Conformity and anti-conformity in a finite population

Conformity to continuous and discrete ordered traits

Models of conformity and anticonformity have typically focused on cultural traits with unordered variants, such as baby names, strategies (cooperate/defect), or the presence/absence of an innovation. There have been fewer studies of conformity to cultural traits with ordered variants, such as level of cooperation (low, medium, high) or proportion of time spent on a task (0% to 100%). In these studies of ordered cultural traits, conformity is defined as a preference for the mean trait value in a population even if no members of the population have variants near this mean; e.g., 50% of the population has variant 0 and 50% has variant 1, producing a mean of 0.5. Here, we introduce models of conformity to ordered traits, which can be either discrete or continuous. In these models, conformists prefer to adopt more popular cultural variants even if these variants are far from the population mean. To measure a variant's "popularity" in cases where no two individuals share precisely the same variant on a continuum, we introduce a metric called k-dispersal; this takes into account a variant's distance to its k closest neighbors, with more "popular" variants having lower distances to their neighbors. We demonstrate through simulations that conformity to ordered traits need not produce a homogeneous population, as has previously been claimed. Under some combinations of parameter values, conformity sustains substantial trait variation over many generations. Furthermore, anticonformity may produce a high level of polarization.

On random conformity bias in cultural transmission of polychotomous traits

Mathematical models of conformity and anti-conformity have commonly included a set of simplifying assumptions. For example, (1) there are m=2 cultural variants in the population, (2) naive individuals observe the cultural variants of n=3 adult "role models," and (3) individuals' levels of conformity or anti-conformity do not change over time. Three recent theoretical papers have shown that departures from each of these assumptions can produce new population dynamics. Here, we explore cases in which multiple, or all, of these assumptions are violated simultaneously: namely, in a population with m variants of a trait where conformity (or anti-conformity) occurs with respect to n role models, we study a model in which the conformity rates at each generation are random variables that are independent of the variant frequencies at that generation. For this model a class of symmetric constant equilibria exist, and it is possible that all of these equilibria are simultaneously stochastically locally stable. In such cases, the effect of initial conditions on subsequent evolutionary trajectories becomes very complicated.

Cultural transmission of move choice in chess

The study of cultural evolution benefits from detailed analysis of cultural transmission in specific human domains. Chess provides a platform for understanding the transmission of knowledge due to its active community of players, precise behaviours and long-term records of high-quality data. In this paper, we perform an analysis of chess in the context of cultural evolution, describing multiple cultural factors that affect move choice. We then build a population-level statistical model of move choice in chess, based on the Dirichlet-multinomial likelihood, to analyse cultural transmission over decades of recorded games played by leading players. For moves made in specific positions, we evaluate the relative effects of frequency-dependent bias, success bias and prestige bias on the dynamics of move frequencies. We observe that negative frequency-dependent bias plays a role in the dynamics of certain moves, and that other moves are compatible with transmission under prestige bias or success bias. These apparent biases may reflect recent changes, namely the introduction of computer chess engines and online tournament broadcasts. Our analysis of chess provides insights into broader questions concerning how social learning biases affect cultural evolution.