Borrowing from the concept of keystone species in ecological food webs, a recent focus in the field of animal behaviour has been keystone individuals: individuals whose impact on population dynamics is disproportionally larger than their frequency in the population. In populations evolving culture, such may be the role of high-magnitude innovators: individuals whose innovations are a major departure from the population's existing behavioural repertoire. Their effect on cultural evolution is

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... old: they produce innovations that constitute a 'cultural leap', and, once copied, their innovations may induce further innovations by conspecifics (socially induced innovations), as they explore the new behaviour themselves. I use computer simulations to study the coevolution of independent innovations, socially induced innovations and innovation magnitude, and show that while socially induced innovation is assumed here to be less costly than independent innovation, it does not readily evolve. When it evolves, it may in some conditions select against independent innovation and lower its frequency, despite it requiring independent innovation in order to operate; at the same time, however, it leads to much faster cultural evolution. These results confirm the role of high-magnitude innovators as keystones, and suggest a novel explanation for low frequency of independent innovation.This article is part of the theme issue 'Bridging cultural gaps: interdisciplinary studies in human cultural evolution'.