10Cultural processes, as well as the selection pressures experienced by individuals in a population over 11 time and space, are fundamentally stochastic. Phenotypic variability, together with imperfect phenotypic 12 transmission between parents and offspring, has been previously shown to play an important role in 13 evolutionary rescue and (epi)genetic adaptation of populations to fluctuating temporal environmental 14 pressures. This type of evolutionary bet-hedging does not confer a direct benefit to a single individual, 15 but instead increases the adaptability of the whole lineage. 16 Here we develop a population-genetic model to explore cultural response strategies to temporally 17 changing selection, as well as the role of local population structure, as exemplified by heterogeneity in 18 the contact network between individuals, in shaping evolutionary dynamics. We use this model to study 19 the evolutionary advantage of cultural bet-hedging, modeling the evolution of a variable cultural trait 20 starting from one copy in a population of individuals with a fixed cultural strategy. We find that the 21 probability of fixation of a cultural bet-hedger is a non-monotonic function of the probability of cultural 22 memory between generations. Moreover, this probability increases for networks of higher mean degree 23 but decreases with increasing heterogeneity of the contact network, tilting the balance of forces towards 24 drift and against selection.
25These results shed light on the interplay of temporal and spatial stochasticity in shaping cultural 26 evolutionary dynamics and suggest that partly-heritable cultural phenotypic variability may constitute 27 an important evolutionary bet-hedging strategy in response to changing selection pressures. 28 Keywords: 29 cultural evolution; cultural plasticity; spatial structure; temporally changing environments; contact network 30 properties and evolutionary dynamics 31 Introduction 32Many foundational models of social learning and cultural evolution are constructed within the framework of 33 theoretical population genetics (Cavalli-Sforza and Feldman, 1981, 1973; Feldman and Cavalli-Sforza, 1976; 34 Cavalli-Sforza et al., 1982; Feldman and Cavalli-Sforza, 1984). With genetic evolution as a starting point, 35 models of cultural evolution emphasize that cultural traits-learned behaviors such as beliefs, practices, and 36 tools-can be transmitted between individuals and are subject to evolutionary forces such as selection and 37 drift (Cavalli-Sforza and Feldman, 1973; Creanza et al., 2012 Creanza et al., , 2017a. In addition, these population-genetic 38 modeling frameworks facilitate the joint consideration of genetic and cultural traits, allowing researchers to 39 track allele frequencies and cultural phenotypes within the same population and assess their evolutionary 40 effects on one another (Feldman and Zhivotovsky, 1992; Laland et al., 1995 Laland et al., , 2000 Odling-Smee et al., 2003).
41These models of cultural evolution have generally assume...