Metrics for quantifying the **similarity among ecological niche models** are important for testing patterns of niche evolution. The *modOverlap* function, used e.g. by Reino et al. (in press) and now included in the *fuzzySim* **package** (>=1.5), calculates three such metrics: Shoener’s *D* statistic for niche overlap, Hellinger distance between probability distributions, and the *I* similarity statistic of Warren *et al*. (2008).

These formulas are also implemented *e.g.* within the *niche.overlap* function of R package *phyloclim*, but there they require input data in complex and software-specific formats. The function below calculates these indices from simply two vectors or columns containing the predictions of the two models to compare.

modOverlap <- function (pred1, pred2, na.rm = TRUE)
{
p1 <- pred1/sum(pred1, na.rm = na.rm)
p2 <- pred2/sum(pred2, na.rm = na.rm)
SchoenerD <- 1 - 0.5 * sum(abs(p1 - p2), na.rm = na.rm)
HellingerDist <- sqrt(sum((sqrt(p1) - sqrt(p2))^2, na.rm = na.rm))
WarrenI <- 1 - ((HellingerDist^2)/2)
list(SchoenerD = SchoenerD, WarrenI = WarrenI, HellingerDist = HellingerDist)
}

[presented with Pretty R]

See also the *fuzSim* function in the *fuzzySim* package, which calculates **fuzzy versions of classic binary similarity indices** such as Jaccard, Baroni-Urbani & Buser, Sorensen and Simpson (Barbosa 2015).

**REFERENCES**

Barbosa A.M. (2015) fuzzySim: applying fuzzy logic to binary similarity indices in ecology. *Methods in Ecology and Evolution*, 6: 853-858

Reino L., Ferreira M., Martínez-Solano I., Segurado P., Xu C. & Barbosa A.M. (in press) Favourable areas for co-occurrence of parapatric species: niche conservatism and niche divergence in Iberian tree frogs and midwife toads.* Journal of Biogeography*

Warren D.L., Glor R.E. & Turelli, M. (2008) Environmental niche equivalency versus conservatism: quantitative approaches to niche evolution. *Evolution*, 62: 2868-83 *[plus ERRATUM]*

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