[R-sig-eco] PCNM calculation using pcnm vegan´s function

[Jari Oksanen]

On 6/05/10 18:01 PM, "Victor Landeiro" <vllandeiro at gmail.com> wrote:

> I have two matrices of distances among sampling points. One is for water
> course distances and the other is for overland distances (Euclidean
> distances). 
...
> 
> When trying to calculate PCNMs for these matrices I had a strange behavior
> with overland distances. For water course distances I got 30 Eigenvalues (24
> positive). For overland distances I got just 10 eigenvalues (8 positive).
> 
> Does anyone know why pcnms calculated for overland distance do not generates
> n-1 PCNMs (Including positive and negative)?

Victor,

One feasible hypothesis is that your Euclidean overland distances are more
... Euclidean. Would they be strictly Euclidean, you'd get only two positive
eigenvalues and no negative eigenvalues: Euclidean distances in 2 dimensions
can be exactly mapped onto two principal coordinates. However, we
"de-euclidify" distances in PCNM: there is a truncation threshold for long
distances, and all longer distances are made into arbitrary constant value.
You really cannot control the effects of this truncation, in particular if
you gave the control to function by not supplying explicit value of the
'threshold' argument. However, the effects of this "de-euclification" may
not be so very drastic in all cases and therefore you may get something
between two positive eigenvalues (= completely Euclidean) and n-1 non-zero
eigenvalues with some negative ones (= absolutely non-Euclidean).

Cheers, Jari Oksanen