Social tipping points are characterized by an abrupt change in behaviour state caused by small changes in environmental parameters. Here, groups of territorial damselfish (brown fishes) may respond with vigilance and inspection (top image) towards intruders or not (bottom image) depending on whether food is limited. One sign of a possible tipping point is a change point in the data, where the data suddenly appear to be nonstationary. In the plot, this is depicted as a sudden change in the mean of aggressiveness (y-axis). If a model for aggressiveness is built for conditions where food supply is low, but then applied to cases where food supply is high, the model will have very large error. This reinforces the point that the old model is no longer valid for the new data if a tipping point has occurred. The three functions fitted to the identical data above have all been used to estimate the position of tipping points along environmental gradients, though the centre panel reinforces the point that entirely new models may be required to explain system properties before versus after a tipping point.