  This paper extends Eigen's quasispecies equations to account for the
semiconservative nature of DNA replication. We solve the equations in the limit
of infinite sequence length for the simplest case of a static, sharply peaked
fitness landscape. We show that the error catastrophe occurs when $ \mu $, the
product of sequence length and per base pair mismatch probability, exceeds $ 2
\ln \frac{2}{1 + 1/k} $, where $ k > 1 $ is the first order growth rate
constant of the viable ``master'' sequence (with all other sequences having a
first-order growth rate constant of $ 1 $). This is in contrast to the result
of $ \ln k $ for conservative replication. In particular, as $ k \to \infty $,
the error catastrophe is never reached for conservative replication, while for
semiconservative replication the critical $ \mu $ approaches $ 2 \ln 2 $.
Semiconservative replication is therefore considerably less robust than
conservative replication to the effect of replication errors. We also show that
the mean equilibrium fitness of a semiconservatively replicating system is
given by $ k (2 e^{-\mu/2} - 1) $ below the error catastrophe, in contrast to
the standard result of $ k e^{-\mu} $ for conservative replication (derived by
Kimura and Maruyama in 1966).
