At this point it is interesting to turn from analysis of reduplication in beetles' legs to another body of data in which reduplication commonly occurs and has been referred to Bateson's Rule. 159 These are the data on reduplication in the experimentally transplanted limbs of larval newts.
(1) There are some cases, mostly of heterotopic trans-plants in which the grafted limb bud develops into a simple and apparently equal binary system, in which the two components are in mirror image symmetry. I was shown about three years ago a very striking preparation by Dr. Emerson Hibbard of the California Institute of Technology. In this specimen the limb bud had been rotated through 180°, so that the anterior edge of the bud faced toward the posterior end of the host, and had been implanted in a median dorsal position on the posterior region of the head of the host. This transplant had developed into two remarkably complete legs in mirror image relationship. This binary system was connected to the head of the host only by a slender bridge of tissue.
Such preparations, where the product is binary and the parts equal, certainly look like what would be expected from a simple loss of one dimension of orienting information. (It was Dr. Hibbard's specimen that suggested to me that the hypothesis of lost information might be applicable to the amphibian material.)
(2) However, apart from these instances of equal binary reduplication, the amphibian material does not at all fit with any hypothesis that would explain the reduplication as due to a simple loss of information. Indeed, if Bateson's Rule were restricted to cases where the explanation is formally analogous to that which fits the
158 G. Bateson, "The Role of Somatic Change in Evolution," Evolution, 1962, 17: 529-39.
159 Harrison, op. cit.; also F. H. Swett, "On The Production of Double Limbs in Amphibians,"
Journal of Experimental Zoology, 1926, 44: 419-72.
reduplication in the beetles' legs, then the amphibian cases would probably not fall under this rubric.
The limitations of a hypothesis are, however, as important as its applications, and I shall therefore summarize here the very complex data on orthotopic transplants.
One schematic paradigm will suffice: if the right anterior limb bud is excised, turned through 180° and replaced in the wound, it will grow to be a left limb. But this primary limb may subsequently form secondary limb buds at its base, usually either immediately anterior or posterior to the point of insertion. The secondary will be a mirror image of the primary, and may even later develop a tertiary which will typically be formed outside the secondary, i.e., on that side of the secondary which is farthest from the primary.
The formation of the left primary on the right side of the body is explained160 by assuming that antero-posterior orientation is received by the limb bud earlier than dorso-ventral information, and that, once received, this antero-posterior information is irreversible. It is supposed that the graft is already antero-posteriorly determined at the time of grafting but later receives dorso-ventral information from the tissues with which it is now in contact. The result is a limb whose dorso-ventral orientation is correct for its new setting but whose antero-posterior orientation is reversed. It is tacitly assumed that the proximo-distal orientation of the bud is undisturbed. The result is a limb which is reversed in regard to one of its three sorts of asymmetry. Such a limb must logically be a left.
This explanation I accept and proceed to consider the reduplications.
These differ in four important respects from the reduplications in beetles' legs discussed above:
(a) In the beetles, the reduplication is usually equal. The two halves of the supernumerary doublet are equal in size, and are usually approximately equal in size to the corresponding parts of the primary leg. Such differences as do appear among the three components are such as might expectably result from trophic differences. But in the larval newts, great differences in size occur between the components of the reduplicated system, and it appears that these differences are determined by time. The secondaries are smaller than the primaries because they are produced later and, similarly, the rare tertiaries are later and smaller than the secondaries. This spacing of events in time indicates clearly that the primary limb received all the information necessary to determine its own asymmetry. It received, in-deed, "wrong" information and grew to be a left leg on the right side of the body but it did not suffer from such a deficiency of information as would make it immediately fail to achieve asymmetry. The reduplication cannot simply be ascribed to loss of orienting information in the primary.
(b) The reduplications in beetles' legs may occur at any point along the length of the leg. But those of amphibian larvae usually arise from the region of attachment of the limb to the body. It is not even sure that the secondary always shares tissue with the primary.
(c) In the case of the beetles, the supernumerary doublets form a continuous series, being given off from any portion of the periphery of the primary. In contrast,
the reduplication of limbs in amphibian larvae is localized either anterior or posterior to the primary.
In the beetles it is clear that the two supernumerary components form together a single unit. In many cases there is actual compounding of the two components (as in Figure 1). In no case161 is that component of the doublet which is nearer to the primary compounded with it rather than with the other supernumerary. In the amphibian preparations, on the other hand, it is not clear that secondary and tertiary form a subunit. The relation between tertiary and secondary seems no closer than between secondary and primary. Above all, the relation is asymmetric in the time dimension.
These profound formal differences between the two bodies of data indicate that the explanations for the amphibian data must be of a different order. It would seem that the processes are located not in the shaft of the limb but in its base and the tissues surrounding the base. Tentatively we may guess that the primary in some way proposes the later formation of a secondary by a reversal of gradient information, and that the secondary similarly proposes a reversed tertiary. Models for such systems are available in cybernetic theory in those circuit structures which propose Russellian paradoxes. 162 To attempt to construct any such model at the present time would be premature.
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