Applicability of Common Algorithms in Species–Area Relationship Model Fitting

The species–area relationship (SAR) describes a law of species richness changes as the sampling area varies. SAR has been studied for more than 100 years and is of great significance in the fields of biogeography, population ecology, and conservation biology. Accordingly, there are many algorithms available for fitting the SARs, but their applicability is not numerically evaluated yet. Here, we have selected three widely used algorithms, and discuss three aspects of their applicability: the number of iterations, the time consumption, and the sensitivity to the initial parameter setting. Our results showed that, the Gauss–Newton method and the Levenberg–Marquardt method require relatively few iterative steps and take less time. In contrast, the Nelder–Mead method requires relatively more iteration steps and consumes the most time. Regarding the sensitivity of the algorithm to the initial parameters, the Gauss–Newton and the Nelder–Mead methods are more sensitive to the choice of initial parameters, while the Levenberg–Marquardt method is relatively insensitive to the choice of initial parameters. Considering that the Gauss–Newton method and the Levenberg–Marquardt method can only be used to fit smooth SAR models, we concluded that the Levenberg–Marquardt model is the best choice to fit the smooth SARs, while the Nelder–Mead method is the best choice to fit the non-smooth SARs.