A re-exam ination of the stochastic corrector model

Abstract

The stochastic corrector model describes the group selection dynamics of compartmentalized replicators. It has been applied to two major evolutionary transitions: the origin of protocell genomes from independently replicating genes, and the origin of metakaryotic cells from simple eukaryotic hosts and prokaryote-derived symbionts. It is assumed that the internal dynamics would lead, owing to differential growth of the replicators within, to deterioration of the compartments as reproducing units. Stochasticity in replication and during cell division generates variation, however, on which natural selection-between the cells-can act, favouring compartments with a template composition closer to optimal. The present mathematical reformulation applies standard multitype branching processes to the full dynamics of the population of compartments. Within- and between-group dynamics are rigorously coupled by the observation that replication of a replicator within a compartment formally results in the death of the compartment with the old, and the birth of a compartment with the updated, template composition. It is shown that compartment size cannot be too small or too large, because otherwise frequent random loss of replicators from compartments, or inefficient group selection, occur, respectively. The formalism opens up the possibility of straightforward analysis of related problems.