Sigmoidal Acquisition Curves Are Good Indicators of Conformist Transmission

Abstract

The potential for behaviours to spread via cultural transmission has profound implications for our understanding of social dynamics and evolution. Several studies have provided empirical evidence that local traditions can be maintained in animal populations via conformist learning (i.e. copying the majority). A conformist bias can be characterized by a sigmoidal relationship between a behavior's prevalence in the population and an individual's propensity to adopt that behavior. For this reason, the presence of conformist learning in a population is often inferred from a sigmoidal acquisition curve in which the overall rate of adoption for the behavior is taken as the dependent variable. However, the validity of sigmoidal acquisition curves as evidence for conformist learning has recently been challenged by models suggesting that such curves can arise via alternative learning rules that do not involve conformity. We review these models, and find that the proposed alternative learning mechanisms either rely on faulty or unrealistic assumptions, or apply only in very specific cases. We therefore recommend that sigmoidal acquisition curves continue to be taken as evidence for conformist learning. Our paper also highlights the importance of understanding the generative processes of a model, rather than only focusing solely on the patterns produced. By studying these processes, our analysis suggests that current practices by empiricists have provided robust evidence for conformist transmission in both humans and non-human animals.Arising from: Acerbi, A. et al. Sci. Rep. 6, 36068 (2016); https://doi.org/10.1038/srep36068 .

Figure 1

Variant preferences. A replication of the model of Acerbi et al. in which individuals prefer one of the two variants. Includes best fit linear and sigmoid curves to data. Top row: Initial frequency of variant A always initialized to 50%, as in Acerbi et al. Bottom row: Initial frequency varied across runs from 0% to 100% in increments of 0.1%. Centre column: Runs in which variant A is preferred and runs in which variant B is preferred are averaged together. Right and left columns: variant A or B is always preferred, respectively.

Figure 2

Explanation of concave-up curve. Curves y₁ and y₂ are simple lines with slopes of 1 and 0.2, reflecting the probability of adopting variant A or B, respectively. Curve y₃ is the weighted average of the two lines, in which y₂ for lower values of x and y₁ is dominant for higher values. Note that y₃ replicates the curve seen in Fig. 1, bottom centre.

Figure 3

Analytical model for variant preferences. (A) When all individuals prefer variant A (r = 1), we replicate the r-shaped curve of Boyd and Richerson. (B) If the environment is always initialized with approximately 50% of each variant and the preferred variant always increases in frequency, an artefactual sigmoidal curve can emerge if all data for both variant preferences are combined. To be consistent with agent-based simulations, curves here are for q = 0.2.

Figure 4

Demonstrators subgroup. Individuals choose a random member of a fixed group of size Dm and copy that individual’s behavioural variant. For all simulations, Dm = 5. (A) Initial frequency of variant A is fixed at 50% for all runs, replicating the results of Acerbi et al.. (B) The sigmoidal curve remains apparent when initial frequency of variant A is varied across runs from 0% to 100% in increments of 0.1%. (C) When variant A is always rare initially, the sigmoidal curve largely disappears, replaced with an r-shaped curve.

Figure 5

Implementations of the model described in van Leeuwen et al., counting the behavioural variants from the current state of the population (A), and from the complete history of actions performed (B). If the history of actions performed is limited to a recent window (here the last 10 solves, (C)), then there is no evidence that a sigmoidal curve could result.

Figure 6

Relative fit of a linear versus sigmoidal model based on the r² value of the model fit. Here a window of size x is used to calculate the variant frequencies, where x is related to the number of previous observations from the population. As x increased, the fit of a linear model (solid line) decreases. However, a linear model remains a better fit than a sigmoid model until a very large window size.