to thank everyone for their responses and recommendations.
Some
of
them were quite helpful and have got me thinking in new ways.
With respect to the use of the Rao index, I didn't express my question
very
well. What I was really trying to discern was whether it was
appropriate to
use the Rao index values as a distance matrix of functional
dissimilarity
between estuaries that could then be evaluated using standard
multivariate
methods (i.e. clustering). I have not seen Shannon entropy used this
way
either, but it is understood that pairwise beta diversity calculated by
either of these approaches is a measure of dissimilarity between sites.
So,
on that basis, it doesn't seem too much of a stretch. Also, the index
values
are used as dissimilarities in Mantel tests or other matrix
calculations.
I am not sure whether the reason these indices have not been used this
way
is because it would be inappropriate statistically or mathematically, or
whether there is some ecological reason for not doing it.
Thanks again.
- Katharine
--
Nicolas PERU, PhD
33-(0)4 72 43 28 94
06-88-15-23-10
CNRS, UMR 5023 - LEHNA
Université Claude Bernard - Lyon 1
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