This package provides functions for fitting unimodal and multimodal
gambin distributions to species-abundance distributions from ecological data. The main function is
fit_abundances(), which estimates the 'alpha' parameter(s) of the gambin distribution using maximum likelihood.
The gambin distribution is a sample distribution based on a stochastic model of species abundances,
and has been demonstrated to fit empirical data better than the most commonly used species-abundance models
(see references). Gambin is a stochastic model which combines the gamma distribution with a binomial sampling method.
To fit the gambin distribution, the abundance data is first binned into octaves. The expected abundance
octave of a species is given by the number of successful consecutive Bernoulli
trials with a given parameter p. The parameter p of species is assumed to distributed
according to a gamma distribution. This approach can be viewed as linking the gamma distribution with
the probability of success in a binomial process with x trials. Use the fit_abundances() function to fit the
gambin model to a vector of species abundances, optionally using a subsample of the individuals. Use the mult_abundances()
function to fit the gambin model to multiple sites / samples and return the alpha values for each model fit (both the raw values
and the alpha values standardised by the number of individuals).The package estimates the alpha (shape) parameter with
associated confidence intervals. Methods are provided for plotting the results, and for calculating the likelihood of fits.
The package now provides functionality to fit multimodal gambin distributions (i.e. a gambin distribution with
more than one mode), and to deconstruct and examine a multimodal gambin model fit (deconstruct_modes).
Matthews, T.J., Borregaard, M.K., Ugland, K.I., Borges, P.A.V, Rigal, F., Cardoso, P. and Whittaker, R.J. (2014) The gambin model provides a superior fit to species abundance distributions with a single free parameter: evidence, implementation and interpretation. Ecography 37: 1002-1011.
Matthews, T.J. et al. (2017) Extension of the Gambin Distribution to Multimodal Species Abundance Distributions. In prep.
Ugland, K.I., Lambshead, F.J.D., McGill, B.J., Gray, J.S., O'Dea, N., Ladle, R.J. & Whittaker, R.J. (2007). Modelling dimensionality in species abundance distributions: description and evaluation of the Gambin model. Evolutionary Ecology Research, 9, 313-324.
# NOT RUN {
data(moths, package = "gambin")
fit = fit_abundances(moths)
barplot(fit)
lines(fit)
AIC(fit)
# }
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