| radfit {vegan} | R Documentation |
Functions construct rank – abundance or dominance / diversity or Whittaker plots and fit brokenstick, pre-emption, log-Normal, Zipf and Zipf-Mandelbrot models of species abundance.
## 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, ...)
## Default S3 method:
radfit(x, ...)
## S3 method for class 'radfit':
plot(x, BIC = FALSE, legend = TRUE, ...)
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':
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", ...)
df |
Data frame where sites are rows and species are columns. |
x |
A vector giving species abundances in a site, or an object to be plotted. |
order.by |
A vector used for ordering sites in plots. |
BIC |
Use Bayesian Information Criterion, BIC, instead of Akaike's AIC. The penalty for a parameter is k = log(S) where S is the number of species, whereas AIC uses k = 2. |
model |
Show only the specified model. If missing, AIC is used to
select the model. The model names (which can be abbreviated) are
Preemption, Lognormal, Veiled.LN,
Zipf, Mandelbrot. |
legend |
Add legend of line colours. |
as.table |
Arrange panels starting from upper left corner (passed
to xyplot). |
family |
Error distribution (passed to glm). All
alternatives accepting link = "log" in family
can be used, although not all make sense. |
xlab,ylab |
Labels for x and y axes. |
type |
Type of the plot, "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. |
... |
Other parameters to functions. |
Rank – Abundance Dominance (RAD) or Dominance/Diversity plots
(Whittaker 1965) display logarithmic species abundances against
species rank order. These plots are supposed to be
effective in analysing types of abundance distributions in
communities. These functions fit some of the most popular models mainly
following Wilson (1991). Function 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.null fits a brokenstick model where the expected
abundance of species at rank r is a[r] = J/S sum(from x=r to 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 α 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*p1*r^gamma where p1 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
p1 of the Zipf model changes into a meaningless scaling
constant c. There are grand narratives 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.
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. Pre-emption
model is fitted as 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. 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.
Function 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; function summary can be
used to display the results for individual radfit objects.
The functions are still
preliminary, and the items in the radline objects may change.
The RAD models are usually fitted for proportions instead of original
abundances. However, nothing in these models seems to require division
of abundances by site totals, and original observations are used in
these functions. If you wish to use proportions, you must standardize
your data by site totals, e.g. with decostand and use
appropriate family such as Gamma.
The lognormal model is fitted in a standard way, but I do think this is not quite correct – at least it is not equivalent to fitting Normal density to log abundances like originally suggested (Preston 1948).
Some models may fail. In particular, estimation of the Zipf-Mandelbrot
model is difficult. If the fitting fails, NA is returned.
Wilson (1991) defined preemption model as a[r] = J*p1*(1 - alpha)^(r-1), where p1 is the fitted proportion of the first species. However, parameter p1 is completely defined by α since the fitted proportions must add to one, and therefore I handle preemption as a one-parameter model.
Veiled log-Normal model was included in earlier releases of this
function, but it was removed because it was flawed: an implicit veil
line also appears in the ordinary log-Normal. The latest release version
with rad.veil was 1.6-10.
Jari Oksanen
Pielou, E.C. (1975) Ecological Diversity. Wiley & Sons.
Preston, F.W. (1948) The commonness and rarity of species. Ecology 29, 254–283.
Whittaker, R. H. (1965) Dominance and diversity in plant communities. Science 147, 250–260.
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[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=".")