Fit the general dynamic model (GDM) of island biogeography using a variety of SAR models. Functions are provided to compare the GDM fitted using different SAR models, and also, for a given SAR model, to compare the GDM with alternative nested candidate models (e.g. S ~ A + T).
gdm(data, model = "linear", mod_sel = FALSE, AST = c(1, 2, 3))
| data | A dataframe or matrix with at least three columns, where one column should include island area values, one island richness values and one island age values. |
|---|---|
| model | Name of the SAR model to be used to fit the GDM. Can be any of 'logo', 'linear', 'power', or 'all'. |
| mod_sel | Logical argument specifying whether, for a given SAR model, a model comparison of the GDM with other nested candidate models should be undertaken. |
| AST | The column locations in |
An object of class 'gdm'. If model is one of "loga",
"linear" or "power" the returned object is a nls model fit
object. If model == "all", the returned object is a list with
three elements; each element being a nls fit object.
If mod_sel == TRUE and model != "all", a list with four
elements is returned; each element being a lm or nls fit
object. When model == "all", a list with three elements is
returned; each element being a list of the four model fits for a
particular SAR model.
The GDM models island species richness as a function of island area and island age, and takes the general form: S ~ A + T + T^2, where S = richness, A =area, and T = island age. The T^2 term is included as the GDM predicts a hump-shaped relationship between island richness and island age. However, a variety of different SAR models have been used to fit the GDM and three options are available here: the logarithmic, linear and power SAR model. Model fitting follows the procedure in Cardoso et al. (2015). For example, when the linear SAR model is used, the GDM can be fitted using the expression: S ~ c + z*Area + k*T + j*T^2, where c,z,k,j are free parameters to be estimated.
For all three SAR models, the GDM is fitted using non-linear regression
and the nls function. For ease of fitting, the logarithmic
and power SAR models are included in their logarithmic form, e.g. the
logarithmic model is fitted using: S ~ c + x*log(A), where c and x are
parameters to be estimated.
For each model fit, the residual standard error (RSE) and AIC values are
reported. However, as the model fit object is returned, it is possible
to calculate or extract various other measures of goodness of fit (see
nls).
If mod_sel == TRUE, the GDM (using a particular SAR model) is
fitted and compared with three other (nested) candidate models: area and
time (i.e. no time^2 term), just area, and an intercept only model. The
intercept only model is fitted using lm rather than nls.
If model == "all", the GDM is fitted three times (using the
power, loga and linear SAR models), and the fits compared using
AIC.
AIC is calculated using the AIC function, which is
based on the log-likelihood and not the residual sum of squares (the
latter is used in the main functions of the sars package).
A plot generic function enabling 3-d plotting of the GDM fit will be provided in a future version of the package.
Whittaker, R. J., Triantis, K. A., & Ladle, R. J. (2008). A general dynamic theory of oceanic island biogeography. Journal of Biogeography, 35, 977-994.
Borregaard, M. K. et al. (2017). Oceanic island biogeography through the lens of the general dynamic model: assessment and prospect. Biological Reviews, 92, 830-853.
Cardoso, P., Rigal, F., & Carvalho, J. C. (2015). BAT–Biodiversity Assessment Tools, an R package for the measurement and estimation of alpha and beta taxon, phylogenetic and functional diversity. Methods in Ecology and Evolution, 6, 232-236.
#create an example dataset and fit the GDM using the logarithmic SAR model data(galap) galap$t <- rgamma(16, 5, scale = 2) g <- gdm(galap, model = "loga", mod_sel = FALSE) #Compare the GDM (using the logarithmic model) with other nested candidate #models g2 <- gdm(galap, model = "loga", mod_sel = TRUE) #compare the GDM fitted using the linear, logarithmic and power SAR models g3 <- gdm(galap, model = "all", mod_sel = FALSE)