Evolution of teaching under the incomplete chance of vertical cultural transmission

Widespread teaching behavior in the society is thought to be unique to humans and it contributes to our success by improving the efficiency of cultural transmission and by enhancing cultural accumulation. However, there is a puzzle in the evolution of teaching because teaching is an altruistic behavior and incompleteness of vertical transmission due to the chance of oblique transmission (cultural transmission from non-related individual). Here we investigate the effect of the probability of oblique transmission by studying to what extent the existence of oblique transmission can lead to evolution of teaching. We assume a life schedule trade off between social learning, individual learning, exploitation, and teaching. In particular, we analyze two scenarios; the one where a role model teaches anyone and the other where one teaches only his/her offspring but does not teach non-relatives. Our results show that teaching becomes dramatically unfavored in both scenarios when the probability of oblique transmission increases. Furthermore, we surprisingly find that teaching evolves in a narrower parameter region in the second scenario than in the first because equilibrium cultural level in the population is lower in the second scenario. Overall, our model implies that we need to consider an additional mechanism to explain the evolution of widespread teaching.