A dynamical framework for biological reproduction

Classically, biological reproduction is depicted as the building of a new organism from replicated genomic instructions. The corresponding theoretical model is von Neumann’s self-reproducing machine, which relies on an invariant universal constructor that can build any machine from instructions. However, the reproductive incompatibility of species and the diversity of developing processes speak against the existence of a universal constructor. Without a universal constructor, the genome as representation of the organism is circularly defined: what the genome represents is specified by the developmental processes represented by the genome.I propose to take invariant reproduction not as a premise, but as an emergent dynamical property. Reproduction is seen as the iteration of a transform that maps one generation to the next, a transform shaped by the genome. Invariant reproduction then occurs when a reproductive sequence converges to a fixed point. A reproductive sequence may also diverge, converge to a cycle (multigenerational life cycle), or to one of several fixed points (non-genomic inheritance). When it does converge, it is necessarily to a stable point, implying that development is robust to perturbations. Finally, speciation can be understood as a process by which reproductive transforms become mutually incompatible, that is, the basins of attractions of the fixed points do not overlap any more.In this view, the genome is a transmissible constraint on development, not a representation of the organism. I suggest that this dynamical framework is a more coherent model of biological reproduction than von Neumann’s computational framework.