In social animals, perturbations may trigger specific behavioural responses with consequences for dispersal and complex population dynamics. Perturbations raise the need for information gathering in order to reduce uncertainty and increase resilience. Updated information is then shared within the group and social behaviours emerge as a self-organized process. This social information factoralizes with the size of the group, and it is finally used for making crucial decisions about, for instance, when to leave the patch and where to go. Indeed, evolution has favoured philopatry over dispersal, and this trade-off is challenged by perturbations. When perturbations accumulate over time, they may decrease the suitability of the patch and erode the philopatric state until crossing a tipping point, beyond which most individuals decide to disperse to better areas. Initially, the decision to disperse is led by a few individuals, and this decision is copied by the rest of the group in an autocatalytic way. This feedback process of social copying is termed runaway dispersal. Furthermore, social copying enhances the evolution of cultural and technological innovation, which may cause additional nonlinearities for population dynamics. Social information gathering and social copying have also occurred in human evolution, especially after perturbations such as climate extremes and warfare. In summary, social feedback processes cause nonlinear population dynamics including hysteresis and critical transitions (from philopatry to patch collapses and invasions), which emerge from the collective behaviour of large ensembles of individuals.