Last chance! 50% off unlimited learning
Sale ends in
fitsad(x, sad = c("bs","gamma","geom","lnorm","ls","mzsm","nbinom","pareto",
"poilog","power","volkov","weibull"), ...)fitbs(x, trunc, ...)
fitgamma(x, trunc, start.value, ...)
fitgeom(x, trunc = 0, start.value, ...)
fitlnorm(x, trunc, start.value, ...)
fitls(x, trunc, start.value, upper = length(x), ...)
fitmzsm(x, trunc, start.value, upper = length(x), ...)
fitnbinom(x, trunc=0, start.value, ...)
fitpareto(x, trunc, start.value, upper = 20, ...)
fitpoilog(x, trunc = 0, ...)
fitpower(x, trunc, start.value, upper = 20, ...)
fitvolkov(x, trunc, start.value, ...)
fitweibull(x, trunc, start.value, ...)
dgs),
<trunc > min(x); truncation point to fit a
truncated distribution. For "poilog", "geom" and "nbinom" set
trunc=NULL to avoid zero-truncation (see details).mle2.
Parameters should be named as in the corresponding density
function,
and in the same order.optim.fitsad further arguments to be passed to the specific fitting
function (most used are trunc, start.value) In the specific fitting functions further
arguments to be passed to mle2.fitsad-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 SADs models
(see fitsad-class).mle2 and methods
from mle function and associated classes and methods;
fitls and fitvolkov use codes and functions from
fitpoilog builds on
fitsad is simply a wrapper that calls the specific functions to fit
the distribution chosen with the argument sad. Users
can interchangeably use fitsad or the individual functions
detailed below
(e.g. fitsad(x, sad="geom", ...) is the same as
fitgeom(x, ...) and so on).
The distributions are fitted by the
maximum likelihood method using numerical optimization,
with mle2.
The resulting object is of fitsad-class
which can be handled with mle2 methods
for fitted models and has also some additional
methods for SADs models (see
fitsad-class and examples).
Functions fitgamma, fitlnorm and fitweibull fit the
standard continuous distributions most used as SADs models.
Functions power and pareto fit power-law continuous distributions
with one and two-parameters, that have been suggested as SADs models.
As species with null abundances in the sample are in general unknown, the
fit to continuous distributions can be improved by truncation to some value
above zero (see example). Convergence problems can occur when fitting
with truncation, and can be solved with sensible starting values.
fitgamma uses Chapman's (1956) fitting method to find starting
values for the truncated gamma distribution, and fitweibull
uses Rinne's (2009, p. 413) method (thanks to Mario Jose Marques-Azevedo).
Functions fitgeom, fitnbinom fits geometric and negative
binomial distributions which are two discrete
standard distributions also used to fit SADs. Since species
with zero individuals in the sample are in general unknown,
these functions fit by default zero-truncated distributions.
To avoid zero-truncation set trunc=NULL.
Using the geometric distribution as a SAD model is not to be
confounded for fitting the Geometric series fitgs
as a rank-abundance distribution (RAD) model. Function fitls implements the original numerical recipe by Fisher (1943) to
fit the log-series distribution, given a vector of species abundances.
Alonso et al. (2008,
supplementary material) showed that this recipe gives the maximum
likelihood estimate of Fisher's alpha, the single parameter of the log-series.
Fitting is done through numerical optimization with the uniroot
function, following the code of the function fishers.alpha of the
dls, using the function mle2.
The total number of individuals in the sample, N, is treated as a fixed
parameter in this implementation, in order to maintain coherence with
similar parameters from fitvolkov and fitmzsm (see below).
Fixed parameters in the model specification do not contribute to the model
degrees of freedom, and are not accounted in standard error calculations.
Function fitbs fits the Broken-stick distribution
(MacArthur 1960). It is defined only by the observed number of
elements S in the collection and collection size N.
Thus once a sample is taken,
the Broken-stick has no free parameters.
Therefore, there is no actual fitting, but still
fitbs calls
mle2 with
fixed parameters N and S and eval.only=TRUE
to return an object of class fitsad
to keep compatibility with other
SADs models fitted to the same data.
Therefore, the resulting objects allows most of the
operations with SAD models, such as
comparison with other models through model selection,
diagnostic plots and so on
(see fitsad-class).
Function fitpoilog fits the Poisson-lognormal distribution.
This is a compound distributions that describes the abundances
of species in Poisson sample of community that follows a
lognormal SAD. This is a sampling model of SAD, which is
approximated by the fitgeom, fitnbinom.
To avoid zero-truncation set trunc=NULL.
fitmzsm fits the metacommunity Zero-sum multinomial distribution
dmzsm from the Neutral Theory of Biodiversity
(Alonso and McKane 2004). The mZSM describes the SAD of a sample
taken from a neutral metacommunity under random drift.
It has two parameters,
the number of individuals in the sample J and theta,
the J is known from the sample size,
the fit resumes to estimate a single
parameter, theta. By default, fitmzsm fits mZSM to a vector of abundances
with Brent's one-dimensional method of optimization (see
optim). The log-series distribution (Fisher et al. 1943)
is a limiting case of mZSM (Hubbel 2001), and theta tends to
Fisher's alpha as J increases. In practice
the two models provide very similar fits to SADs (see example).
Function fitvolkov fits the SAD model for a community
under neutral drift with immigration
(Volkov et al. 2003).
The model is a stationary distribution deduced from
a stochastic process compatible with the Neutral Theory
of Biodiversity (Hubbell 2001). It
has two
free parameters, the theta, and the
immigration rate m (see dvolkov)
fitvolkov builds on function volkov from package
Alonso, D. and Ostling, A., and Etienne, R.S. 2008 The implicit assumption of symmetry and the species abundance distribution. Ecology Letters, 11: 93-105.
Bolker, B. and R Development Core Team 2012. bbmle: Tools for general maximum likelihood estimation. R package version 1.0.5.2. http://CRAN.R-project.org/package=bbmle
Chapman, D. G. 1956. Estimating the parameters of a truncated gamma distribution. The Annals of Mathematical Statistics, 27(2): 498--506.
Fisher, R.A, Corbert, A.S. and Williams, C.B. (1943) The Relation between the number of species and the number of individuals in a random sample of an animal population. The Journal of Animal Ecology, 12(1): 42--58.
Rinne, H. 2009. The Weibull distribution: a handbook. CRC Press
Volkov, I., Banavar, J. R., Hubbell, S. P., Maritan, A. 2003. Neutral theory and relative species abundance in ecology. Nature 424:1035--1037.
dls, dmzsm, dpareto,
dpoilog, dpower,dvolkov
for corresponding density functions created for fitting SADs;
standard distributions dweibull,
dgamma, dgeom, dlnorm, dnbinom;
fitsad-class.## Magurran (1989) example 5:
## birds in an Australian forest
mag5 <- c(103, 115, 13, 2, 67, 36, 51, 8, 6, 61, 10, 21,
7, 65, 4, 49, 92, 37, 16, 6, 23, 9, 2, 6, 5, 4,
1, 3, 1, 9, 2)
mag5.bs <- fitsad(mag5, "bs")
summary(mag5.bs)## no estimated coefficient
coef(mag5.bs) ## fixed coefficients N and S
## Diagnostic plots
par(mfrow=c(2, 2))
plot(mag5.bs)
par(mfrow=c(1, 1))
data(moths) #Fisher's moths data
moths.mzsm <- fitmzsm(moths) ## same as fitsad(moths, sad="mzsm")
## fit to log-series
moths.ls <- fitsad(moths, sad="ls")
coef(moths.ls)
coef(moths.mzsm) ## Compare with theta=38.9, Alonso&McKanne (2004)
## Diagnostic plots
par(mfrow=c(2, 2))
plot(moths.mzsm)
par(mfrow=c(1, 1))
## Graphical comparison
plot(rad(moths))
lines(radpred(moths.ls))
lines(radpred(moths.mzsm), col="red", lty=2)
legend("topright", c("log-series", "mZSM"), lty=1, col=c("blue","red"))
## Two more models: truncated lognormal and Poisson-lognormal
moths.ln <- fitsad(moths, "lnorm", trunc=0.5)
moths.pln <- fitsad(moths, "poilog")
## Model selection
AICtab(moths.ln, moths.pln, moths.ls, moths.mzsm, weights=TRUE)
## Biomass as abundance variable
data(ARN82.eB.apr77) #benthonic marine animals
AR.ln <- fitsad(ARN82.eB.apr77, sad="lnorm")
AR.g <- fitsad(ARN82.eB.apr77, sad="gamma")
AR.wb <- fitsad(ARN82.eB.apr77, sad="weibull")
plot(octav(ARN82.eB.apr77))
lines(octavpred(AR.ln))
lines(octavpred(AR.g), col="red")
lines(octavpred(AR.wb), col="green")
legend("topright", c("lognormal", "gamma", "weibull"),lty=1, col=c("blue","red", "green"))
AICctab(AR.ln, AR.g, AR.wb, nobs=length(ARN82.eB.apr77), weights=TRUE)Run the code above in your browser using DataLab