fitrad(x, rad =c("gs", "mand", "rbs", "zipf"), ...)
fitgs(x, trunc, ...)
fitmand(x, trunc, start.value, ...)
fitrbs(x, trunc, ...)
fitzipf(x, N, trunc, start.value, upper = 20, ...)rad-class.
In the context of
rads, the numerical vector contains abundances of species in a sample or ecological
assemblage accordindgeom),
"mand" for Zipf-Mandelbrodt distribution,
trunc > min(x); truncation point to fit a
truncated distribution.mle2.
Parameters should be named as in the corresponding density
function, and in the same order.optim.trunc and
start.value ). In the specific fitting functions further
arguments to be passed to mle2.fitrad-class which inherits from mle2-class
and thus has methods for handling
results of maximum likelihood fits from mle2
and also specific methods to handle rank-abundance models.mle2 and methods
from 'bbmle' package (Bolker 2012), which in turn builds on
mle function and associated classes and methods.rad-class.
RADs assign probabilities p(i) to each rank i, which can be interpreted as
the expected proportion of total individuals in the sample that are of
the i-th species.
fitrad is simply a wrapper that calls the specific functions to fit
the distribution chosen with the argument rad. Users
can interchangeably use fitrad or the individual functions
detailed below
(e.g. fitrad(x, sad="rbs", ...) is the same as
fitrbs(x, ...) and so on).
The distributions are fitted by the
maximum likelihood method using numerical optimization,
with mle2.
The resulting object is of fitrad-class
which can be handled with mle2 methods
for fitted models and has also some additional
methods for RADs models (see
fitrad-class and examples).
By default, fitting to one-parameter distributions (fitgs,
fitzipf) uses Brent's one-dimensional method of optimization (see
optim). fitgs fits Motomura's Geometric Series (Whittaker
1965, May 1975) to abundance ranks.
This was the first model fitted to species
abundance data (Motomura 1932, apud Doi and Mori 2012),
which was subsequently described as the result
of niche pre-emption at a constant rate (Numata et. al. 1953 apud Doi
and Mori 2012).
fitrbs fits the Broken-stick distribution
(MacArthur 1960) to abundance ranks. It is defined only by the observed number of
elements S in the collection and collection size N.
Therefore, once a sample is taken,
the Broken-stick has no free parameters.
Therefore, there is no actual fitting, but still
the fitrbs calls
mle2 with
fixed parameters N and S and eval.only=TRUE
to return an object of fitrad-class
to keep compatibility with other
RAD models fitted to the same data.
Therefore the resulting objects allows most of the
operations with RAD models, such as
comparison with other models through model selection,
diagnostic plots and so on
(see fitrad-class).
fitzipf and fitmand fit the Zipf distribution and its
two-parameter generalization, the Zipf-Mandelbrodt distribution. Both
are discrete power-law distributions commonly proposed as RAD models,
though they in general provide poor fit to species abundances (Newman 2005).
Doi, H. and Mori, T. 2012. The discovery of species-abundance distribution in an ecological community. Oikos 122: 179--182.
MacArthur, R.H. 1960. On the relative abundance of species. Am Nat 94:25--36.
May, R.M. 1975. Patterns of Species Abundance and Diversity. In Cody, M.L. and Diamond, J.M. (Eds) Ecology and Evolution of Communities. Harvard University Press. pp 81--120.
Newman, M.E.J. 2005. Power laws, Pareto distributions and Zipf's law. Contemporary Physics, 46: 323--351. Whittaker, R.H. 1965. Dominance and diversity in land plant communities. Science 147: 250--260.
dgs, dmand, drbs,
dzipf,
for corresponding density functions created for fitting RADs;
fitrad-class.## Figure 2 of Motomura (1932)
data(okland)
plot(rad(okland))
ok.gs <- fitrad(okland, "gs")
lines(radpred(ok.gs))
## Comparison with Zipf-Mandelbrodt
ok.zm <- fitrad(okland, "mand")
AICctab(ok.gs, ok.zm, nobs=length(okland))
lines(radpred(ok.zm), col="red")Run the code above in your browser using DataLab