[R-sig-Geo] How to estimate sig2 attribute for functions linker and kernelbb from the adehabitatHR package

[Clément Calenge]

Hi all,

> in my study we followed the birds for the whole day from sunrise (ca. 5.15 h)
 > until sunset (ca. 21.45 h) and recorded every change in position (if 
we were
 > fast enough). So I could have a temporal resolution of one minute
 > if want to.  Of course we have gaps and the individuals have not
 > been followed every day, but for one burst the data are indeed
 > highly serial autocorrelated. That is why I was thinking about
 > using the BB-Kernels to have a look on the differences to the more
 > traditional UD-Kernels.

BB-kernels are not designed only for GPS data. They were developed by 
Bullard (1991), at a time when GPS monitoring was not that current in 
ecology. It was developed precisely to take into account the fact that a 
high serial autocorrelation in the successive relocations bring 
informations not only on the places where the animal was at the time of 
monitoring (the relocations), but also on the places where the animal 
might have been between successive relocations. And this is justified by 
the fact that there is a strong autocorrelation in the relocations, and 
not by the technology used to obtain them (GPS, VHF, visual 
observations, etc.). Therefore, the use of VHF does not preclude the use 
of kernelbb. As Andy noted, the important aspect is that a high serial 
autocorrelation is required, which seems to be the case with your data.

Now, the equal time intervals between successive relocations is not, in 
theory, a requirement of the method. The method uses a Brownian bridge 
to estimate the probability density that the animal used any particular 
pixel, given its relocations. Roughly, the brownian bridge supposes that 
the animal is moving completely randomly between two successive 
relocations, and under this model, it is possible to estimate the 
probability density that the animal was present in a pixel, given its 
locations. The kernelbb is an improvement of the classical kernelUD 
approach, as it takes into account the movement constraints (the animal 
has a limited maximum speed). Therefore, under this model, the "shape" 
of the Brownian bridge characterizing two successive relocations is 
adjusted as a function of the time lag separating these two relocations: 
if the time lag is short, the bridge will be narrower than if the time 
lag is long. Therefore, *in theory*, there is no need for regular 
trajectories to use this approach.

However, as all models, the brownian bridge is false: the animal is 
actually not moving completely randomly. Even though this approximation 
may be useful to account for the movement constraints (e.g. an animal 
cannot move 20 km in two minutes), its implications may be problematic 
if the time lag between successive relocations is highly variable (e.g. 
relocations separated by time lags distributed over several orders of 
magnitude, e.g. 10-20 min in some cases and 2 days in other). See this 
thread for an example of the problems that may arise in those cases:
http://www.mail-archive.com/animov@faunalia.it/msg00106.html
But for moderate variations in this time-lag, kernelbb should perform 
reasonably well.

Concerning sig2, there no particular "automatic" method to estimate it. 
It is a common procedure to set it equal to the imprecision of the 
relocations. Note that Benhamou and Cornelis (2010) and Benhamou (2011) 
proposed another approach using biased random bridge (BRB) instead of 
pure random walk in this estimation (i.e. an approach similar to 
kernelbb, but adding a "drift" component to the animal movement between 
successive relocations) leading to estimates more biologically 
consistent. Note also that this method gives you a finer control on 
biologically relevant parameters, and that the diffusion can be 
different for different habitat types. Have a look at the vignette of 
adehabitatHR, page 38:

 > vignette("adehabitatHR")

Note that the discussion concerning the hmin parameter of the BRB 
approach p. 40 and 41 of this vignette is also relevant for the problem 
of the argument sig2 of kernelbb.
Hope this helps,


Clément Calenge

-- 
Clément CALENGE
Cellule d'appui à l'analyse de données
Direction des Etudes et de la Recherche
Office national de la chasse et de la faune sauvage
Saint Benoist - 78610 Auffargis
tel. (33) 01.30.46.54.14