Values, conventions, innovation and sociopolitical struggles in a local food system: Conflict between organic and conventional farmers in Sierra de Segura

•Local Food Systems are not always homogeneous places in which agents have similar interests and values.•Conflict is an essential feature of processes of social construction of quality inside Local Food Systems.•Convention Theory offers a set of key concepts for approaching agents' coordination and conflict inside Local Food Systems.•Compromises are essential for understanding social construction and competition between organic and local olive oil farmers.•Compromises are supported by strong discursive mobilisation, being clashes one of their major distinctive elements.