How to describe and measure phenology? An investigation on the diversity of metrics using phenology of births in large herbivores

Proposed in 1849 by Charles Morren to depict periodical phenomena governed by seasons, the term 'phenology' has spread in many fields of biology. With the wide adoption of the concept of phenology flourished a large number of metrics with different meaning and interpretation. Here, we first a priori classified 52 previously published metrics used to characterise the phenology of births in large herbivores according to four biological characteristics of interest: timing, synchrony, rhythmicity and regularity of births. We then applied each metric retrieved on simulation data, considering normal and non-normal distributions of births, and varying distributions of births in time. We then evaluated the ability of each metric to capture the variation of the four phenology characteristics via a sensitivity analysis. Finally, we scored each metric according to eight criteria we considered important to describe phenology correctly. The high correlation we found among the many metrics we retrieved suggests that such diversity of metrics is unnecessary. We further show that the best metrics are not the most commonly used, and that simpler is often better. Circular statistics with the mean vector orientation and mean vector length seems, respectively, particularly suitable to describe the timing and synchrony of births in a wide range of phenology patterns. Tests designed to compare statistical distributions, like Mood and Kolmogorov-Smirnov tests, allow a first and easy quantification of rhythmicity and regularity of birth phenology respectively. By identifying the most relevant metrics our study should facilitate comparative studies of phenology of births or of any other life-history event. For instance, comparative studies of the phenology of mating or migration dates are particularly important in the context of climate change.