State-dependent dynamics of cycles in red grouse abundance

Abstract

Fluctuating populations are frequently demonstrated to co-vary in abundance over space, but the dynamics of coupling between populations that gives rise to this synchrony are poorly understood. Synchrony may arise through coupling that is weak and continuous, but in populations that cycle with a characteristic period, synchrony can be maintained through stronger coupling that acts only intermittently. Here, we apply a discrete Markov model that describes the state of a population trajectory to be in one of four possible states. The Markov model reveals the nature of the coupling that gives rise to the weakly synchronous cycles of red grouse abundance. Using time-series data from 287 populations across the species range in the UK, we show that grouse populations appear mostly uncoupled through time, but that approximately one year in six, ''collective forcing events'' occur, where populations in a region are forced into synchrony to a significantly greater degree than would be expected if their dynamics proceeded independently. In the absence of these events, synchrony between populations dissipates within ~3 yr. Smaller, low abundance populations tend to make the less probable phase shifts required to synchronize with nearby high abundance populations, suggesting that these low abundance populations are more susceptible to the perturbations responsible for phase shifts than larger populations.