Frequency distribution curves and the identification of hotspots: response to comments

Abstract

This is a response to the criticism by Cayuela et al. (2011) of our proposal for a frequency distribution approach (Bartolino et al. 2011) to the identification of hotspots in conservation and ecology. The main criticism from Cayuela et al. (2011) does not concern or affect the validity of the method per se, but mainly relates to a presumed lack of objectivity in the identification of a spatially global threshold derived from geometric properties of cumulative relative frequency distribution (CRFD) curves. As we will demonstrate, their critique mainly originates from the loose biological/ecological meaning of hotspots, and from misreading and misinterpreting the methodology we proposed. As we noted at the very beginning of our paper (Bartolino et al. 2011), it is not easy to identify a sharp boundary between hotspots and non-hotspots for phenomena that are essentially continuous (Fortin and Dale 2005), such as species richness and/or abundance. A number of statistical techniques have been proposed to perform this task (Nelson and Boots 2008), but clearly there is no insurance that the resulting hotspots will be ecologically and/or biologically significant. Moreover, the identification of hotspots is mostly driven by practical, socioeconomic or conservation objectives, partially accounting for the properties of the spatial processes under investigation. Cayuela et al. (2011) based their criticism of our paper on the widely recognised difficulty involved in adequately defining hotspots. In particular, they claim that our method is as subjective as any other global method (sensu Nelson and Boots 2008), because the hotspots identified using CRFD curves have no particular ecological meaning— although we have never claimed that they do. We do, however, claim that our method is more objective than other global methods (all subjective from an ecological point of view), because it is not left up to the author to identify the threshold used to define hotspots. We reiterate here that the a priori selection of a threshold, based on whatever percentile (e.g., the classical 5, 10, or 15% thresholds), is different from the identification of a threshold according to the geometric property of CRFD curves. In any case, neither are necessarily related to ecological and/or biological significance. However, according to Cayuela et al. (2011), utilizing the 45 slope tangent to the curve corresponding to the highest richness/ density value as the global threshold is no better than using any arbitrary 5%. In this respect, Cayuela et al. (2011) claim that there are two elements of subjectivity: considering the highest relative density value (when there may be many tangents to the CRFD curve with a slope of 45 ), and considering only a slope of 45 . The first critique is irrelevant, since during the identification of hotspots, we are interested by definition in the highest values of the phenomenon under study. The criticism of the use of a slope of This reply refers to the ‘‘notes and comments’’ at doi:10.1007/s10144-011-0272-7.