sar_habitat: Fit habitat SAR models

In txm676/mmSAR2: Fit and Compare Species-Area Relationship Models Using Multimodel Inference

Fit habitat SAR models

Description

Fit three SAR regression models that include habitat diversity: the choros model, the Kallimanis model, and the jigsaw model.

Usage

sar_habitat(data, modType = "power_log", con = NULL, logT = log)

Arguments

data	A dataset in the form of a dataframe with at least three columns: the first with island/site areas (A), the second with island / site habitat diversity (H), and the third with the species richness of each island/site (S).
modType	What underlying SAR model form should be used. Should be one of "power" (non-linear power), "logarithmic" (logarithmic SAR), or "power_log" (log-log power; default).
con	The constant to add to the species richness values in cases where at least one of the islands has zero species.
logT	The log-transformation to apply to the area and richness values. Can be any of log(default), log2 or log10.

Details

These functions are described in more detail in the accompanying paper (Furness et al., 2023). The code to fit the models was also taken from this paper.

Three habitat SAR models are available:

• choros model: Proposes that species richness is better predicted by the product of habitat heterogeneity and area (S = c.(A.H)^z)

• Kallimanis model: Proposes that increasing habitat heterogeneity increases species richness by increasing the slope (on a log-log plot) of the Arrhenius power model (S = c1.A^(z + d.H))

• jigsaw model: Models species richness in an area as the sum of the species richness values of several smaller component subareas, which can be visualised as pieces of a jigsaw puzzle, i.e., it partitions the species–area and species–heterogeneity scaling relationships (S = (c1.H^d).((A / H)^z))

In addition to these three models, a simple 'non-habitat' SAR model is also fit, which varies depending on modType: the non-linear power, the logarithmic or the log-log power model.

The untransformed (modType = "power") and logarithmic (modType = "logarithmic") models are fitted using non-linear regression and the nlsLM function. For the jigsaw and Kallimanis models in untransformed space, a grid search process is used to test multiple starting parameter values for the nlsLM function - see details in the documentation for sar_average - if multiple model fits are returned, the fit with the lowest AIC is returned. Providing starting parameter estimates for multiple datasets is tricky, and thus you may find the jigsaw and Kallimanis models cannot be fitted in untransformed space or with the logarithmic models. If this is the case, please let the package maintainer know and we can edit the starting parameter values. The log-log models (modType = "power_log") are all fitted using linear regression ( lm function).

sar_habitat() uses the nlsLM from the minpack.lm package rather than nls as elsewhere in the package as we found that this resulted in better searches of the parameter space for the habitat models (and less convergence errors), particularly for the logarithmic models. nlsLM is a modified version of nls that uses the Levenberg-Marquardt fitting algorithm, but returns a standard nls object and thus all the normal subsequent nls functions can be used. Note also that occasionally a warning is returned of NaNs being present, normally relating to the jigsaw model (logarithmic version). We believe this mostly relates to models fitted during the optimisation process rather than the final returned model. Nonetheless, users are still recommended to check the convergence information of the returned model fits.

Value

A list of class "habitat" and "sars" with up to four elements, each holding one of the individual model fit objects (either nls or lm class objects). summary.sars provides a more user-friendly ouput (including a model summary table ranked by AICc and presenting the model coefficients, and R2 and information criteria values etc.) and plot.habitat provides a simple bar of information criteria weights. For the models fitted using non-linear regression, the R2 and adjusted R2 are 'pseudo R2' values and are calculated using the same approach as in the rest of the package (e.g., sar_power.

Note that if any of the models cannot be fitted - this is particularly the case when fitting the untransformed or logarithmic models which use non-linear regression (see above) - they are removed from the returned object.

Note

The jigsaw model is equivalent to the trivariate power-law model of Tjørve (2009), see Furness et al. (2023).

The jigsaw model (power-law form) cannot have a poorer fit than the choros or power model based on RSS and thus R2. Comparing models using information criteria is thus advised.

Author(s)

Euan N. Furness and Thomas J. Matthews

References

Furness, E.N., Saupe, E.E., Garwood, R.J., Mannion, P.D. & Sutton, M.D. (2023) The jigsaw model: a biogeographic model that partitions habitat heterogeneity from area. Frontiers of Biogeography, 15, e58477.

Kallimanis, A.S., Mazaris, A.D., Tzanopoulos, J., Halley, J.M., Pantis, J.D., & Sgardelis, S.P. (2008) How does habitat diversity affect the species–area relationship? Global Ecology and Biogeography, 17, 532-538

Tjørve, E. (2009) Shapes and functions of species– area curves (II): a review of new models and parameterizations. Journal of Biogeography, 36, 1435-1445.

Triantis, K.A., Mylonas, M., Lika, K. & Vardinoyannis, K. (2003) A model for the species-area-habitat relationship. Journal of Biogeography, 30, 19–27.

Examples

data(habitat)
#Fit the models in log-log space
s <- sar_habitat(data = habitat, modType = "power_log", 
con = NULL, logT = log)
#Look at the model comparison summary
s2 <- summary(s)
s2
#Make a simple plot of AICc weights
plot(s, IC = "AICc", col = "darkred")

#Fit the logarithmic version of the models

txm676/mmSAR2 documentation built on Nov. 16, 2023, 2:33 p.m.