clement.calenge at oncfs.gouv.fr
Thu Feb 5 11:25:44 CET 2009
> This is a first point: I've used Nams' FRACTAL on several species up to now,
> that is Brown bear, the Alpine Ibex, Leisler's noctule and a putativa
> invasive bird species (Paradoxornis webbianus).
> I found the vFractal estimator rather useful to have an idea not just of
> the 'path tortuosity', but of the scale level at which 'search patterns'
> occur. The results achieved are quite interesting, i.e. Brown bears released
> in NE Italy showed significant differences in D calculated in the release
> year and in subsequent years, Ibexes showed a 'random walk peak' in the
> D-vs-scale diagram ad about 1 km (which does make perfect sense for an Ibex)
> and P. webbianus, already known as a short distamce mover, showed a 300 to
> 500 m search range.
> I found this very useful to have an idea of the scale of habitat perceprtion
> by a species, and since I run all my analyses in R (what else? :) I'm annoyed
> to go back and forth from FRACTAL to adehabitat.
> This could be an example of fractal dimension use (...hope so...)
Many thanks for this answer, you made a very interesting point.
Actually, my point of view is anchored in the field of statistical tools
development for animal movement analysis, and I sometimes overlook the
need of biologists in practical studies. I of course acknowledge that
this approach could be used presently with benefits as a heuristic tool,
to explore scale-related patterns in the trajectory.
However, this leads to an interesting question from a theoretical point
of view: the fractal D has a clear mathematical meaning only when
objects are self-similar (same properties at large and small scale), and
from an "applied studies" point of view, this measure is mainly used on
objects which are not self-similar, precisely to study this deviation
from self-similarity, and the scale at which this deviation occurs (but
IMHO, we should not call it "fractal" D in this context). What I do not
understand is why a parameter measuring a property on one category of
objects would necessarily be a meaningful measure of the deviation of
one object from this category?
The main argument of Nams (2005; Oecologia 143: 179-188), a strong one
actually, is an empirical observation: all the simulations he did seem
to confirm that D changes continuously within domains, and that
discontinuity occur at domain changes (under the hypothesis of spatial
homogeneity of the trajectory). Both your successes in using this
approach and this empirical argument make the approach interesting for
multiscale analysis (together with the present lack of alternative
approaches in the ecological literature).
This is a bit off-topic, so I do not pursue further, but I think that
more theoretical research may be needed here to establish clearly the
theoretical foundations of this approach, which would define the context
on which it relies (hypotheses on which it relies, required properties
for the trajectories, etc.; but I may have missed such work in the
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