Sean R. Connolly, David R. Bellwood, and Terence P. Hughes. 2003. Indo-Pacific biodiversity of coral reefs: deviations from a mid-domain model. Ecology 84:2178–2190.

In the original analysis, latitudinal and longitudinal range locations are randomized independently of one another. In latitudinal randomizations, any species can lie anywhere between the northern and southern extremities of the domain. Similarly, in longitudinal randomizations, any species can lie anywhere between the eastern and western extremities of the domain. Alternatively, one can randomize location along one axis, depending upon a species' limits along another axis. This has no effect if the domain is rectangular—boundaries are the same along one axis, regardless of position along the other axis. However, if the domain is irregular, longitudinal domain boundaries will vary, depending on latitude, and vice versa. To determine the extent to which these differences in approaches to randomization affect our analyses, we re-analyzed the data, using a randomization method in which range extent and location along one axis were taken as given, and range location along the other axis randomized with domain boundaries depending upon the location along the first axis. For instance, a species longitudinally confined to the mid-Pacific would be latitudinally constrained by mid-Pacific domain boundaries: the atolls just north of Hawaii (29�N), and the southern extremity of French Polynesia (29�S), whereas a species longitudinally confined to the western Indian Ocean would be latitudinally constrained by African margin boundaries: South Africa (35�S) and the northern Gulf of Suez (30�N). These randomizations actually allow mid-domain effects to be tested separately for latitude and longitude, in addition to accounting for an irregularly-shaped domain boundary. For instance, if latitudinal distributions were strongly influenced by factors other than boundary constraints, but longitudinal distributions driven principally by a mid-domain effect, then this test would effectively remove any latitudinal effect from the longitudinal randomization, and vice versa.

In the original analyses, and the ones described above, a species' range can end anywhere between the appropriate domain boundaries. However, range limits are defined by most-distal populations, and thus pre-suppose the existence of an appropriate habitat type within which they can persist. To fully assess the extent to which our results may have been influenced by this phenomenon, one would need a grid recording the locations of suitable habitat, and conduct randomizations in which ranges are constrained to end only at locations that contained suitable habitat. Unfortunately, identifying habitat that is "suitable" for reef-associated corals and fishes is somewhat problematic (see Appendix A). Nevertheless, if the grid is sufficiently coarse in scale and records only the presence or absence of some reef, and if "suitable habitat" is extended north and south beyond the limits of coral reef along the coastlines of Australia, Japan, Asia, South America, and South Africa, then a reasonable approximation to the distribution of available habitat can be constructed. We have done this, extending the grid of coral reef habitat presented by Roberts et al. (2002) northward and southward as necessary. We then re-ran the randomizations described above, applying the constraint that range limits could only fall within grid squares containing suitable habitat.  For instance, the latitudinal limits of a species longitudinally restricted to the mid-Pacific would have to fall at latitudes where suitable shallow-water habitat is available (islands or atolls in the mid-Pacific).

Results of these analyses are summarized in the text, and figures are presented in Appendix C.

Literature Cited

Roberts, C. M., C. J. McClean, J. E. N. Veron, J. P. Hawkins, G. R. Allen, D. E. McAllister, C. G. Mittermeier, F. W. Schueler, M. Spalding, F. Wells, C. Vynne, and T. B. Werner. 2002. Marine biodiversity hotspots and conservation priorities for tropical reefs. Science 295:1280–1284.