General Issues of Reproduction

The description of self-reproduction in the definitions of the previous section is stated in terms of the configuration d of object A forcing surrounding S to produce a copy of A. It says nothing of how exactly d can (or should) achieve this feat, although this is a rather fundamental question when comparing different sorts of reproduction. Indeed, when looking at any sort of reproduction, I think it is useful to look at the process by which reproduction is accomplished in (at least) three different ways:

1.

The degree to which the algorithm for reproduction (the way in which the process is specified and controlled) is explicitly encoded on the configuration being reproduced (cf. d in Definition 1), rather than being implicit in the physical laws of the world (cf. S in Definition 1).

2.

Whether reproduction happens purely by the action of the physical laws of the world on the configuration to be reproduced (auto-reproduction), or whether it also requires auxiliary physical (or logical) machinery (assisted-reproduction). I use the term auto-reproduction rather than self-reproduction here because the latter is often used less specifically. I wish to emphasise that this auto-assisted distinction is only one of a variety of issues involved in the general concept of reproduction.

3.

The number of different configurations that exist, connected by mutational pathways, that are capable of reproducing their specific form (i.e. the distinction between limited hereditary reproducers and indefinite hereditary reproducers). From the point of view of an individual reproducer, this can be expressed in terms of the proportion of all possible mutations it may experience that will result in the production of distinct, yet viable, reproducers.

There are a number of points to note about these distinctions. First it should be said that (3), in contrast to (1) and (2), does not properly relate to individual reproducers per se, but rather to lineages of reproducers. It is therefore not relevant when considering self-reproduction in and of itself, but is an important factor when considering the evolutionary potential of a class of reproducers.

Secondly, with regard to distinction (2) in the context of material as opposed to logical systems, I do not consider the fact that objects in material systems need to collect raw materials to be relevant. As long as the surrounding S ordinarily contains sufficient raw materials for a reproducing object A to build a copy of itself, and that the configuration d of A, and the surrounding S between them effect the collection of these materials to build the copy without further assistance, then our definition of self-reproduction given in Section 7.2.1 is still satisfied.

The distinction between auto- and assisted-reproduction is a dichotomy, but the other two distinctions each define a spectrum of possibilities. The distinctions are generally independent of each other, although the more explicitly encoded the reproduction algorithm is, the less likely, in general, it is to be an indefinite hereditary reproducer (because of the increased chance of mutations disrupting the copying process; see Section 7.2.3).

Figure 7.1 shows how some of the reproducers that have been discussed so far can be categorised according to each of these three distinctions. The diagram is not supposed to be quantitatively accurate (not least because the limited-indefinite heredity axis is in fact infinitely long, and also because I have not offered any way of quantifying these factors), but I have tried at least to highlight the general relationships between different types of reproducers according to each of the three distinctions.

  

Figure 7.1: Categorisation of Reproducers.

There are a number of points about this diagram that require further explanation:

• Tierran organisms and von Neumann's self-reproducing automata are placed midway along the limited-indefinite hereditary scale because, although both representations are capable of supporting universal computation in principle, only mutations which retain the ability to reproduce will be viable. In particular, in von Neumann's architecture (described in Section 3.2.1), a mutation which affects a section of the tape which encodes the constructing automaton A, the copying automaton B, or the control automaton C, will generally disrupt the ability of the combined automaton to produce viable offspring. Likewise, in Tierra, a mutation which affects a section of the program which encodes the self-reproduction algorithm will generally disrupt the ability of the program to reproduce. We will return to these issues in Section 7.2.3.
• Trivial cellular automata self-reproducers (e.g. where the state of a single cell is reproduced in neighbouring cells purely due to the CA's transition rules) are, in general, limited hereditary reproducers, because even though a single state may be able to reproduce, a compound set of states will usually not be able to reproduce as a whole. Notice that in much of the recent artificial life work with self-reproduction (e.g. [Langton 84] and other studies mention in Section 3.2.1), the distinction between trivial and non-trivial self-reproduction is perceived to be a distinction on the implicit-explicit axis. However, from an evolutionary point of view, the limited-indefinite heredity axis is clearly the most relevant. Indeed, this is exactly what von Neumann himself says:

  ``One of the difficulties in defining what one means by self-reproduction is that certain organizations, such as growing crystals, are self-reproductive by any naive definition of self-reproduction, yet nobody is willing to award them the distinction of being self-reproductive. A way around this difficulty is to say that self-reproduction includes the ability to undergo inheritable mutations as well as the ability to make another organism like the original'' [von Neumann 49] (p.489).

  Barry McMullin has presented an enlightening discussion on the history of the confusion over von Neumann's work, which he refers to as the `von Neumann Myth' (see, for example, Section 4.2.7 of [McMullin 92a]). One result of this confusion has been that the majority of subsequent research concerning this issue of trivial self-reproduction has concentrated on the implicit-explicit distinction, rather than the limited-indefinite heredity distinction.<sup>7.8</sup>
• DNA reproduction is assisted, because it can only do so with the aid of a host of enzymes to control the unwinding of the double helical structure, the polymerisation of the individual bases of the new molecule, etc. (see Section 7.2.3). At the same time, DNA is, in the presence of suitable enzymes, capable of indefinite heredity assisted-reproduction; the enzymes are able to copy any DNA double helix, no matter what sequence of bases it comprises. Within this context, the copying process is implicitly encoded in the DNA's environment (in the enzymes which support the reproduction process, and in the physical laws governing the inherent bonding affinities of the bases) rather than being explicitly encoded upon individual strands on DNA. In contrast, a cell as a whole can be considered an auto-reproducer, as it can completely direct its own reproduction (in the presence of sufficient energy and raw materials from the environment), but its hereditary potential is slightly more restricted than DNA assisted-reproduction, because some mutations may disrupt the ability of the cell to reproduce. Similarly, each of Barricelli's symbioorganisms (described in Section 3.2.2) can be considered, collectively, as an auto-reproducer, although individual digits within the symbioorganism are assisted-reproducers. The same analysis can be applied to collectively-autocatalytic reaction networks (e.g. [Kauffman 93]).
• Most importantly, I have placed the hypothetical `proto-DNA' (i.e. a desirable seed for open-ended evolution) in the auto-implicit-indefinite hereditary corner of the space. The seed should be auto-reproducing (i.e. not rely upon auxiliary machinery) if it is to have a reasonable chance of spontaneously emerging, and it should be an indefinite hereditary reproducer to support an on-going, open-ended evolutionary process. The requirement that it be an indefinite hereditary reproducer is most easily fulfilled if it reproduces implicitly. I will talk about this in more detail in the next section.