  The origin of heredity is studied as a recursive state in a replicating
proto-cell consisting of many molecule species in mutually catalyzing reaction
networks. Protocells divide when the number of molecules, increasing due to
replication, exceeds a certain threshold. We study how the chemicals in a
catalytic network can form recursive production states in the presence of
errors in the replication process. Depending on the balance between the total
number of molecules in a cell and the number of molecule species, we have found
three phases; a phase without a recursive production state, a phase with
itinerancy over a few recursive states, and a phase with fixed recursive
production states. Heredity is realized in the latter two phases where molecule
species that are population-wise in the minority are preserved and control the
phenotype of the cell. It is shown that evolvability is realized in the
itinerancy phase, where a change in the number of minority molecules controls a
change of the chemical state.
