Parturition Synchrony Index: A Method for Assessing Individual Parturition Synchrony Within a Group or Population.

The phenomenon of parturition synchrony at the population level has been studied for decades using various methods. To assess the tendency of individual mothers to synchronize their parturition timing with others, we developed a novel parturition synchrony index (PSI). The PSI quantifies an individual mother's degree of parturition synchrony within a group or population by detecting variation in the synchrony of parturitions, regardless of their actual timing within the season. A value of 1 indicates complete synchrony (i.e., a parturition occurring on the same day as others), whereas values approaching 0 reflect increasing asynchrony. To evaluate the robustness of the PSI, we conducted simulations examining how parturition-date distribution (completely synchronous, lognormal, normal, bimodal, and uniform), parturition-season duration (1, 10, 50, 100, 200, and 365 days), and group size (5, 10, 25, 50, 100, 500, 1000, and 5000 mothers) influence the PSI and its inter-individual variability. A PSI value was calculated for each of the 140,490 individual mothers in the 168 simulated groups. For each group, we subsequently calculated both the mean PSI and the coefficient of variation (CV) of PSI values. All examined parameters influenced both metrics. Across all distributions (excluding complete synchrony), mean PSI values were higher in shorter than in longer parturition seasons. However, only in lognormal and normal distributions were mean PSI values markedly higher in larger than in smaller groups. Conversely, the CV was higher in longer seasons and in smaller groups across all distributions. Our results highlight the PSI's broad applicability to diverse socio-ecological contexts. However, its reliability decreases under constrained conditions, such as very short seasons or extremely small groups, where wider confidence intervals were observed. The PSI thus provides a robust and flexible tool for quantifying and functionally analyzing individual parturition synchrony in mammals, and potentially in other viviparous vertebrates.