[AniMov] fractals

[Clément Calenge]

Hi Damiano,

> 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 
literature)...
Best wishes,


Clément Calenge
-- 

Clément CALENGE
Office national de la chasse et de la faune sauvage
Saint Benoist - 78610 Auffargis
tel. (33) 01.30.46.54.14