## S3 method for class 'default':
radfit(x, ...)
rad.null(x, family=poisson, ...)
rad.preempt(x, family = poisson, ...)
rad.lognormal(x, family = poisson, ...)
rad.zipf(x, family = poisson, ...)
rad.zipfbrot(x, family = poisson, ...)
## S3 method for class 'radline':
predict(object, newdata, total, ...)
## S3 method for class 'radfit':
plot(x, BIC = FALSE, legend = TRUE, ...)
## S3 method for class 'radfit.frame':
plot(x, order.by, BIC = FALSE, model, legend = TRUE,
as.table = TRUE, ...)
## S3 method for class 'radline':
plot(x, xlab = "Rank", ylab = "Abundance", type = "b", ...)
radlattice(x, BIC = FALSE, ...)
## S3 method for class 'radfit':
lines(x, ...)
## S3 method for class 'radfit':
points(x, ...)
as.rad(x)
## S3 method for class 'rad':
plot(x, xlab = "Rank", ylab = "Abundance", log = "y", ...)Null, Preemption, Lognormal, Zipf,
Mandelbrot.xyplot).x and y axes."b" for plotting both observed points
and fitted lines, "p" for only points, "l" for only
fitted lines, and "n" for only setting the frame.log = "y" gives the traditional plot of community ecology
where the pre-emption model is a straight line, and with
log = "xy" Zipf model is a straight line. With
<rad.null, rad.preempt, rad.lognormal,
zipf and zipfbrot fit each a single RAD model to a
single site. The result object has class "radline" and
inherits from glm, and can be handled by some (but not
all) glm methods. Function radfit fits all models either to a single site or to
all rows of a data frame or a matrix. When fitted to a single site,
the function returns an object of class "radfit" with items
y (observed values), family, and models
which is a list of fitted "radline" models. When applied for a
data frame or matrix, radfit function returns an object of
class "radfit.frame" which is a list of "radfit"
objects, each item names by the corresponding row name.
All result objects ("radline", "radfit",
"radfit.frame") can be accessed with same method functions.
The following methods are available: AIC,
coef, deviance, logLik. In
addition the fit results can be accessed with fitted,
predict and residuals (inheriting from
residuals.glm). The graphical functions were discussed
above in Details.
Functions rad.null, rad.preempt, rad.lognormal,
rad.zipf and zipfbrot fit the individual models
(described below) for a single vector (row of data frame), and
function radfit fits all models. The argument of the function
radfit can be either a vector for a single community or a data
frame where each row represents a distinct community.
Function rad.null fits a brokenstick model where the expected
abundance of species at rank $r$ is $a_r = (J/S)
\sum_{x=r}^S (1/x)$ (Pielou
1975), where $J$ is the total number of individuals (site total)
and $S$ is the total number of species in the community. This
gives a Null model where the individuals are randomly distributed
among observed species, and there are no fitted parameters.
Function rad.preempt fits the niche preemption model,
a.k.a. geometric series or Motomura model, where the expected
abundance $a$ of species at rank $r$ is $a_r = J \alpha
(1 - \alpha)^{r-1}$. The only
estimated parameter is the preemption coefficient $\alpha$ which
gives the decay rate of abundance per rank. The niche preemption
model is a straight line in a RAD plot. Function
rad.lognormal fits a log-Normal model which assumes that the
logarithmic abundances are distributed Normally, or $a_r = \exp(
\log \mu + \log \sigma N)$,
where $N$ is a Normal deviate. Function rad.zipf fits
the Zipf model $a_r = J p_1 r^\gamma$ where
$p_1$ is the fitted proportion of the most abundant species,
and $\gamma$ is a decay coefficient. The Zipf--Mandelbrot model
(rad.zipfbrot) adds one parameter: $a_r = J c (r +
\beta)^\gamma$ after which $p_1$
of the Zipf model changes into a meaningless scaling constant
$c$.
Log-Normal and Zipf models are generalized linear models
(glm) with logarithmic link function. Zipf--Mandelbrot
adds one nonlinear parameter to the Zipf model, and is fitted using
nlm for the nonlinear parameter and estimating other
parameters and log-Likelihood with glm. Preemption
model is fitted as a purely nonlinear model. There are no estimated
parameters in the Null model.
The default family is poisson which is
appropriate only for genuine counts (integers), but other families
that accept link = "log" can be used. Families
Gamma or gaussian may be appropriate for
abundance data, such as cover. The ``best'' model is selected by
AIC. Therefore ``quasi'' families such as
quasipoisson cannot be used: they do not have
AIC nor log-Likelihood needed in non-linear models.
All these functions have their own plot functions. When
radfit was applied for a data frame, plot uses
Lattice graphics, and other plot
functions use ordinary graphics. The ordinary graphics functions
return invisibly an ordiplot object for observed points,
and function identify.ordiplot can be used to label
selected species. Alternatively, radlattice uses
Lattice graphics to display each radfit
model of a single site in a separate panel together with their AIC or
BIC values.
Function as.rad is a base function to construct ordered RAD
data. Its plot is used by other RAD plot functions
which pass extra arguments (such as xlab and log) to
this function.
Wilson, J. B. (1991) Methods for fitting dominance/diversity curves. Journal of Vegetation Science 2, 35--46.
fisherfit and prestonfit.
An alternative approach is to use
qqnorm or qqplot with any distribution.
For controlling graphics: Lattice,
xyplot, lset.data(BCI)
mod <- rad.lognormal(BCI[5,])
mod
plot(mod)
mod <- radfit(BCI[1,])
## Standard plot overlaid for all models
## Pre-emption model is a line
plot(mod)
## log for both axes: Zipf model is a line
plot(mod, log = "xy")
## Lattice graphics separately for each model
radlattice(mod)
# Take a subset of BCI to save time and nerves
mod <- radfit(BCI[3:5,])
mod
plot(mod, pch=".")Run the code above in your browser using DataLab