Eigen has shown that there is a paradox in prebiotic evolution, the so
called error threshold. The paradox is as follows: an accurate complex
replication mechanism needs a large enough amount of information, and to
maintain that much information a replicator needs the very mechanism of
acuracy and complexity. Both need each other to emerge, and both are not
likely to emerge at the same moment in single species replicators.

As a solution to this paradox, Szathmary proposed compartmentalization
of a replicator system in the so called Stochastic Corrector Model. In
this model, stochasticity in the replicator dynamics and group selection
enhance the coexistence of multiple species of replicators, and thus may
facilitate the emergence of more complex replicators. However, the
compartmentalization imposes limited diffusibility and small population
size on the replicator dynamics, and both are known to reduce the
information threshold and thus decrease the amount of information which
can be maintained.

Here, we study the overall effect of the compartmentalization on the
error threshold of one single species.  We made a comparison
between a simple non-interacting self-replicator system with and without
compartmentalization. We introduce a two dimensional two layer Cellular
Automata model, in which replicators and compartments are explicitly
represented and both dynamics are interwoven parallel in time and
space. We set our models such that the dynamics of a vesicle depends on
its replicator population in several ways. The simulation results showed
that, in the case that the growth of a vesicle depends only on the total
number of its replicators (not on the composition of its replicators),
group selection was not strong enough to compensate the two other
effects. Compartmentalization reduced the error threshold, and
thus decreased the amount of information which can be kept in one
species of self-replicators. The results also showed that the spatial
pattern formation on the compartment level also reduced the error
threshold, and the difference in the speed of dynamcis between
replicators and vesicles is a delicate key feature in the determination
of error threshold.