From individual thresholds to collective hysteresis: a mechanistic model of the dawn chorus

At dawn, many bird communities exhibit a rapid and highly synchronous transition from silence to vocal activity. Although light levels increase gradually, the onset of this dawn chorus can appear abrupt, suggesting the possibility of tipping behaviour. While such dynamics are frequently described using catastrophe theory, direct mechanistic links between individual behavioural rules and macroscopic bifurcation structure remain limited. We develop a stochastic threshold model for this phenomenon in which each individual sings when a combination of light and social stimulation exceeds its activation threshold. Under mean-field scaling, the population dynamics converge to a deterministic equation for the proportion of singing individuals, with nonlinearity determined entirely by the cumulative distribution of thresholds. We show that for a broad class of threshold distributions, this system exhibits cusp bifurcations and hysteresis. Thus, the abrupt onset of singing can emerge directly from heterogeneity and social feedback, without imposing nonlinearities at the population level. Extending the model to spatially structured populations yields travelling waves, providing an explanation for the spatial variation of song across a landscape. Our results demonstrate how heterogeneity in behavioural thresholds can generate hysteresis in socially coupled populations, offering a general framework for linking individual decision rules to emergent ecological transitions.