Hello Consuelo,

Have a look at:

      Calenge, C., Darmon, G., Basille, M., Loison, A. and Jullien J.M.
      (2008) The factorial decomposition of the Mahalanobis distances in
      habitat selection studies. _Ecology_, *89*, 555-566.

See especially the section "The MADIFA and the ecological-niche factor 
analysis" (p. 559), which explains the reasons for this message. 
Basically: the ENFA distinguishes two very different parameters: the 
marginality (the vector connecting the mean of available points to the 
mean of used points) and the specialization (ratio of the available 
variance/used variance). From this paper:

"On the other hand, as the marginality axis does not have the same 
mathematical status as the specialization axes of the ENFA (the 
marginality axis is orthogonal to the specialization axes, but the 
specialization axes are not orthogonal among each other; Hirzel et al. 
2002), it is often difficult to combine all these axes into one single 
index of environmental suitability. So far, existing methods trying to 
combine the marginality and specialization axes use ad hoc algorithms 
(Hirzel et al. 2002, Hirzel and Arlettaz 2003). Although these 
ENFA-based methods have proven to return biologically consistent
environmental suitability maps (ESMs; e.g., Bryan and Metaxas 2007), the 
MADIFA is probably a better way to build environmental suitability maps: 
it returns axes, all with the same mathematical status, which can be 
combined into ESMs in a consistent manner."

The function predict.enfa uses the Mahalanobis distances (Clark et al. 
1993) calculated on the marginality and specialization axes to calculate 
these suitability maps. But, as for other methods (such as those 
implemented in Biomapper), the "habitat suitability modelling" is a 
second step of the analysis; the ENFA itself is not optimal for such 
mapping. On the other hand, the ENFA can be very useful for the 
exploration of the niche (see the help page of the function enfa, and 
references therein). A deeper description of these aspects can be found 
in the paper cited above.
HTH,


Clément Calenge


On 05/04/2010 01:41 PM, Consuelo Hermosilla wrote:
> Hello guys,
>
> I have a couple of questions regarding enfa (adehabitat package).
>
> The first is related to this message: "In predict.enfa(enfa1,
> octopus.hab$index, octopus.hab$attr) :
>    the enfa *is not mathematically optimal for prediction*:
>   please consider the madifa instead".
> I was wondering why that message and if it does appear every time you make
> your analysis or it means you have a problem with your data/grids. Do I
> explain myself? I mean, is this the default message? does it always appear?
> And if it so, why madifa is better?
> I'm curious since this code should do the same as Biomapper does, right?
> Then, is biomapper not mathematically optimal for prediction too? Maybe I'm
> misunderstanding something...
>
> Another thing, what would you suggest to compare maxent and enfa outputs?
>
> One last thing is regarding plotting the result. If I use image(), then, how
> do I plot the legend? I tried plot() with the prediction, and it does plot
> the legend, but I don't understand the values it has. Shouldn't it range
> from 1 to 100, like in other prediction models? Again, I'm sorry if I'm
> making wrong assumptions...
>
> I hope this is helpful to someone else too!
>
> Thank you very much!
>
> Consuelo
>
> PS. You know Mathieu, another big advantage of the enfa implementation in R
> is that you don't have to convert all your grids to Idrisi format... it can
> be really a pain...  I love that!
>
> -------------
> Consuelo Hermosilla
> PhD student
> Departamento de Ecología y Biología Animal
> Departamento de Bioquímica, Genética e Inmunología, Área de Genética
> Facultad de Ciencias del Mar
> Campus de As Lagoas-Marcosende
> Universidad de Vigo
> 36310 Vigo
> SPAIN
> Mobile: +34 692 633 298
>
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