Appendix S1 – Examples of alpha hulls calculated for the observed distributions of diadromous and non-diadromous fish species in New Zealand. For each species, we show alpha-hulls computed using maximum triangle lengths of 50 and 200 km, i.e. all triangles with at least one side having a length greater than this critical value are deleted. All maps use the same scaling of x and y coordinates and have the same geographic extents. Figure 1. Anguilla dieffenbachii, a diadromous species with an extensive geographic range that is occupied to a high degree. Figure 2. Galaxias fasciatus, a diadromous species with an extensive geographic range that is occupied in a sparse fashion. Figure 3. G. eldoni, a non-diadromous species with a very restricted geographic range. Figure 4. G. vulgaris, a non-diadromous species with a moderately restricted geographic range. Figure 5. Gobiomorphus breviceps, a non-diadromous species with a moderately extensive geographic range.