Communicative complexity relates to social complexity, as individuals in more complex social systems either use more signals or more complex signals than individuals living in less complex ones. Taking the individual group member's perspective, here we examine communicative complexity in relation to social complexity, which arises from two components of social systems: social structure and social organization. We review the concepts of social relationships and social complexity and evaluate their implications for communicative and cognitive complexity using examples from primate species. We focus on spider monkeys (Ateles geoffroyi), as their social organization is characterized by flexibility in grouping dynamics and they use a variety of communicative signals. We conclude that no simple relationship exists among social complexity, communicative complexity and cognitive complexity, with social complexity not necessarily implying cognitive complexity, and communicative and cognitive complexity being independently linked to social complexity. To better understand the commonly implied link between social complexity and cognitive complexity it is crucial to recognize the complementary role of communicative complexity. A more elaborated communicative toolkit provides the needed flexibility to deal with dynamic and multifaceted social relationships and high variation in fission-fusion dynamics. This article is part of the theme issue 'Cognition, communication and social bonds in primates'.
Keywords: cognitive complexity; communicative complexity; communicative signal; fission–fusion dynamics; social complexity; social relationship.