An asymptotic fractal model for logistic species-area curves

Species-area curves (SACs) are generally described as power laws. As power laws, SACs imply fractality in the relation between the number of species and area. In nature, however, the power-law form of SACs is generally observed only within a certain range of areas, not at all spatial scales. Full-scale nested SACs, from the smallest (a few individuals) to largest (regional) scales, may be best fitted by a logistic function. This is because large-scale and small-scale species richness are generally not under similar controls and, consequently, the shape of the SAC changes with scale. At the smallest scales, the form of the SAC is shaped by the autocorrelation structure of environmental conditions among neighboring sites. At the opposite end, the scaling behavior of SACs is controlled by the richness of the regional species pool. Therefore, a unifying scaling theory that bridges the gap between small-scale and large-scale species-area relationships is desirable. In this paper, I suggest that, logistic SACs can be considered ‘asymptotic fractals’ that are characterized by a scaling exponent continuously changing with scale.