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))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.
Name of the SAR model to be used to fit the GDM. Can be any of 'expo', 'linear', 'power', or 'all'.
Logical argument specifying whether, for a given SAR model, a model comparison of the GDM with other nested candidate models should be undertaken.
The column locations in data for the area, richness and
time values (in that order).
An object of class 'gdm'. If model is one of "expo",
"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 exponential, 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 exponential and
power SAR models are included in their logarithmic form, e.g. the
exponential 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, expo
and linear SAR models), and the fits compared using AIC.
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<U+2013>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.
# NOT RUN {
#create an example dataset and fit the GDM using the exponential SAR model
data(galap)
galap$t <- rgamma(16, 5, scale = 2)
g <- gdm(galap, model = "expo", mod_sel = FALSE)
#Compare the GDM (using the exponential model) with other nested candidate models
g2 <- gdm(galap, model = "expo", mod_sel = TRUE)
#compare the GDM fitted using the linear, exponential and power SAR models
g3 <- gdm(galap, model = "all", mod_sel = FALSE)
# }
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