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.