Hello everyone.
I received requests for the answers to my negative spatial autocorrelation
question so below I have summarised them. I thank everyone (Suzanne
Sadedin, Craig Streatfield, Filipe Alberto, Kathryn Elmer, Heribert Hofer,
Paul Sunnucks, Ross Croizer and Xavier Turon) very much for their kind
attention to it.
It seems I had simply gotten mixed up in a jumble of words (more similar,
less dissimilar, more genetic distance: more difference, less distance..).
The term negative spatial autocorrelation refers to individuals being
less similar (more different) than expected, not the other way around
as I said in the past email. Now things do make biological sense to me!
I am glad I sent the question not only because this has been made clear
to me but because some of the answers, including one from an email sent
directly to Genalex authors Peter Smouse and Rod Peakall, have turned
my attention to the fact that because of the way calculations are made,
a see-saw effect comes into play: if you push up on one side (positive
autocorrelation) the opposite side goes down (negative autocorrelation).
No pushing on either side makes for a flat see-saw (no autocorrelation,
no restrictions to gene flow at the scale that is being measured). I
incorporated the see-saw analogy myself and it's not without its
imperfections so please see Smouse's explanation below.
Thanks again,
Gisselle
Gisselle Perdomo
Laboratorio de Ecolog�a del Comportamiento
Departamento de Estudios Ambientales
Divisi�n de Ciencias Biol?gicas
Universidad Sim�n Bol�var
Apdo. 89.000, Caracas 1080-A, Venezuela
Telf: (58-212) 906 3043
Fax: (58-212) 906 3039
email: gisselle_p@yahoo.com
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Peter Smouse quote:
The correlation of two individuals is defined, relative to what would
happen for the average pair in the study, which average is (by virtue
of the way the autocorrelation is computed from the covariance matrix)
precisely zero. If the average autocorrelation (over the whole data
set) is centered at zero (and it is), then if some of the N(N-1)/2
pairs are positively autocorrelated, others must be negatively
autocorrelated. Otherwise, the whole set would not average out to
zero! If the close neighbors are positively autocorrelated, and they
typically are, then those that are more distant will be negatively
autocorrelated. As I said, not profound, just a matter of having the
algebra add up properly. Another way to say it, in less algebraic terms,
is that if some individuals are more correlated (related) than average,
others must be less correlated (related) than average, since the average
is defined to be "uncorrelated".
gisselle_p@yahoo.com