posvectord: Position Vector and Species Vector Ordination

In jarioksa/natto: An Extreme 'vegan' Package of Experimental Code

Position Vector and Species Vector Ordination

Description

Position Vector Ordination (PVO) finds ordination axes that go through sample points in species space and maximize the projections of other points onto them. These are similar to Principal Components. Species Vector Ordination (SVO) finds a set of species that maximize the projections of other species on species axes. This also can be similar to Principal Components and can be used to select a subset of species that cover most of the variance in the data.

Usage

posvectord(x, scale = FALSE)

spvectord(x, scale = FALSE)

## S3 method for class 'posvectord'
plot(x, ...)

Arguments

x	Input data.
scale	Scale variables to unit variance.
...	Other arguments (passed to ordiplot).

Details

Position Vector Ordination (PVO, function posvectord) is a simple educational method that resembles Principal Component Analysis, PCA (Orlóci 1966, 1973a). Function posvectord positions vectors from the data centroid (origin) to sample points in species space and evaluates the projections of other sample vectors on these positioned axes, and selects the one with highest total projection as the ordination axis. Then the effects of that selected axis are removed from the covariance matrix, zeroing the row and column of selected sampling unit, and the process is repeated. Principal Components maximize this projection, but PVO axes can be close to the Principal Component, in particular in the large data sets with many observations. The method was proposed as a computationally light approximation to PCA suitable for the computers of 1960s (Orlóci 1966). Now it can only be regarded as historically interesting, and also as an educational tool in introducing PCA.

Species Vector Ordination (SVO; function spvectord) is similar, but it picks the species vector that maximizes the species projected onto that vector (Orlóci 1973b). The method picks the species or variable that explains largest proportion of variance and uses the centred values of this variable as the axis. Then it orthogonalizes all species or variables to that selected axis and repeats the selection process. PCA finds a linear combination of species or variables that minimizes the residual variance, but in SVO only one species or variable is used. The axes are named by the species or variables, and the axis scores are the centred (residual) observed values. The resulting plot has orthogonalized set of species as axes. SVO can be similar to PCA, in particular when some few species contribute most of the the total variance. The method only has educational use in explaining PCA in species space. Orlóci (1973b) suggesed SVO as a method of selecting a subset of species or variables that contributes most of the variance in the data. The current spvectord function can also be used for this purpose, although it is mainly geared for ordination. dave package has function orank specifically written for variable or species selection using the same algorithm.

Value

posvectord returns an object of class "posvectord", and spvectord returns an object of class "spvectord" that inherits from "posvectord". Both result objects have the following elements:

• points: The ordination scores. In SVO, these are named by the species (variable) the axes is based on, the numerical scores are the centred (residual) values of observed data. In PVO, they are called as PVO, and they are scaled similarly as in PCA and can reconstitute (a low-rank approximation of) covariances.

• totvar: The total variance in the input data.

• eig: Eigenvalues of axes.

References

Orlóci, L. (1966) Geometric models in ecology. I. The theory and application of some ordination methods. J. Ecol. 54: 193–215.

Orlóci, L. (1973a) Ordination by resemblance matrices. In: R. H. Whittaker (ed.) Ordination and Classification of Communities. Handbook of Vegetation Science 5: 249–286.

Orlóci, L. (1973b) Ranking characters by dispersion criterion. Nature 244: 371–373.

See Also

polarord (Polar Ordination) is a similar educational tool to approximate Principal Coordinates Analysis (PCoA).

Examples

data(spurn)
spvectord(spurn)
m <- posvectord(spurn)
m
plot(m)
if (require(vegan, quietly = TRUE)) {
plot(procrustes(rda(spurn), m, choices=1:2))
}

jarioksa/natto documentation built on March 28, 2024, 12:45 a.m.