Sigmund indicated that in reality, a hypercycle can maintain only fewer than five members. In agreement with Eigen and Schuster's principal analysis, they argued that systems with five or more species exhibit limited and unstable cyclic behaviour, because some species can die out due to stochastic events and break the positive feedback loop that sustains the hypercycle. The extinction of the hypercycle then follows. It was also emphasized that a hypercycle size of up to four is too small to maintain the amount of information sufficient to cross the information threshold. Several researchers proposed a solution to these problems by introducing space into the initial model either explicitly or in the form of a spatial segregation within compartments. Bresch et al. proposed a package model as a solution for the parasite problem. Later on, Szathmáry and Demeter proposed a stochastic corrector machine model. Both compartmentalized systems proved to be robust against parasites. However, package models do not solve the error threshold problem that originally motivated the idea of the hypercycle. A few years later, Maarten Boerlijst and Paulien Hogeweg, and later Nobuto Takeuchi, studied the replicator equations with the use of partial differential equations and cellular automata models, methods that already proved to be successful in other applications. They demonstrated that spatial self-structuring of the system completely solves the problem of global extinction for large systems and, partially, the problem of parasites. The latter was also analysed by Robert May, who noticed that an emergent rotating spiral wave pattern, which was observed during computational simulations performed on cellular automata, proved to be stable and able to survive the invasion of parasites if they appear at some distance from the wave core. Unfortunately, in this case, rotation decelerates as the number of hypercycle members increases, meaning that selection tends toward decreasing the amount of information stored in the hypercycle. Moreover, there is also a problem with adding new information into the system. In order to be preserved, the new information has to appear near to the core of the spiral wave. However, this would make the system vulnerable to parasites, and, as a consequence, the hypercycle would not be stable. Therefore, stable spiral waves are characterized by once-for-ever selection, which creates the restrictions that, on the one hand, once the information is added to the system, it cannot be easily abandoned; and on the other hand, new information cannot be added.