Error propagation in the hypercycle

We study analytically the steady-state regime of a network of n error-prone self-replicating templates forming an asymmetric hypercycle and its error tail. We show that the existence of a master template with a higher noncatalyzed self-replicative productivity a than the error tail ensures the stability of chains in which $m<n-1$ templates coexist with the master species. The stability of these chains against the error tail is guaranteed for catalytic coupling strengths K on the order of a. We find that the hypercycle becomes more stable than the chains only if K is on the order of $a^2.$ Furthermore, we show that the minimal replication accuracy per template needed to maintain the hypercycle, the so-called error threshold, vanishes as $\sqrt{n/K}$ for large K and $n<~4.$