Quantifying phenological diversity: a framework based on Hill numbers theory.

Background: Despite the great concern triggered by the environmental crisis worldwide, the loss of temporal key functions and processes involved in biodiversity maintenance has received little attention. Species are restricted in their life cycles by environmental variables because of their physiological and behavioral properties; thus, the timing and duration of species' presence and their activities vary greatly between species within a community. Despite the ecological relevance of such variation, there is currently no measure that summarizes the key temporal aspects of biological diversity and allows comparisons of community phenological patterns. Here, we propose a measure that synthesizes variability of phenological patterns using the Hill numbers-based attribute diversity framework. Methods: We constructed a new phenological diversity measure based on the aforementioned framework through pairwise overlapping distances, which was supplemented with wavelet analysis. The Hill numbers approach was chosen as an adequate way to define a set of diversity values of different order q, a parameter that determines the sensitivity of the diversity measure to abundance. Wavelet transform analysis was used to model continuous variables from incomplete data sets for different phenophases. The new measure, which we call Phenological Hill numbers (PD), considers the decouplings of phenophases through an overlapping area value between pairs of species within the community. PD was first tested through simulations with varying overlap in phenophase magnitude and intensity and varying number of species, and then by using one real data set. Results: PD maintains the diversity patterns of order q as in any other diversity measure encompassed by the Hill numbers framework. Minimum PD values in the simulated data sets reflect a lack of differentiation in the phenological curves of the community over time; by contrast, the maximum PD values reflected the most diverse simulations in which phenological curves were equally distributed over time. PD values were consistent with the homogeneous distribution of the intensity and concurrence of phenophases over time, both in the simulated and the real data set. Discussion: PD provides an efficient, readily interpretable and comparable measure that summarizes the variety of phenological patterns observed in ecological communities. PD retains the diversity patterns of order q characteristic of all diversity measures encompassed by the distance-based Hill numbers framework. In addition, wavelet transform analysis proved useful for constructing a continuous phenological curve. This methodological approach to quantify phenological diversity produces simple and intuitive values for the examination of phenological diversity and can be widely applied to any taxon or community's phenological traits.