Evolutionarily stable learning schedules and cumulative culture in discrete generation models |
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Authors: | Aoki Kenichi Wakano Joe Yuichiro Lehmann Laurent |
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Affiliation: | a Department of Biological Sciences, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japanb Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, 1-1-1 Higashi-Mita, Tama-ku, Kawasaki, Kanagawa 214-8571, Japanc Department of Ecology and Evolution, UNIL Sorge, Le Biophore, CH-1015 Lausanne, Switzerland |
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Abstract: | Individual learning (e.g., trial-and-error) and social learning (e.g., imitation) are alternative ways of acquiring and expressing the appropriate phenotype in an environment. The optimal choice between using individual learning and/or social learning may be dictated by the life-stage or age of an organism. Of special interest is a learning schedule in which social learning precedes individual learning, because such a schedule is apparently a necessary condition for cumulative culture. Assuming two obligatory learning stages per discrete generation, we obtain the evolutionarily stable learning schedules for the three situations where the environment is constant, fluctuates between generations, or fluctuates within generations. During each learning stage, we assume that an organism may target the optimal phenotype in the current environment by individual learning, and/or the mature phenotype of the previous generation by oblique social learning. In the absence of exogenous costs to learning, the evolutionarily stable learning schedules are predicted to be either pure social learning followed by pure individual learning (“bang-bang” control) or pure individual learning at both stages (“flat” control). Moreover, we find for each situation that the evolutionarily stable learning schedule is also the one that optimizes the learned phenotype at equilibrium. |
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Keywords: | Population genetics Cumulative culture Optimal strategy |
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