arXiv2026
Teaching is ubiquitous across human societies. Instruction from parents to offspring is the most fundamental form of teaching, explained primarily through kin selection and inclusive fitness. Instruction to non-kin, known as oblique teaching, also plays a dominant role in modern societies, where teaching is often institutionalized. Nonetheless, it remains puzzling how or when oblique teaching can evolve. Here we address the evolution of oblique teaching by developing a mathematical model of stage-structured populations. Younger individuals engage in a useful activity, called hunting, and reproduce. At some point in life, they cease contributing directly to hunting and reproduction, and instead serve exclusively as teachers who increase the hunting expertise of the young. We refer to this transition in life stage as retirement, and we analyze the evolution of the retirement rate, and the resulting frequency of post-reproductive teachers, in a population subject to a global carrying capacity. We find that retirement and teaching can evolve without kinship or inclusive fitness, but only in populations above a threshold size. Unlike in classical adaptive dynamics, the evolutionarily stable retirement rates depend on the absolute population size of a mutant type upon introduction. In many regimes, evolution produces fewer teachers than would maximize the population's per-capita hunting returns or intrinsic birth rate. A mutant that differs only slightly from the resident type generally cannot invade from a minority, so teaching cannot emerge through gradual evolution. The mechanism we describe is therefore available to cultural evolution, where a distinct norm for retirement and elder care may be adopted by a sub-population simultaneously. Our account is thus tied closely to theories of cultural evolution, including the "information grandmother hypothesis" of Henrich and Henrich.