Package gambin. June 23, 2016
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1 Type Package Package gambin June 23, 2016 Title Fit the GamBin Model to Species Abundance Distributions Version 1.4 Date Author Michael Krabbe Borregaard, Thomas Matthews & Karl Ugland Maintainer Michael Krabbe Borregaard Fits the gambin distribution to species-abundance distributions from ecological data. 'gambin' is short for 'gamma-binomial'. The main function is fitgambin, which estimates the 'alpha' parameter of the gambin distribution using maximum likelihood. Functions are also provided to generate the gambin distribution and for calculating likelihood statistics. Depends stats License GPL-3 NeedsCompilation no Repository CRAN Date/Publication :05:59 R topics documented: gambin-package create_octaves fitgambin loglik.gambin moths The gambin distribution Index 9 1
2 2 gambin-package gambin-package Fit the gambin model to species abundance distributions Details This package provides functions for fitting the gambin distribution to species-abundance distributions from ecological data. The main function is fitgambin(), which estimates the alpha parameter of the gambin distribution using maximum likelihood. Package: gambin Type: Package Version: 1.4 Date: License: GPL-3 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 speciesabundance 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 successfull 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 fitgambin function fit the gambin model to a vector of species abundances, optionally using a subsample of the 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. Michael Krabbe Borregaard, Thomas J. Matthews & Karl I. Ugland Maintainer: Michael Krabbe Borregaard <mkborregaard@snm.ku.dk> 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: 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,
3 create_octaves 3 fit <- fitgambin(moths) plot(fit) AIC(fit) create_octaves Reclassify a vector of species abundances into abundance octaves Creates abundance octaves by a log2 transform that doubles the number of abundance classes within each octave (method 3 of Gray, Bjoergesaeter & Ugland 2006). Octave 0 contains the number of species with 1 individual, octave 1 the number of species with 2 or 3 individuals, octave 2 the number of species with 4 to 7 individuals, and so forth. create_octaves(abundances, subsample = 0) Arguments abundances subsample A numerical vector of species abundances in a community If > 0, the community is subsampled by this number of individuals before creating octaves. This is useful for analyses where alpha is estimated from a standardized number of individuals Value A data.frame with two variables: octave with the name of each octave and species with the number of species in that octave Michael Krabbe Borregaard Gray, J.S., Bjoergesaeter, A. & Ugland, K.I. (2006) On plotting species abundance distributions. Journal of Animal Ecology, 75, create_octaves(moths)
4 4 fitgambin fitgambin Fit the GamBin model to a species abundance distribution Uses maximum likelihood methods to fit the GamBin model to binned species abundances. To control for the effect of sample size, the abundances may be subsampled prior to fitting. fitgambin(abundances, subsample = 0) plot(x, barcol = "grey", barwidth = 1, cex.dots = 1, dotpch = 16, dotcol = par("fg"), line = FALSE, lwd = 1, linecol = par("fg"),...) predict(object,...) confint(object, parm = "alpha", level = 0.95,...) Arguments abundances subsample object x parm level barcol barwidth cex.dots dotpch dotcol line lwd linecol Either a vector of abundances of all species in the sample/community; or the result of create_octaves The number of individuals to sample from the community before fitting the GamBin model. If subsample == 0 the entire community is used a codegambin object created by fitgambin a codegambin object created by fitgambin the parameter to calculate confidence intervals from. Only alpha is implemented the significance level of the confidence intervals the colour of the bars illustrating the empirical abundance of species in octaves the width of the bars illustrating the empirical abundance of species in octaves the size of the dots illustrating the fitted abundance of species in octaves the point character of the dots illustrating the fitted abundance of species in octaves the colour of the dots illustrating the fitted abundance of species in octaves should the dots be connected with a line? the width of the line connecting dots the colour of the line connecting dots... further arguments to pass to barplot
5 fitgambin 5 Details The gambin distribution is fit to the number of species in abundance octaves, as specified by the create_octaves function. Because the shape of species abundance distributions depend on sample size, abundances of different communities should be compared on equally large samples. The sample size can be set by the subsample parameter. To estimate alpha from a standardised sample, the function must be run several times; see the examples. The plot method creates a barplot showing the observed number of species in octaves, with the fitted GamBin distribution shown as black dots. Value The fitgambin function returns an object of class gambin, with the alpha and MaxOctave parameters of the GamBin distribution, the likelihood of the fit, and the empirical distribution over octaves. Michael K. Borregaard, Thomas J. Matthews & Karl I. Ugland 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, Matthews, T.J., Borregaard, M.K., Ugland, K., Borges, P.A.V., Rigal, F. & Whittaker, R.J. (Early View Online). The gambin model provides a superior fit to species abundance distributions with a single free parameter: evidence, implementation and interpretation. Ecography, DOI: /ecog See Also create_octaves fit <- fitgambin(moths) plot(fit) summary(fit) # gambin parameters based on a standardized sample size of 1000 individuals stand_fit <- replicate(20, fitgambin(moths, 1000)$Alpha) #may take a while on slower computers print(c(mean = mean(stand_fit), sd = sd(stand_fit)))
6 6 loglik.gambin loglik.gambin Likelihood statistics for the GamBin model Uses likelihood and information theoretical approaches to reveal the degree of fit of the GamBin model to empirical species abundance distributions. loglik(object,...) AIC(object,...) AICc(object,...) BIC(object,...) Arguments Value object an object of type gambin... further arguments to pass to the function loglik returns an R object of type loglik. The other function return the numerical value of the statistic Michael K. Borregaard & Thomas J. Matthews Akaike, Hirotugu. "A new look at the statistical model identification." Automatic Control, IEEE Transactions on 19.6 (1974): See Also fitgambin fit <- fitgambin(moths) AIC(fit)
7 moths 7 moths Williams Rothamsted moth data Macro-Lepidoptera captured in a light trap at Rothamsted Experimental Station during 1935 Format A numerical vector with the abundance of 195 moth species. Source Williams, C.B. (1964) Patterns in the balance of nature. Academic Press, London. The gambin distribution Calculate the gambin distribution calculate the expected number of species in octaves for a given value of alpha and maxoctave dgambin(alpha, maxoctave) gambin_exp(alpha, maxoctave, total_species) Arguments alpha maxoctave total_species the shape parameter of the GamBin distribution the scale parameter of the GamBin distribution - which octave is the highest in the empirical dataset? the total number of species in the empirical dataset
8 8 The gambin distribution Details Value dgambin gives the distribution function of gambin, so all octaves sum to 1. gambin_exp multiplies this by the total number of species to give the expected GamBin distribution in units of species, for comparison with empirical data. A vector with length MaxOctave + 1 of the expected number of species in each octave Michael K. Borregaard, Gabriel Arellano, Thomas J. Matthews & Karl I. Ugland 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, Matthews, T.J., Borregaard, M.K., Ugland, K., Borges, P.A.V., Rigal, F. & Whittaker, R.J. (Early View Online). The gambin model provides a superior fit to species abundance distributions with a single free parameter: evidence, implementation and interpretation. Ecography, DOI: /ecog expected <- gambin_exp(4, 13, 200) plot(expected, type = "l")
9 Index Topic \textasciitildekwd1 create_octaves, 3 The gambin distribution, 7 Topic \textasciitildekwd2 create_octaves, 3 The gambin distribution, 7 Topic datasets moths, 7 Topic package gambin-package, 2 AIC.gambin (loglik.gambin), 6 AICc (loglik.gambin), 6 BIC.gambin (loglik.gambin), 6 confint.gambin (fitgambin), 4 create_octaves, 3, 5 dgambin (The gambin distribution), 7 fitgambin, 4, 6 gambin (gambin-package), 2 gambin-package, 2 gambin_exp (The gambin distribution), 7 loglik.gambin, 6 moths, 7 nobs.gambin (fitgambin), 4 plot.gambin (fitgambin), 4 predict.gambin (fitgambin), 4 print.gambin (fitgambin), 4 print.summary.gambin (fitgambin), 4 summary.gambin (fitgambin), 4 The gambin distribution, 7 9
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