Standish, Russell K. “An ecolab perspective on the Bedau evolutionary statistics.” arXiv preprint nlin/0004026 (2000).
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At Alife VI, Mark Bedau proposed some evolutionary statistics as a means of classifying different evolutionary systems. Ecolab, whilst not an artificial life system, is a model of an evolving ecology that has advantages of mathematical tractability and computational simplicity. The Bedau statistics are well defined for Ecolab, and this paper reports statistics measured for typical Ecolab runs, as a function of mutation rate. The behaviour ranges from class 1 (when mutation is switched off), through class 3 at intermediate mutation rates (corresponding to scale free dynamics) to class 2 at high mutation rates. The class 3/class 2 transition corresponds to an error threshold. Class 4 behaviour, which is typified by the Biosphere, is characterised by unbounded growth in diversity. It turns out that Ecolab is governed by an inverse relationship between diversity and connectivity, which also seems likely of the Biosphere. In Ecolab, the mutation operator is conservative with respect to connectivity, which explains the boundedness of diversity. The only way to get class 4 behaviour in Ecolab is to develop an evolutionary dynamics that reduces connectivity of time.