At an early stage in pre-biotic evolution, groups of replicating molecules
must coordinate their reproduction to form aggregated units of selection.
Mechanisms that enable this to occur are currently not well understood. In this
paper we introduce a deterministic model of primitive replicating aggregates,
proto-organisms, that host populations of replicating information carrying
molecules. Some of the molecules promote the reproduction of the proto-organism
at the cost of their individual replication rate. A situation resembling that
of group selection arises. We derive and analytically solve a partial
differential equation that describes the system. We find that the relative
prevalence of fast and slow replicators is determined by the relative strength
of selection at the aggregate level to the selection strength at the molecular
level. The analysis is concluded by a preliminary treatment of finite
population size effects.Comment: 6 page
