  How does social complexity depend on population size and cultural
transmission? Kinship structures in traditional societies provide a fundamental
illustration, where cultural rules between clans determine people's marriage
possibilities. Here we propose a simple model of kinship interactions that
considers kin and in-law cooperation and sexual rivalry. In this model,
multiple societies compete. Societies consist of multiple families with
different cultural traits and mating preferences. These values determine
interactions and hence the growth rate of families and are transmitted to
offspring with mutations. Through a multilevel evolutionary simulation, family
traits and preferences are grouped into multiple clans with inter-clan mating
preferences. It illustrates the emergence of kinship structures as the
spontaneous formation of interdependent cultural associations. Emergent kinship
structures are characterized by the cycle length of marriage exchange and the
number of cycles in society. We numerically and analytically clarify their
parameter dependence. The relative importance of cooperation versus rivalry
determines whether attraction or repulsion exists between families. Different
structures evolve as locally stable attractors. The probabilities of formation
and collapse of complex structures depend on the number of families and the
mutation rate, showing characteristic scaling relationships. It is now possible
to explore macroscopic kinship structures based on microscopic interactions,
together with their environmental dependence and the historical causality of
their evolution. We propose the basic causal mechanism of the formation of
typical human social structures by referring to ethnographic observations and
concepts from statistical physics and multilevel evolution. Such
interdisciplinary collaboration will unveil universal features in human
societies.
