Tuesday, September 7, 2010

Error in I metric (but don't panic!)

Thanks to a manuscript by Dennis Rödder and Jan Engler that is currently in revision for Global Ecology and Biogeography (entitled “Quantitative metrics of overlaps in Grinnellian niches: advances and possible drawbacks”), we have discovered a typographical error in our description of the niche overlap metric I, Eq. (3) of Warren, Glor and Turelli (2008, Evolution 62:2868-2883). Unfortunately, this error also found its way into ENMTools. Fortunately, the error is only a scaling issue. It does not affect the statistical tests presented in our paper or any known test based on ENMTools. Those tests use only relative rankings of overlaps (rather than specific values), and our error does not change relative rankings.

The formula we provided for Hellinger distance, H, is one of several alternatives. In the form we provided, H ranges from 0 to Sqrt(2). The incorrect formula we published is I = 1 – (H/2), which ranges from 1 – (1/Sqrt(2)) to 1 (not 0 to 1 as we stated). The correct formula is 1 – (H^2/2), which ranges from 0 to 1. Denoting our incorrect formula, Iold, and the intended formula, Icorrect,

Icorrect = 1 – 2(1 – Iold)^2.

Because both formulas decrease monotonically from 1 with increasing H, our typo does not alter relative rankings of I values. Hence, it does not affect P values obtained from resampling-based tests of niche identity or similarity, such as those in Warren et al. (2008). If you have manuscripts that use the I metric, there is no need to re-run any analyses based on ranks; and resulting conclusions about niche identity or similarity remain valid.

We will release an updated version of ENMTools shortly that corrects this error. We thank Dennis Rödder and Jan Engler for bringing it to our attention. We apologize for any inconvenience it has caused.