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The ultimate payoff of behaviours depends not only on their direct impact on an individual, but also on the impact on their relatives. Local relatedness-the average relatedness of an individual to their social environment-therefore has profound effects on social and life history evolution. Recent work has begun to show that local relatedness has the potential to change systematically over an individual's lifetime, a process called kinship dynamics. However, it is unclear how general these kinship dynamics are, whether they are predictable in real systems and their effects on behaviour and life history evolution. In this study, we combine modelling with data from real systems to explore the extent and impact of kinship dynamics. We use data from seven group-living mammals with diverse social and mating systems to demonstrate not only that kinship dynamics occur in animal systems, but also that the direction and magnitude of kinship dynamics can be accurately predicted using a simple model. We use a theoretical model to demonstrate that kinship dynamics can profoundly affect lifetime patterns of behaviour and can drive sex differences in helping and harming behaviour across the lifespan in social species. Taken together, this work demonstrates that kinship dynamics are likely to be a fundamental dimension of social evolution, especially when considering age-linked changes and sex differences in behaviour and life history.