Submitted 5 November 2021 Accepted 19 April 2022 Published 12 May 2022 Corresponding author Hibraim Adán Pérez-Mendoza, hibraimperez@ciencias.unam.mx Academic editor Sandrine Pavoine Additional Information and Declarations can be found on page 14 DOI 10.7717/peerj.13412 Copyright 2022 Sánchez-Ochoa et al. Distributed under Creative Commons CC-BY 4.0 OPEN ACCESS Quantifying phenological diversity: a framework based on Hill numbers theory Daniel Sánchez-Ochoa 1 ,2 , Edgar J. González 3 , Maria del Coro Arizmendi 4 , Patricia Koleff 5 , Raúl Martell-Dubois 5 , Jorge A. Meave 3 and Hibraim Adán Pérez-Mendoza 1 1 Laboratorio de Ecología Evolutiva y Conservación de Anfibios y Reptiles, Facultad de Estudios Superiores Iztacala, Universidad Nacional Autónoma de México, Tlalnepantla de Baz, México, Mexico 2 Posgrado en Ciencias Biológicas, Unidad de Posgrado, Circuito de Posgrados, Universidad Nacional Autónoma de México, Ciudad Universitaria, Coyoacán, Ciudad de México, Mexico 3 Departamento de Ecología y Recursos Naturales, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Coyoacán, Ciudad de México, Mexico 4 Laboratorio de Ecología, UBIPRO, Facultad de Estudios Superiores Iztacala, Universidad Nacional Autónoma de México, Tlalnepantla de Baz, México, Mexico 5 Comisión Nacional para el Conocimiento y Uso de la Biodiversidad, Tlalpan, Ciudad de México, Mexico ABSTRACT Background. Despite the great concern triggered by the environmental crisis world- wide, 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 aforemen- tioned 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 How to cite this article Sánchez-Ochoa D, González EJ, Arizmendi MC, Koleff P, Martell-Dubois R, Meave JA, Pérez-Mendoza HA. 2022. Quantifying phenological diversity: a framework based on Hill numbers theory. PeerJ 10:e13412 http://doi.org/10.7717/peerj.13412