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Waddington's Paradigm for an Evolutionary Process

A characterisation of a process which might be capable of supporting open-ended evolution was proposed by C.H. Waddington 30 years ago [Waddington 69]. Waddington goes as far as to call this characterisation a new paradigm under which biological evolution should be studied. This paradigm is of particular interest because it provides a general characterisation of the individuals involved, of how they interact, and of the kind of environment in which they reside. To my knowledge, little work has been devoted to exploring Waddington's proposal, probably because of the difficulties in capturing it fully with an analytical model (the traditional approach of theoretical biology). However, it is formulated in a way which makes it particularly amenable to synthetic (artificial life) modelling, and is therefore an ideal starting place for developing a better theoretical understanding of open-ended evolution within an artificial life framework.

Waddington describes a replicator as ``a material structure P with a characteristic Q such that the presence of P with Q produces Q in a range of materials Pi under circumstances Ej'' (ibid. p.115).7.23 The overall scenario is summarised as follows:

``The complete paradigm must therefore include the following items: A genetic system whose items (Qs) are not mere information, but are algorithms or programs which produce phenotypes (Q*s). There must be a mechanism for producing an indefinite variety of new Q'*s, some of which must act in a radical way which can be described as `rewriting the program'. There must also be an indefinite number of environments, and this is assured by the fact that the evolving phenotypes are components of environments for their own or other species. Further, some at least of the species in the evolving biosystem must have means of dispersal, passive or active, which will bring them into contact with the new environments (under these circumstances, other species may have the new environments brought to them). These environments will not only exert selective pressure on the phenotypes, but will also act as items in programs, modifying the epigenetic processes with which the Qs become worked out into [Q*s].'' [Waddington 69] (p.120).7.24

This general characterisation raises a number of important issues. First of all, the requirement that Qs act not only as information but also as algorithms--that they must act as operators as well as operands--locates the relationship between genotype and phenotype at the very heart of the paradigm. (The same requirement was suggested for proto-DNA, in Section 7.2.3.)

This insistence that the replicator be treated as an operator as well as an operand is reminiscent of Langton's suggestion that this is the crucial distinction between trivial and non-trivial reproduction (Section 7.2.2). However, the difference is that Waddington's insistence arises through consideration of how to achieve an open-ended evolutionary process. Moreover, Waddington does not claim that this is the only important factor in this respect. In particular, he points out that the open-ended nature of his model relies on the fulfillment of two conditions: (1) that Ej is an infinite-numbered set; and (2) that there are sufficient Qs to provide Q*s suitable for an infinite sub-set of Ejs.

The first condition is satisfied by the fact that Q*s are components of Ejs. A vital direction for future research is the investigation of the different sorts of ways in which Q*s could be components of Ej s, and the evolutionary consequences of such choices.

Of the other condition, Waddington says that ``the second requirement, that the available genotypes must be capable of producing phenotypes which can exploit the new environments, requires some special provision of a means of creating genetic variation ... It is important to emphasize that the new genetic variation must not only be novel, but must include variations which make possible the exploration of environments which the population previously did not utilize ... It is not sufficient to produce new mutations which merely insert new parameters into existing [programs]; they must actually be able to rewrite the [program]'' (ibid. pp.116-118). Another important direction for future research is to explore how this second condition can be satisfied. Providing the Qs with access to sufficient processes to ensure (something close to) universal construction will undoubtedly be part of the solution. This does not necessarily mean that each Q* has to be a universal constructor, but they should at least have access to a basic set of operations to give the set of all Qs the ability to construct a sufficient set of Q*s. This task may be related to the ability to perform universal computation, which depends on the combination and conditional iteration of a simple set of operations (e.g. [Gandy 88]), although the spatial aspect of construction is an extra complication.

It is worth mentioning at this point that some of the artificial evolutionary systems described in Chapter 3, such as Barricelli's later studies with evolving game strategies (e.g. [Barricelli 63]), Conrad and Pattee's model [Conrad & Pattee 70], and Holland's α-Universes [Holland 76]}, do have the notion of emergent operators (phenotypes). However, these phenotypes generally have a limited range of action, thereby preventing the systems from engaging in truly open-ended evolutionary processes.

Returning to Waddington's paradigm, notice that his second condition for open-ended evolution is more subtle than that of universal construction alone. A full analysis of this condition would also involve the question of how phenotypes which are, in some sense, fundamentally new may be introduced into the population to take advantage of new environments. This question is related to Pattee's, of how fundamentally new measuring devices may evolve ([Pattee 88]}: see Section 3.1.2.

Now, the requirement in systems capable of open-ended evolution that individual reproducers have selectively significant phenotypic properties, on top of the ability to reproduce, has already been discussed (see Section 7.2.3). However, it may turn out that the fulfillment of Waddington's second condition would require reproducing structures to possess not just one, but multiple phenotypic properties, possibly of different functional modalities (e.g. catalysis, light sensitivity, motility, etc.). Maynard Smith has observed that "it seems to be a general feature of evolution that new functions are performed by organs which arise, not de novo, but as modifications of pre-existing organs" ([Maynard Smith 86], p.46: see Section 2.3.5). This principle could potentially solve the problem raised by Waddington and Pattee, of how new measuring devices (or fundamentally new phenotypes) arise during evolution: a structure with multiple properties might originally be selected for one of these properties, but it might later turn out (quite accidentally) that some of its other properties also confer (unrelated) adaptive advantages upon the bearer of that structure. In such a scenario, an organism which duplicated this structure might have an adaptive advantage over those possessing a single copy, because each structure could be optimised for a single property. In this way, the organism can acquire fundamentally new phenotypic properties. This perspective may bring some light to bear upon the evolution of fundamental innovations, but it also opens up a whole range of new problems relating to the modelling of multiple, and mostly (initially at least) irrelevant, properties of objects. Such questions require much more investigation, but existing work reported in the biological literature on multifunctional enzymes may be helpful (e.g. [Kacser & Beeby 84]).

I end this section with the observation that Waddington's paradigm for an evolutionary process is very similar to what Bedau has recently referred to as `supple adaptation' ([Bedau 98b]: see Section 2.1.1). Bedau says that ``natural selection produces supple adaptation only when it is continually creative. Adaptation cannot be continually creative without ongoing environmental change. One way to bring about ongoing change is for the evolving system's own evolution to continually reshape the selection criteria ... [which could perhaps be achieved if] each organism's environment consists to a large degree of its interactions with other organisms'' (ibid. p.127).


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Tim Taylor