## S3 method for class 'data.frame':
radfit(df, ...)
## S3 method for class 'radfit.frame':
plot(x, order.by, BIC = FALSE, model, legend = TRUE,
as.table = TRUE, ...)
## S3 method for class 'default':
radfit(x, ...)
## S3 method for class 'radfit':
plot(x, BIC = FALSE, legend = TRUE, ...)
rad.preempt(x, family = poisson, ...)
rad.lognormal(x, family = poisson, ...)
rad.veil(x, family = poisson, ...)
rad.zipf(x, family = poisson, ...)
rad.zipfbrot(x, family = poisson, ...)
## S3 method for class 'radline':
plot(x, xlab = "Rank", ylab = "Abundance", type = "b", ...)
## S3 method for class 'radline':
lines(x, ...)
## S3 method for class 'radline':
points(x, ...)
as.rad(x)
## S3 method for class 'rad':
plot(x, xlab = "Rank", ylab = "Abundance", ...)Preemption, Lognormal, Veiled.LN,
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.rad.XXXX will return an object of class
radline, which is constructed to resemble results of glm
and has many (but not all) of its components, even when only
nlm was used in fitting. At least the following
glm methods can be applied to the result:
fitted, residuals.glm with alternatives
"deviance" (default), "pearson", "response",
function coef, AIC,
extractAIC, and deviance.
Function radfit applied to a vector will return
an object of class radfit with item y for the
constructed RAD, item family for the error distribution, and
item models containing each radline object as an
item. In addition, there are special AIC, coef and
fitted implementations for radfit results.
When applied to a data frame
radfit will return an object of class radfit.frame which
is a list of radfit objects. The functions are still
preliminary, and the items in the radline objects may change.as.rad constructs observed
RAD data.
Functions rad.XXXX (where XXXX is a name) fit
the individual models, 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. All these functions have their own plot
functions. When the argument is a data frame, plot uses
Lattice graphics, and other 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. The most complete control of graphics can be achieved
with rad.XXXX methods which have points and lines
functions to add observed values and fitted models into existing
graphs. 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. In addition there is a fixed scaling
parameter $J$ which is the total abundance.
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.veil is similar, but it assumes
that only a proportion veil of most common species were
observed in the community, the rest being too rare or scanty to occur
in a sample plot of this size (but would occur in a larger
plot). 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 $c$. There are great histories about ecological
mechanisms behind each model (Wilson 1991), but
several alternative and contrasting mechanisms can produce
similar models and a good fit does not imply a specific mechanism.
Log-Normal and Zipf models are generalized linear
models (glm) with logarithmic link function.
Veiled log-Normal and Zipf -- Mandelbrot add one
nonlinear parameter, and these two models are fitted using
nlm for the nonlinear parameter and estimating other
parameters and log-Likelihood with glm. Pre-emption
model is fitted as purely nonlinear model. The default
family is poisson which is appropriate only for
genuine counts (integers), but other families that accept link =
"log" can be used. Family Gamma 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.
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.veil(BCI[1,])
mod
plot(mod)
mod <- radfit(BCI[1,])
plot(mod)
# Take a subset of BCI to save time and nerves
mod <- radfit(BCI[2:5,])
mod
plot(mod, pch=".")Run the code above in your browser using DataLab