Natural selection shapes how individuals learn and acquire knowledge from their environment. Under the right conditions, this can lead to the evolution of learning schedules-how individuals allocate resources to acquire knowledge throughout their lifespan-that promote the accumulation of knowledge across generations ('cumulative knowledge' or 'cumulative culture'). In spite of having been observed across multiple taxa, the role of parental teaching in this evolutionary process remains understudied. Using mathematical modelling, we show that learning schedules and parental teaching coevolve, resulting in greater time spent learning individually and innovating, as well as greater intergenerational transfer of knowledge from parent to offspring. These outcomes together enhance cumulative knowledge. Our analyses further reveal that within populations, selection typically favours an association between teaching and individual learning whereby some individuals innovate and teach within the family ('knowledge producers' with extensive knowledge), while others teach less and learn socially outside of the family ('knowledge scroungers' with less knowledge). Overall, our findings indicate that the coevolution of learning schedules and teaching promotes knowledge accumulation within and between generations and favours diversity within and between populations in knowledge acquisition, possession and transmission.
