A REEXAMINATION OF THE STOCHASTIC CORRECTOR MODEL

The stochastic corrector model describes the group selection dynamics of compartmentalized replicators. It has been applied to two major evo lutionary transitions: the origin of protocell genomes from independen tly replicating genes, and the origin of metakaryotic cells from simpl e eukaryotic hosts and prokaryote-derived symbionts. It is assumed tha t the internal dynamics would lead, owing to differential growth of th e replicators within, to deterioration of the compartments as reproduc ing units. Stochasticity in replication and during cell division gener ates variation, however, on which natural selection - between the cell s - can act, favouring compartments with a template composition closer to optimal. The present mathematical reformulation applies standard m ultitype branching processes to the full dynamics of the population of compartments. Within- and between-group dynamics are rigorously coupl ed by the observation that replication of a replicator within a compar tment formally results in the death of the compartment with the old, a nd the birth of a compartment with the updated, template composition. It is shown that compartment size cannot be too small or too large, be cause otherwise frequent random loss of replicators from compartments, or inefficient group selection, occur, respectively. The formalism op ens up the possibility of straightforward analysis of related problems .