Consuelo,
Here are some elements that you might find useful.
I had already read the paper. I understood the idea of the scatter plot,
that the arrows were a projection of the marginality and specialization but
I didn't understand where the length of arrows came from. I was somehow lost
thinking how their length represent the marginality and specialization. Now
you tell me that they "correspond to the scores of the environmental
variables on the axes of the ENFA". Hmmm.... Are these scores given
somewhere in the output of enfa?
Yes they are. Look at the $co element of the enfa object. Following the
example in ?enfa:
> enfa1$co
Mar Spe1
forets 0.7178829 0.29304902
hydro 0.0977121 -0.94018385
routes -0.5394778 0.15001749
artif 0.4290224 -0.08758622
It gives you the coordinates of the arrow. The starting point of the
vector is the average availability which is centred on zero.
You see, the main issue for me is that if I put that graph in a manuscript,
I'd like to be able to tell, the arrow length represent XX times the
marginality and XX times the specialization of each variable or something
like that. In order to give an idea of the real value of marginality and
specialization. Does it make any sense? Maybe it doesn't make any sense and
it's not necessary, what do you think? I hope you understand me this time...
otherwise, I'll give up!!!
You should interpret the scatter plot qualitatively. E.g. in the example
of ?enfa, the marginality is very strong on "forets" (forest) with a
shift towards high values, on "routes" (roads) with a shift on low
values, and to a lesser extent on "artif" (artificial areas) with a
shift on high values. On the other hand, the specialization is very
pronounced on "hydro" only, with a restriction around the mean (you have
to look at the specific distributions on this particular variable to say
more about it).
Regarding the global specialization issue. Not sure about something again.
You told me that there's not global specialization, but Hirzel et al (2002),
described it. Why you say "it cannot be measured globally over the
ecological space"? Is it wrong if I use the global specialization formula of
Hirzel et al (square root of the sum of the eigeinvalues divided by the
number of variables) to estimate this global specialization (sensu Hirzel et
al)? Can I do that?
You can indeed compute such an index. But now, how would you interpret
it? The only case it could be useful is the comparison of two niches in
the same environment, i.e. same availability. Two study sites cannot be
compared on such basis. So that it would give you an idea of a global
specialization that is totally context dependent. This is why it is not,
from my point of view, very useful.
And regarding the tolerance, just to be sure we're talking about the same,
is it the inverse of the specialization, right? if I calculate it, could I
use it to estimate the specialization? Actually, I have tried to calculate
the tolerance, but I think I have used the wrong "wei". Can you please
confirm I'm using the correct terms?
It is conceptually the inverse of the specialization: the specialization
is a ratio of variances (available over used) while the tolerance is the
sum of used variances over all variables (which is similar to divide it
by an available variance of 1). You might have a look at ?niche.test for
a global measure of tolerance.
You told me to use this formula: sum(dudi.pca(tab, row.w=wei,
scan=FALSE)$eig); in which "tab" is the dataframe containing the values of
environmental variables and "wei" is vector describing the utilization
weight of each pixel. Using the manual example for enfa:
data(lynxjura)
map <- lynxjura$map
tmp <- lynxjura$locs[,4]!="D"
locs <- lynxjura$locs[tmp, c("X","Y")]
dataenfa1 <- data2enfa(map, locs)
enfa1 <- enfa(pc, dataenfa1$pr,+ scannf = FALSE)
For me, in this case, "tab" would be kasc2df(map) and "wei" would be
dataenfa1$pr
so, the tolerance would be: sum(dudi.pca(kasc2df(map), row.w=dataenfa1$pr,
scan=FALSE)$eig)
Is this correct? I got this huge value (2355). It's kind of high, isn't it?
Maybe try:
sum(dudi.pca(kasc2df(map), row.w = dataenfa1$pr/sum(dataenfa1$pr),
scan=FALSE)$eig)
which gives you 5 only. The weights should sum to 1 (i.e. they are
proportions). But then, how would you interpret this? This is the same
as for the "global specialization".
And about the specialization axis you keep in enfa (or madifa or gnesfa or
any other one of these analysis), is there a way to get the % variation
explained by each eigenvalue? I mean, a referee can ask that, right? I have
tried to figure it out, but without any luck... I have chosen only one
eigenvalue of specialization, but I wasn't able to calculate how much
variation it accounted for.
There is no way to give a percentage of variation for a specialization
axis, by nature: the eigenvalue of each axis gives you a ratio of
variance. E.g. an eigenvalue of 12 tells you that the available variance
on this axis is 12 times higher than the used variance. It is up to you
to interpret this (is it a strong specialization or not).
I hope you don't mind all these question... I need to be sure of what I'm
doing if I want to publish these results...
No problem about it. The ENFA, however, should be seen as a very elegant
way of exploring the data, at the manner of a PCA (and the
interpretation is in many ways similar, when you take into account the
specificity of the analysis).
Hope this helps a bit,
Mathieu.
Thanks!!!
Consuelo
-------------
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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Stop Gaza Massacre
2010/6/7 Clément Calenge <clement.cale...@gmail.com>
On 06/04/2010 09:40 AM, Consuelo Hermosilla wrote:
Hummm, true, I got confused! Sorry!! I meant scatter.enfa.
What I don't understand is the length of the arrows. The grid is d=2,
different from the grid set with the biplot of marginality and
specialization (d=0.5). In that case, the length make senses to me, but I
don't understand it in the scatter.enfa. They don't have the same lenght
/value as they have in the biplot. Do you understand me?
I do not understand you... The function scatter.enfa draws the biplot
associated with the results of the ENFA. The following paper explains this
graph in detail:
Basille, M., Calenge, C., Marboutin, E., Andersen, R. and Gaillard, J.M.
2008. Assessing habitat selection using multivariate statistics: some
refinements of the ecological niche factor analysis. Ecol. model. 211:
233--240.
I am not sure what you mean by "biplot of marginality and specialization".
There is only one way to draw a biplot with the ENFA: it is provided by
scatter.enfa (see the paper cited above). So I do not understand how the
result of scatter.enfa could be inconsistent with the biplot, since the
result of scatter.enfa *is* the biplot.
Best,
Clément Calenge
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