The observed pattern and hidden process of female reproductive trajectories across the life span in a non-human primate.

Age-specific fertility trajectories are fundamental to understanding population structure and the evolutionary ecology of diverse life histories. However, characterizing reproductive ageing has been difficult with cross-sectional data, where senescence especially late in life can be confounded by selective disappearance. Addressing such challenge requires longitudinal data tracking the reproductive life span of known individuals, but such data are rare, especially for very long-lived species such as primates. We analyse the entire life span trajectory of annual fertility, from reproductive maturity to death, for 673 free-ranging female rhesus macaques, Macaca mulatta, on Cayo Santiago, Puerto Rico. Using generalized linear mixed-effects models (GLMMs), we first tested if time to death explains the ageing pattern independently of and additionally to chronological age, and if so, whether there is interaction between them. While GLMM captures the patterns in the data well, it is not a generative model. For example, given the GLMM and an individual's reproductive trajectory up to a given age, we cannot directly predict the probability of reproduction or death in the next year. For this reason, we further fitted a hidden Markov chain model (HMM) which allows just such a prediction, and additionally helps infer the process underlying the observed trajectory. We show that, after accounting for individual differences in fertility, reproductive ageing exhibits both age-dependent decline and also an abrupt terminal decline independently of age at death. We infer from the HMM that the underlying process of reproductive trajectory is where individuals cycle between reproductive bouts until they enter an irreversible frail condition that constrains fertility. The findings provide valuable insights into the longitudinal progression of reproductive trajectories in primates, by revealing both age-dependent and age-independent patterns and processes of ageing, and contribute to a growing body of literature on reproductive ageing and senescence across animal taxa.