Fig. 1. An assembly of amphiphilic molecules could spontaneously form according to two regimens governed by the following two parameters: N, the number of molecules within an assembly (i.e. assembly size), and NG, the fixed, global number of different ‘monomer’ compounds attainable under the constraints of chemistry (i.e. repertoire size). For randomly formed large assemblies, fulfilling N>>NG, (top), every type of molecule is, on average, represented in multiple copies within each assembly, and therefore all assemblies are practically identical. By splitting, they form nearly identical replicas (+) but, because the assemblies manifest no diversity, evolution and selection are impossible. For small assemblies, where N<<NG, (bottom), diversity is high, each molecular species is typically present in only one copy within an assembly and each assembly a different assortment of molecules. (For example, for an assembly containing N = 100 molecules and having a repertoire size of NG = 1000, there are in excess of 10100 different assemblies possible, entering the realm of unlimited heredity (Szathmary and Maynard Smith, 1997). However, as previously pointed out (Morowitz, 1967; Szathmary and Maynard Smith, 1997), a split under the conditions N<<NG will invariably lead to two very different progeny, resulting in ineffective replication (bottom left, –). In order to reach an intermediate regimen in which both diversity and replication fidelity are achieved, it is necessary for the small assemblies to undergo a process of molecular repertoire restriction. The GARD model (see text) demonstrates that this is possible through the formation of organized, mutually catalytic networks (inset, A, thicker arrows). Importantly, repertoire restriction will not occur under conditions of equilibrium (inset, B) but a limited repertoire will be selected out of equilibrium (inset, C) (Segré et al., 1998a,b). This process might happen only for a minute fraction within the huge diversity of assemblies formed under the N<<NG conditions. Such assemblies will gradually reach a critical point, at which each molecule type will be present at two or more copies. Above this threshold, termed the ‘Morowitz boundary’ (Morowitz, 1967; Segré and Lancet, 1999), effective replication by splitting would take place (bottom right, +), potentially leading to natural selection.