The catchment basin boundaries used were based initially on the global dataset on the GlobalARC CR-ROM made available by CERL (the US Army Corps of Engineers Construction Engineering Research Laboratories). This is generated from a relatively coarse elevation model. Data for North America and Africa were replaced with improved boundaries generated by the United States Geological Survey (USGS). The most inclusive basin boundaries, ie. the entire drainage system passing through one river mouth (or delta region) to the sea were used in the analysis, selected to provide a reasonable sample from each continent. A very few internally draining systems were also included. In addition, and particularly outside N America and Africa, the major catchment boundaries were inspected by eye against appropriate paper maps, and adjustments made. USGS hydrological data are available from:

http://edcwww.cr.usgs.gov/landdaac/gtopo30/hydro/index.html.

The number of native fish species per catchment ranges from 5 to an estimate of 2500 for the Amazon system. Because of this very wide range in numbers, the data are easier to manage when log-transformed; that is, the natural logs of both the species number and the measure of river size are used. The size of the river can be expressed both in terms of the size of the catchment and of the mean annual discharge (essentially a measure of the volume of water in the river). As confirmed by Guégan et al. (1998) where data for both these are available, the latter is a considerably better predictor of fish species number than the former (r=0.49 in the case of catchment area, r=0.67 in the case of discharge for log-transformed data, n=69, p<0.0001 in both cases). As might be expected, discharge and catchment area themselves are strongly correlated (r=0.74, n=69, p<0.0001), with the major deviations being large rivers (e.g. the Niger and Nile) whose catchments lie mainly in arid regions and which thus have less discharge than expected from the size of the catchment. However, because we have data for catchment area for considerably more rivers than we have data for discharge (data on species number and catchment size available for 166 rivers, compared with data on species number and discharge for 69 rivers), we have used the former as an imperfect surrogate for the latter, in order to maximise our use of information.

Because the range of values for fish families is much smaller than for fish species, these data can be analysed without log-transforming them (although, as in all species-area relationships, the log of the area concerned is used, rather than the absolute value). A comparison of the logged and unlogged data shows that the two yield similar results. For this reason, and because unlogged data are intuitively easier to understand, we have used these.