R-Models: A mathematical framework for capturing notions of abstraction and assistance in reproductive systems

R-Models are an approach to capturing notions of assistance and abstraction in reproductive systems, based on labelled transition systems and Gibson's theory of affordances. R-Models incorporate a labelled transition system that describes how a reproductive system changes over the course of reproduction. The actors in the system are represented by a set of entities together with a relation describing the states in which those entities are present, and an affordance-modelling function mapping actions to sets of entities which enable those actions to be performed. We show how R-models can be classified based on whether the reproducer is assisted or unassisted in reproduction, and whether or not the reproducer is active during reproduction. We prove that all assisted and unassisted R-models have a related R-model which has the opposite classification. We discuss the relevance to the field of artificial life, give a potential application to the fields of computer virology, and demonstrate reproduction modelling and classification in action using examples.