Abstract
Given a population with internal structures determining possible interactions between population members, what can be said about the spread of innovation? In genetics, this is a question of the spread of a favorable mutation within a genetically homogeneous population. In a model society, it is the question of rumors, beliefs, or innovation [1,2,3,4,5]. This paper sketches a simple iterative model of populations with structure represented in terms of edge weighted graphs. Use of such graphs has become a powerful tool in evolutionary dynamics [e.g. 6]. The model presented here employs a Markov process on a state space isomorphic to the vertex set of the N-hypercube. In analogy to genetics, spread of innovation is first modeled as a biased birth-death process in which the innovation provides a fitness r as compared to the fitness of 1 assigned to non-innovative individuals. Following on this, a probabilistic model is developed that, in the simplest cases, corresponds to an elementary probabilistic cellular automata.
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Voorhees, B. (2012). Introducing Innovation in a Structured Population. In: Sirakoulis, G.C., Bandini, S. (eds) Cellular Automata. ACRI 2012. Lecture Notes in Computer Science, vol 7495. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33350-7_26
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DOI: https://doi.org/10.1007/978-3-642-33350-7_26
Publisher Name: Springer, Berlin, Heidelberg
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