Species–area relationship and a tentative interpretation of the function coefficients in an ecosystem simulation

Abstract

In this paper, we identified the best species–area relationship (SAR) models from amongst 28 different models gathered from the literature, using an artificial predator–prey simulation (EcoSim), along with investigating how sampling approaches and sampling scales affect SARs. Further, we attempted to determine a plausible interpretation of SAR model coefficients for the best performing SAR models. This is the most extensive quantitatively based investigation of the species–area relationship so far undertaken in the literature.We gathered 28 different models from the literature and fitted them to sampling data from EcoSim using non-linear regression and ΔAICc as the goodness-of-fit criterion. Afterwards, we proposed a machine-learning approach to find plausible relationships between the models’ coefficients and the spatial information that likely affect SARs, as a basis for extracting rules that provide an interpretation of SAR coefficients.We found the power function family to be a reasonable choice and in particular the Plotkin function based on ΔAICc ranking. The Plotkin function was consistently in the top three in terms of the best ranked SAR functions. Furthermore, the simple power function was the best-ranked model in nested sampling amongst models with two coefficients. We found that the Plotkin, quadratic power, Morgan–Mercer–Floid and the generalized cumulative Weibull functions are the best ranked models for small, intermediate, large, and very large scales, respectively, in nested sampling, while Plotkin (in small to intermediate scales) and Chapman–Richards (in large to very large scales) are the best ranked functions in random sampling. Finally, based on rule extractions using machine-learning techniques we were able to find interpretations of the coefficients for the simple and extended power functions. For instance, function coefficients corresponded to sampling scale size, patch number, fractal dimension, average patch size, and spatial complexity.Our main conclusions are that SAR models are highly dependent on sampling scale and sampling approach and that the shape of the best ranked SAR model is convex without an asymptote for smaller scales (small, intermediate) and it is sigmoid for larger scales (large and very large). For some of the SAR model coefficients, there are clear correlations with spatial information, thereby providing an interpretation of these coefficients. In addition, the slope z measuring the rate of species increase for SAR models in the power function family was found to be directly proportional to beta diversity, which confirms the view that beta diversity and SAR models are to some extent both measures of species richness.