Resolving Rogers' paradox
Culture is widely considered to be an evolutionary adaptation that enhances reproductive fitness. Social learning, the mechanism underlying cultural transmission, is thought to enhance fitness by avoiding the greater costs of individual learning. However, this explanation was famously contradicted by Rogers (1988), with a mathematical model showing that social learning can invade a population without raising its fitness. This surprising result is illustrated in Figure 1. As the proportion of social learners increases, their fitness and that of the whole population declines. This finding became known as Rogers’ paradox, and it inspired numerous searches for a resolution using theory, simulations, and math models. The upshot was that it is difficult to find successful resolutions in which social learning enhances mean fitness over large areas of the space defined by important parameters.
Figure 1. In Rogers' (1988) analytical model, the fitness of social learners declines as the proportion of social learners increases. At equilibrium, mean fitness of the population is no greater than that of individual learners.
Our resolution extended Rogers’ model to include a more complex environment and limited resources, where individuals could not reliably learn everything about the environment on their own (Kharratzadeh et al., 2017). Under such conditions, social learning evolves and enhances mean fitness. The key is to allow for hybrid learners who specialize their individual learning on one problem and learn another problem socially. Our math model results plotted in Figure 2 shows that such hybrid learners can evolve and resist invasion in a large swath of the space defined by the key parameters of u (rate of environmental change), c (cost of individual learning), b (benefit of accurate learning), and n (number of different states for each of the two problems). Degree of redness in this region corresponds to the percent relative fitness advantage of social learning. The predictions of this mathematical model were confirmed in our agent-based computer simulations of evolution.
Our resolution extended Rogers’ model to include a more complex environment and limited resources, where individuals could not reliably learn everything about the environment on their own (Kharratzadeh et al., 2017). Under such conditions, social learning evolves and enhances mean fitness. The key is to allow for hybrid learners who specialize their individual learning on one problem and learn another problem socially. Our math model results plotted in Figure 2 shows that such hybrid learners can evolve and resist invasion in a large swath of the space defined by the key parameters of u (rate of environmental change), c (cost of individual learning), b (benefit of accurate learning), and n (number of different states for each of the two problems). Degree of redness in this region corresponds to the percent relative fitness advantage of social learning. The predictions of this mathematical model were confirmed in our agent-based computer simulations of evolution.
Figure 2. Hybrid learners evolve and remain stable in the colored region, defined by u < (1-u) / (1+u) and c/b < u / 0.5(1+u). Degree of redness indicates the relative fitness advantage of social learning across that region. The fitness advantage of social learning is highest in the lower left, where the environment is stable.
Our simulations also show that, although spatial or social constraints can hinder the evolution of hybrid learners, a previously ignored social learning strategy, which we call complementary copying, can mitigate this hindrance. Complementary copying is a bias toward learning socially from agents who devote more attention to, and thus presumably master, a particular problem.
Kharratzadeh, M., Montrey, M., Metz, A., & Shultz, T. R. (2017). Specialized hybrid learners resolve Rogers’ paradox about the adaptive value of social learning. Journal of Theoretical Biology, 414(February 2017), 8–16. http://doi.org/10.1016/j.jtbi.2016.11.017
Rogers, A. R. (1988). Does biology constrain culture? American Anthropologist, 90, 819–831.
Our simulations also show that, although spatial or social constraints can hinder the evolution of hybrid learners, a previously ignored social learning strategy, which we call complementary copying, can mitigate this hindrance. Complementary copying is a bias toward learning socially from agents who devote more attention to, and thus presumably master, a particular problem.
Kharratzadeh, M., Montrey, M., Metz, A., & Shultz, T. R. (2017). Specialized hybrid learners resolve Rogers’ paradox about the adaptive value of social learning. Journal of Theoretical Biology, 414(February 2017), 8–16. http://doi.org/10.1016/j.jtbi.2016.11.017
Rogers, A. R. (1988). Does biology constrain culture? American Anthropologist, 90, 819–831.
