hillscale: Hill indices of Beta diversity and gradient scaling to...
In jarioksa/gravy: Gradient Analysis of Vegetation

Description Usage Arguments Details Value Author(s) References See Also Examples

The function finds two kinds of Hill indices of Beta diversity and tries to scale the gradient to constant Hill index 2 by segments.

hillscale(veg, grad, cycles = 4, freq.lim = 1)
betahill(veg, grad, freq.lim = 1)
## S3 method for class 'hillscale'
plot(x, which=c(1,2), xlab, ...)

`veg`	Community data matrix.
`grad`	Environmental gradient.
`cycles`	Number of Hill scaling cycles in rescaling.
`freq.lim`	Frequency limit for including species.
`which`	Plots for indices 1 and 2.
`xlab`	Label for graphs. If missing, gradient name used.
`x`	A `"hillscale"` result object.
`...`	Other graphical parameters.

Mark Hill (1979) suggested two indices of Beta diversity:

Mean width of species responses, measured as weighted standard deviation of gradient values.
Weighted variance of species scores within a site.

Hill & Gauch (1980) discuss only the former index, but the program decorana uses only the second index. Function betahill calculates both indices for all sample plots. In addition, the function smooths these on 20 segments along the gradient, using the same algorithm as decorana (Hill 1979, Hill & Gauch 1980).

Function hillscale rescales the gradient by segments using Hill index 2 (weighted variance of species scores) following as faithfully as possible the rescaling algorithm in decorana. However, the function evaluates Hill index 1 (mean weighted sd of species), unlike decorana.

The major difference is that decorana scales a correspondence analysis axis where site scores are direct weighted averages of species scores. Function hillscale uses original gradient values, but finds the species scores as weighted averages of gradient values, and expands the species scores that they have the same weighted variance as the species scores would have in correspondence analysis. If a correspondence analysis axis is given as a gradient, same species scores will be found as in decorana. Another major difference is that decorana never rescales site scores. It rescales species scores instead, and always finds the site scores as direct weighted averages of species scores. Function hillscale rescales gradients. This difference is so significant that a rescaled correspondence analysis axis will be different in hillscale and decorana.

Both functions return an object of class "hillscale" with following items:

`grad`	Rescaled gradient in `hillscale` or the original gradient in `betahill`
`Hill.1`	Hill index 1 (mean weighted sd).
`Hill.2`	Hill index 2 (weihted variance of species scores).
`zv1`	The smoothed values of Hill.1 on 20 segments.
`zv2`	The smoothed values of Hill.2 on 20 segments.
`rug`	21 rug tics equally distributed on the original gradient.
`cycles`	The number of rescaling cycles.
`gradname`	The name of the gradient variable.
`Call`	The function call.