Harem size should be measured by more than the sum of its parts: Phenology-based measurements reveal joint effects of intrinsic and extrinsic factors on a polygamous herbivore under non-stationary climatic conditions.

Social behaviour is thought to be a major component of survival, reproduction, and resilience of populations. Thus, it is a key component in management and conservation of wild populations. In polygynous breeding species, group size influences the reproductive success of males and females, and hence it is essential to understand the environmental and demographic factors that shape the phenology of group size within populations. Here, we investigate harem size and its determinants using a 15-year dataset of annual harem size phenology-based metrics from a reintroduced population of wild Przewalski horses in Hortobágy National Park, Hungary. From the initial reintroduction of 21 animals in 1997, the population grew to 174 animals in 2012. During that same period, the number of harems increased from three to 23. Despite the 8-fold increase in population size, harem sizes remained stable, and variability among harems within years decreased. The annual phenological cycle of harem size was not consistent over the 15-year period, and the associated annual phenology-based metrics varied differently over the years. The best predictors of our phenology-based harem size metrics were adult sex ratio, annual adult mortality and annual mean number of harems, with some evidence that mean age of harem stallions and drought severity were contributing factors. Our findings reveal that complex interactions between demography, climate, and harem size can emerge in social animals. Taken together, our results demonstrate that intrinsic population processes can regulate group size even in the presence of non-stationary climatic conditions during periods of growth in human-introduced, semi-free ranging animal populations.