Contributed talk in Emergence of Innovation & Cooperation 1, July 29, 2019, 3 p.m. in room USB.2.022

Simplified Modeling of the Evolution of Skills in a Spatially Resolved Environment

Rudolf M. Füchslin, Johannes J. Schneider, Richard Walker

watch Publication We present a model for the spread, transmission and competition of skills with an emphasis on the role of spatial mobility of individuals. From a methodological point of view, we seek mathematical and computational simplicity in the sense of a minimal model. In the presented model, individuals may have no skill or either skill A or B. Individuals are born unskilled and may acquire skills by being taught from a skilled individual. Skill A results in a small reproductive advantage but is easy to transmit (teaching happens at high rate), whereas skill B is harder to teach but results in a high benefit. The model exhibits a rich behavior; after an initial transient, the system settles to a fix point (constant distribution of skills), whereby the distribution of skills depends on a mobility parameter m. We observe different regimes, and as the main result, we conclude that for some settings of the system parameters, the spread of the harder to learn but more beneficial skill B is only possible in a certain window of the mobility parameter. From a technical point of view, this paper presents the application of the PRESS–method (probability reduced evolution of spatially resolved species) that enables the study of spatial effects in very efficient manner. We analyze the consequences of spatial organization and argue that social dynamics can be studied in an infinite dimensional simplex space. In spite of this maybe daunting name, the dynamics on such a structure is comparably easy to implement.