The Origin of Informational Replicators by Serial Dilution of a Primordial Soup

How can informational replicators (Zachar and Szathmáry 2010) such as template replicators, arise from noninformational autocatalysts (Szathmáry and Maynard Smith 1997; Szathmary 2000)? Variants of an informational replicator have a high probability of being autocatalytic, thus allowing potentially unlimited heritable variants to be replicated, for example, mutants of a DNA sequence have this property. Variants of non-informational replicators such as glycolaldehyde in the Formose cycle are not in general autocatalytic; therefore, there is little capacity for hereditary variation (Szathmáry 2006). This paper asks; what are the necessary and sufficient conditions for an increase in the probability that a variant of an autocatalyst will itself be capable of autocatalysis? Given some well-defined assumptions, serial dilution in a rich generative chemistry such as that found in the Miller experiment should result in the emergence of informational replicators, i.e. autocatalysts whose variants have a high probability of themselves being capable of autocatalysis.