We use recently developed technical methods to study species–area relationships from a spatially explicit extension of Hubbell's neutral model on an infinite landscape. Our model includes variable dispersal distances and exhibits qualitatively different behaviour from the cases of nearest-neighbour dispersal and finite periodic landscapes that have previously been studied. We show that different dispersal distances and even different dispersal kernels produce identical species–area curves up to rescaling of the two axes. This scaling property provides a straightforward method for fitting the model to empirical data. The species–area curves display all three phases observed empirically and enable the exponent describing the power law relationship for species–area curves to be identified as the gradient at the central phase. This exponent can take all values between 0 and 1 and is given by a simple function of the speciation rate, independent of all other model variables.