Analyze causal relations between climatic and biotic velocities using circular statistics so as to inform biodiversity conservation

Abstract

Directional (or circular) biodiversity data are characterized by a series of values within the range 0 –360 . This constrained range implies that conventional statistical methods suitable for the analysis of linear data do not apply to directional data. Circular statistics, which have been well developed over the past several decades (Upton and Fingleton 1989; Jammalamadaka and SenGupta 2001), are an ideal tool to analyze directional data. However, in climate change-related biodiversity studies, circular statistics have been rarely employed, even though some previous macroecological studies began to use this powerful technique (Cunningham et al. 2015; Du et al. 2015). Velocity is a vector containing both magnitude and direction components. Both components should be analyzed so as to provide a holistic understanding on the general relations between climatic and biotic velocities. Here climatic velocity is defined as the change speed of climate over time, while biotic velocity is defined as the shift speed of species’ range over time (Loaire et al. 2009; Chen 2015; Comte and Grenouillet 2015). The magnitudinous relation between climatic and biotic velocities can be analyzed using conventional regression techniques, while the directional relation between these velocities may be analyzed by circular statistics. In a recent study, Comte and Grenouillet (2015) found that there were either nonsignificant or significant associations between climatic and biotic velocities for the distribution of freshwater fish in French streams. However, from Figs. 3 and 5 in their paper, only the magnitude component of these velocities was analyzed actually. The directional relations were not analyzed and interpreted at all. Here, I recommend applying circular–