Lay summary
Recent years have seen an explosion in the diversity of partner control mechanisms hypothesized to stabilise cooperative behaviour among unrelated individuals. Examples include cheating, punishment or partner switching in response to being cheated. However, theoreticians explore cooperation under rather abstract conditions and control mechanisms are typically explored one by one, while individuals may often have the choice between several options, raising the question which conditions favour the use of which option. Here we propose to develop models that will be strongly based on empirical evidence. We will explore parameters that affect the relative efficiency of competing partner control mechanisms under increasingly realistic population structures. For example, we will introduce group sizes that are realistic for social mammals, asymmetries between sexes with respect to migration, and asymmetries between individuals like differences in fighting abilities (rank-order). The aim is to analyse how these factors will affect strategies and levels of cooperation. The models will allow us to create an interactive process between theory and empirical research on systems as diverse as marine cleaning mutualism, cooperatively breeding vertebrates, and primate societies.