An essential component of most theories of pattern formation in epimorphic systems is that growth and pattern formation are strictly linked. Furthermore it has been assumed that epimorphic systems display size dependence, i.e. the pattern elements are always of a fixed size. These assumptions are challenged in the work described here on amphibian limb regeneration. The sizes of elements regenerating from small and large limbs and from normal and partially denervated limbs have been measured along with a detailed study of their subsequent growth stages. It is shown that the size of elements within one group of animals is remarkably constant even though their final, adult size is very different. But between groups of animals (large versus small or normal versus partially denervated) their sizes vary considerably. Therefore this classical epimorphic system is not size dependent, calling for a revision of current theoretical concepts. The similarities between this type of behaviour and that in morphallactic systems is discussed as well as similarities with growth control in limb development.

During the many years that the science of experimental embryology has been in existence, the concepts derived from this line of enquiry have been categorized and defined in many different ways by different authors. None more so than the phenomenon of regeneration which was variously described by Roux, Barfuth, Driesch and Hertwig. The definition which seems to have been generally accepted, however, is that of Morgan (1901) who used the term regeneration to mean ‘not only the replacement of a lost part but also the development of a new, whole organism or even part of an organism, from a piece of an adult, or of an embryo, or of an egg’. He further divided the phenomenon of regeneration into two modes - epimorphosis, ‘in which proliferation of material preceeds the development of the new part’ and morphallaxis, ‘in which a part is transformed directly into a new organism without proliferation at the cut surfaces’. Morgan also added that ‘these two processes are not sharply separated and may even appear combined in the same form’.

In the years since Morgan published these definitions, but particularly since the advent of the concept of positional information (Wolpert, 1969) and the subsequent proliferation of theories of pattern formation, these terms have assumed additional meanings. Morphallactic systems of regeneration such as the early embryos of many vertebrate and invertebrate species (e.g. Cooke, 1979), Hydra (Wolpert, Hornbruch & Clarke, 1974) and Dictyostelium (Stenhouse & Williams, 1977) are now characterized as systems which show size independence of pattern. This means that the amount of tissue within which the pattern can be formed is variable. Since there is no cell proliferation during regeneration after removal of tissue one can therefore produce embryos, Hydras or Dictyostelium slugs of varying sizes depending on the amount of tissue remaining.

Conversely, epimorphic systems of regeneration such as insect and amphibian limbs, are now characterized as systems which show size dependence of pattern. This means that irrespective of how much tissue is removed, the regenerated elements will always be of the same size. This situation has arisen because most theories of pattern formation in epimorphic systems (e.g. Summerbell, Lewis & Wolpert, 1973; French, Bryant & Bryant, 1976) have assumed that the same cell interactions control both the growth and spatial pattern of differentiation within the tissue (i.e. cell division is stimulated by removal of tissue and ceases when that pattern is restored. When a greater amount of tissue is removed a correspondingly greater amount of cell division is stimulated).

In amphibian limb regeneration, the system on which the work described below was performed, just such a size dependent theory was proposed by Faber (1971, 1976). He assumed that within the limb field, positional information is in the form of a linear gradient of constant slope, a common concept in epimorphic systems which has its origin in Wolpert’s (1969) notion of the relation between positional information and growth control. Thus regeneration blastemas from distal levels are smaller than those from proximal levels because the latter contains more pattern elements. Furthermore, this theory holds that by making distal blastemas bigger, they would produce more pattern elements than normal and, conversely, by making proximal blastemas smaller, they would produce less elements than normal.

No critical test of these specific assumptions or even of the general assumption, that epimorphic systems are size dependent has ever been performed. I report here two such tests on the regenerating amphibian limb. The first concerns blastemas on small and large animals to ask the question - do smaller animals produce smaller blastemas? The second involves reducing the size of blastemas growing on limbs by partial denervation to ask the question - do blastemas experimentally made smaller produce fewer elements than normal ? The results reveal that in each case blastemas produce the same number of pattern elements, but the size of the elements vary according to the size of the blastema. This is typical size independent behaviour, occurring in an epimorphic system and it thus calls for a revision of our current theories of pattern formation.

The first series of experiments were performed on Pleurodeles waltl and the second on Ambystoma mexicanum.

Blastemas on small and large animals

For this series a total of 56 young Pleurodeles were used with an average snout to tail length of 36 mm. This group of animals was selected on the basis of their similarity in size which varied from 32to40 mm. After anaesthetizing in 0·1% MS222theirforelimbswereamputated through the mid-humerus and the amputated portion of the limbs fixed in neutral formalin. When the regenerates reached the following stages the limbs were reamputated and fixed in neutral formalin - late cone (on day 13), palette (days 13 –15), notch (days 15 –16), 3-digit (days 16 –17) and 4-digit (day 19).

Both the regenerates and amputees were then stained in Alcian green and cleared in methyl salicylate, to reveal cartilage elements. Alcian green was chosen for staining (as used routinely by those working on developing chick limbs, for method see Summerbell, 1981) because it stains cartilage at an earlier stage of differentiation than Victoria blue or methylene blue (as used routinely by those working on regenerating amphibian limbs). Once stained, the lengths of the cartilage elements were determined at each stage by drawing them with a camera lucida, measuring with a ruler and converting to microns.

This same experiment was repeated when the larvae had doubled in sizeaverage snout to tail length of 79 mm (84 –72 mm). Regeneration was slower with these bigger animals, taking about 4 weeks to reach the stages of late cone to notch, rather than 2 weeks. The amputees and regenerates were fixed, stained and cartilage elements measured as described above.

Size reduction by partial denervation

Two experiments were performed in this series. In the first, 30 axolotls, 70 –100 mm long had their left forelimbs partially denervated by severing spinal nerve 4 at the brachial plexus. Both forelimbs were then amputated through the mid-humerus, the right limbs serving as controls. Experimental left limbs were continually redenervated every 4 days to prevent regrowth of nerve 4 into the limb. Camera-lucida drawings of the external form of experimental and control limbs were obtained every two days to monitor blastemal growth. Regenerates were harvested at the stages of late cone, palette, notch, 3 digit and 4 digit. They were fixed and serially sectioned at 10μm. The blastemal length, volume and stage reached were determined for each blastema and graphs drawn.

In the second experiment the above regime was repeated exactly on 35 axolotls, 120 –140 mm long. After fixing blastemas at the stages mentioned above, they were stained whole in Alcian green and the sizes of cartilage elements measured as in the first series on Pleurodeles.

Stages in the growth of the blastema

Growth stages from the point of view of the sequential laying down of new elements do not seem to have been studied in detail in the past. Most effort was concentrated on measuring cell densities, mitotic indices etc. on sectioned material or staging by external appearance and it has always been assumed that redifferentiation occurs in a straightforward proximodistal sequence. But this is not the case, as the following observations, which apply to both Ambystoma and Pleurodeles, reveal.

Stage 1 - humerus. The first stainable cartilage element to appear after amputation through the mid-humerus is the distal part of the humerus (Fig. 1 a). Externally, blastemas are at the late bud stage (Tank, Carlson & Connelly, 1976; Stocum, 1979).

Fig. 1

(a) Stage 1 - the humerus (h) has just redifferentiated in a late cone blastema, (b) Stage 2 - now the humerus (h), radius (r) and ulna (u) are present in a palette stage blastema. The radius is larger and redifferentiates before the ulna, (c) Stage 3 - next the anterior carpals (ac) and digits 1 and 2 develop. (d) Stage 3 - slightly later than (c) in which the middle row of carpals has now redifferentiated and digits 1 and 2 are more distinct, (e) Stage 4 - the 3rd digit is just beginning to appear along with the most posterior carpals (pc), (f) Stage 4 - the 3rd digit is now much more distinct and digits 1 and 2 have begun to fragment into the metacarpals and phalanges, (g) Stage 5 - the 4th digit finally appears. All blastemas shown at the same scale. Bar = 500 μm.

Fig. 1

(a) Stage 1 - the humerus (h) has just redifferentiated in a late cone blastema, (b) Stage 2 - now the humerus (h), radius (r) and ulna (u) are present in a palette stage blastema. The radius is larger and redifferentiates before the ulna, (c) Stage 3 - next the anterior carpals (ac) and digits 1 and 2 develop. (d) Stage 3 - slightly later than (c) in which the middle row of carpals has now redifferentiated and digits 1 and 2 are more distinct, (e) Stage 4 - the 3rd digit is just beginning to appear along with the most posterior carpals (pc), (f) Stage 4 - the 3rd digit is now much more distinct and digits 1 and 2 have begun to fragment into the metacarpals and phalanges, (g) Stage 5 - the 4th digit finally appears. All blastemas shown at the same scale. Bar = 500 μm.

Stage 2 a - humerus, radius. The next element(s) to redifferentiate is not as one might expect, radius and ulna together, but only the radius.

Stage 2b- humerus, radius and ulna (Fig. 1 b). Then the ulna redifferentiates and remains smaller and stains less intensely than the radius throughout its early growth. Externally, blastemas have reached the palette or early redifferentiation stage (Stocum, 1979).

Stage 3 - humerus, radius and ulna, anterior wrist, digits 1 and 2 (Fig. 1 c, d). One might expect the wrist to appear next, but this could never be detected without digits 1 and 2 present. In fact the digits always stained more intensely than the wrist suggesting that the digits had redifferentiated before the wrist. This phenomenon can also be seen in fig. 19 of Stocum (1979). Similarly, digit 1 stains more intensely than digit 2 and thus probably differentiated before it although a 1-digit stage was never detected. Externally, the regenerates are now at the notch stage.

Stage 4 - humerus, radius and ulna, wrist, digits 1, 2 and 3. Next the posterior part of the wrist appears along with digit 3 (Fig. 1e,f). By comparing Fig. 1 c, d, e, the anterior to posterior spread of redifferentiation of the wrist can be seen.

Stage 5-humerus, radius and ulna, wrist, digits 1, 2, 3 and 4. Finally, the fourth digit appears (Fig. 1 g). By now the more proximal and anterior elements are well differentiated with individual anterior carpals appearing and digits 1 and 2 beginning to subdivide into metacarpals and phalanges. As reported by Smith (1978) it seems that metacarpals and phalanges appear by subdivision of a long rod of cartilage rather than by sequential addition at the distal end.

In summary, it is clear that there is an anterior to posterior spread of redifferentiation in each segment of the regenerating limb and a proximal to distal spread but the latter seems to ‘skip a beat’ at the wrist.

Size of regenerated elements from small and large animals

At each of the stages described above about ten blastemas were sampled from small and large Pleurodeles. The length of each element was measured from the time of its first appearance and throughout the growth to the 4-digit stage. In Table 1 the size of the elements at first appearance is recorded as well as the size of the elements amputated. In Fig. 2 the growth curves for each element are drawn.

Table 1

Sizes of elements in small and large regenerates and amputated portions of the limbs

Sizes of elements in small and large regenerates and amputated portions of the limbs
Sizes of elements in small and large regenerates and amputated portions of the limbs
Fig. 2

Graphs of the lengths of elements (in microns) at stages 1 –5 (see Fig. 1 and text for stages), x and y axes of each graph are drawn to the same scale. The element to which each graph applies is marked at the top of the graph. Solid lines are the calculated regression lines for elements from large blastemas and dashed lines those from small blastemas.

Fig. 2

Graphs of the lengths of elements (in microns) at stages 1 –5 (see Fig. 1 and text for stages), x and y axes of each graph are drawn to the same scale. The element to which each graph applies is marked at the top of the graph. Solid lines are the calculated regression lines for elements from large blastemas and dashed lines those from small blastemas.

Considering first small blastemas, what is immediately apparent is that, with the exception of the humerus, the size of the elements at first appearance is remarkably similar being 300 –330μm (Table 1). The humerus was amputated mid-way down its length so we are not considering the size of the whole element. The remaining part of the humerus in the stump could have had an effect to cause this discrepancy, a hypothesis which is currently being tested. The growth curves (Fig. 2 - dashed lines) reveal that the humerus and radius and ulna have identical growth rates, the wrist has a slower rate and the digits a faster rate. Thus although the size of the elements was originally identical, due to their own intrinsic growth rates they do not end up being of equal length in the fully grown form (see size of amputees, line 3, Table 1).

In large blastemas, again with the exception of the humerus, the size of the elements at first appearance is similar, being 440 –570 μ m (Table 1). Fig. 2-solid lines reveal differences in the growth rates of individual elements. The humerus and radius and ulna have identical rates, being the fastest, the wrist is slightly slower and the digits slower still. Thus as in small blastemas, each segment has its own intrinsic growth rate and the segments are not the same length in the final form (see line 7, Table 1).

A comparison of these two sets of data immediately reveals that the size of elements at first appearance is smaller in small blastemas than in larger ones. This size difference is maintained throughout subsequent growth of the humerus, radius and ulna and wrist (Fig. 2). In the digits, however, the growth rates for small blastemas is faster than larger ones and this is reflected in the final form since the digits in small animals occupy a larger fraction of the total length of the arm than in large animals (see lines 4, 8, Table 1).

Despite the absolute differences in size of elements between small and large blastemas, the proportion of the total length that each element occupies is virtually identical (lines 2, 6, Table 1). This demonstrates that the mechanism of pattern formation which operates in regeneration seems to divide up the available tissue, whether it be a small amount or a larger amount, into the same proportions. This is typical size-independent behaviour, as described in the Introduction.

Blastemal size in normal and partially denervated limbs

Blastemas on limbs which have had nerve 4 removed grow more slowly than normal controls (Fig. 3). Previous experiments had established that, for the purposes of this experiment, removal of nerve 4 provided the most useful test. Nerve 5 contributes the least number of nerve fibres to the limb, about 10 –20% (Singer, 1946; Karczmar, 1946) and removal of this nerve alone did not have a significant effect on blastemal growth. Nerve 3 provides 30% of the limb innervation and removal of this had an effect, but it was small in magnitude. Nerve 4 provides the greatest contribution (50 –60%) and has the greatest and most consistent effect on blastemal growth.

Fig. 3

Camera-lucida drawings of blastemas from control (upper row) and partially denervated (lower row) limbs. Cross hatching marks the stump, clear areas are the blastemas, (a) Day 12; (b) day 14; (c) day 16; (d) day 19; (e) day 21; (f) day 24 post amputation. Clearly partially denervated blastemas are delayed in their development and they are also smaller at equivalent stages - compare control e with partially denervated f. Bar = 1 mm.

Fig. 3

Camera-lucida drawings of blastemas from control (upper row) and partially denervated (lower row) limbs. Cross hatching marks the stump, clear areas are the blastemas, (a) Day 12; (b) day 14; (c) day 16; (d) day 19; (e) day 21; (f) day 24 post amputation. Clearly partially denervated blastemas are delayed in their development and they are also smaller at equivalent stages - compare control e with partially denervated f. Bar = 1 mm.

Clearly, from external observations, growth is retarded in such partially denervated blastemas (Fig. 3), but when these blastemas get to the same stages have they caught up in size? In the first experiment normal and partially denervated blastemas were sampled and serially sectioned. For each sample, the blastemal length, volume and stage reached was recorded. Figure 4 reveals that partially denervated blastemas are both shorter in length (Fig. 4a) and smaller in volume (Fig. 4b) than controls at equivalent stages. The difference in slope between the normal and partially denervated plots is greater for blastemal volume than for blastemal length. This confirms the observation of Singer & Craven (1948) and Singer & Egloff (1949) that denervation affects blastemal volume to a greater degree than blastemal length.

Fig. 4

Lengths (a) and volumes (b) of blastemas at stages 1 –5 (see Fig. 1 and text for details of stages). Solid lines are the regression lines calculated for normal, control blastemas (crosses) and dashed lines those calculated for partially denervated blastemas (circles).

Fig. 4

Lengths (a) and volumes (b) of blastemas at stages 1 –5 (see Fig. 1 and text for details of stages). Solid lines are the regression lines calculated for normal, control blastemas (crosses) and dashed lines those calculated for partially denervated blastemas (circles).

The second experiment was a repeat of the first except that blastemas were stained whole for cartilage elements rather than serially sectioned. The size of elements at first appearance is recorded in Table 2. The controls revealed that just as in the previous series on Pleurodeles, the humerus is much larger than the other elements, which varied in size between 480 μm and 590 μm. These sizes are very similar to the data for large Pleurodeles (Table 1), although the axolotls used here were nearly twice as large. This suggests that there is a maximum size of element which can be produced in a developing blastema, the size does not linearly increase with size of animal. Similarly the percentage of the total length of the blastema that each element occupies (line 2, Table 2) is virtually identical to the data on Pleurodeles, both large and small (lines 2, 6, Table 1), attesting to the common mode of pattern formation in the two species.

Table 2

Sizes of elements at redijferentiation in normal and partially denervated blastemas

Sizes of elements at redijferentiation in normal and partially denervated blastemas
Sizes of elements at redijferentiation in normal and partially denervated blastemas

Although the total length of partially denervated blastemas was smaller than normal (Fig. 4a) the length of individual elements as they redifferentiated was not uniformly smaller, but more variable. The humerus was 28% smaller, the radius and ulna 19% smaller, the wrist 14% smaller, but the digits were the same size (Table 2, line 4). Reasons for this differential effect are considered in the Discussion. Growth curves revealed that these initial differences in size were maintained throughout subsequent growth, resulting in significant differences in size between normal and partially denervated limbs at the 4-digit stage (Fig. 5).

Fig. 5

Sections of 4-digit-stage blastemas from control (left) and partially denervated (right) limbs. Each is a composite photograph since the plane of section did not pass through all the elements at once. However, both sections are at the same magnification (bar = 500 μm) and it is clear that the partially denervated blastema is considerably smaller both in length and width at the same stage, h = humerus, r = radius, w = ulna, 1, 2, 3, 4 = digits.

Fig. 5

Sections of 4-digit-stage blastemas from control (left) and partially denervated (right) limbs. Each is a composite photograph since the plane of section did not pass through all the elements at once. However, both sections are at the same magnification (bar = 500 μm) and it is clear that the partially denervated blastema is considerably smaller both in length and width at the same stage, h = humerus, r = radius, w = ulna, 1, 2, 3, 4 = digits.

Normal growth of the blastema

It has, in the past, always been tacitly assumed that redifferentiation of cartilage elements within the blastema proceeds in a proximal to distal direction (e.g. Thornton, 1968; Faber, 1971). But there are two complicating factors in this oversimplified supposition.

The first is that not all the segments (humerus, radius and ulna, wrist, digits) form in a strict sequence. Certainly the humerus redifferentiates first followed by the radius and ulna, but then the digits seem to develop before the wrist. The phenomenon has also recently been noted during regeneration of adult Notophthalmus limbs (Neufeld & Settles, 1981; Settles & Neufeld, 1981) and thus seems to be common to regenerating systems. A similar anomaly, but at a different level is observed in chick limb development where the ulna and humerus appear simultaneously (Summerbell, 1976).

The second complicating factor is that imposed upon this sequence there is an anterior to posterior spread of redifferentiation. The radius develops before the ulna, the anterior wrist before the posterior wrist and digits 1 and 2 before 3 and 4. Stocum (1979) also reported this in Ambystoma maculatum regenerates and, again, it seems to be common to regenerating systems. We can also extrapolate this principle to Urodele limb development since the anterior digits develop before the posterior ones in both axolotls (Hinchliffe & Johnson, 1980; Maden, unpublished) and Pleurodeles (Lauthier, 1971).

Interestingly, in Anuran (Taylor & Kollros, 1946,-Rana pipiens; Tarin & Sturdee, 1971 - Xenopus laevis) and chick (Summerbell, 1976) limb development, the transverse redifferentiation sequence is in the opposite direction - posterior develops before anterior. This correlation between the higher growth rate on the posterior side of the chick limb bud (Cooke & Summerbell, 1980) and the existence of the zone of polarizing activity (ZPA) in the same position provides support for the idea that the ZPA controls both growth and pattern in the developing limb. But since Urodele limb buds have a posterior organizer which controls the pattern (Slack, 1976, 1977), yet the redifferentiation sequence and thus presumably the growth rate progresses from anterior to posterior, the same principles cannot apply here. This adds weight to the proposition discussed below that growth and pattern formation are independently controlled and that the characteristics of the growth of a limb bud are not strictly related to the pattern which will appear within it.

Size regulation in normal blastemas

By examining blastemas from small and large Pleurodeles, it was clear that the size of elements when they first appeared was variable. Larger animals (twice the size of smaller ones) regenerated larger elements (1·3 –2 × the size), but in the second series of experiments larger animals still (twice the size again) did not produce correspondingly larger elements. Consequently there seems to be a maximum size of element and perhaps a minimum too. However, within those constraints, element size can vary while maintaining constant propor-tionality. Therefore it is not true that larger blastemas form more elements than smaller ones and vice versa (see Introduction), instead, there is a range of sizes. Pattern formation within the blastema does not thus depend on absolute size relationships, but on an intrinsic level-specific property of the cells which dedifferentiate from the stump, combined with a proportion regulating mechanism.

Within each group of blastemas (either large or small) the size of different elements at first appearance was remarkably constant. In the smaller ones the radius and ulna, wrist and digits were each between 300 and 330 μm in length. Although their initial sizes were identical, further development of each element then continued at their own intrinsic rate to produce a fully grown form in which the elements are grossly unequal in size with respect to each other. Nevertheless the size of any one element in the fully grown population (measured from the amputees) was accurate to ± 5%.

This property of constancy of size proportions in regenerating limbs is identical to that found in developing chick limb buds. In the latter the size of elements at first appearance are all the same, they then progress at their own intrinsically different growth rates (Summerbell, 1976) to produce a limb whose proportions are accurate to ±5% (Summerbell & Wolpert, 1973). This coincidence adds weight to the proposition that development and regeneration are guided by the same mechanisms. These observations are currently being extended to developing amphibian limbs to attempt further generalizations.

Size regulation in partially denervated blastemas

It has been known for many years that partially denervated limbs regenerate slower than normal (Schotté, 1923), the speed of regeneration being dependent on the number of nerve fibres present, and that the final size of the regenerate is smaller than normal (Singer & Egloff, 1949). Similarly, if the limb is totally denervated at later stages of blastemal growth, in the nerve-independent phase, the final product is smaller than normal (Schotté & Butler, 1944; Singer & Craven, 1948). But it has never been questioned whether the individual elements in such denervated regenerates are actually smaller at comparable stages or they simply grow slower to reach the same initial length. The data presented here shows that the former is indeed the case - partial denervation causes a decrease in the size of the elements when they first redifferentiate.

It is thought that the role of the nervous system in limb regeneration is to provide a neurotrophic factor which permits the cells of the blastema to divide (Singer, 1974). That is, the nerves simply provide a mitogen rather than having any instructive role in pattern formation. Clearly, this has been confirmed here - decreasing the growth rate (presumably by elongating the cell cycle time or permitting fewer cells to divide) and thereby generating a blastema of smaller size does not decrease the number of pattern elements formed. Instead each element is reduced in size.

It is interesting that the effect on element size is not uniform, but is greatest in the humerus, decreases in the radius and ulna and wrist, and is négligeable in the digits. The reason for this can only be surmized, but seems most likely due to some aspect of neurotrophic growth control rather than an alteration of pattern formation mechanisms. For example, the regenerates could have been gradually reinnervated and thereby recovered from the decrease in growth rate. Direct reinnervation was foreseen as a possibility and the limbs were redenervated every 4 days to prevent such an occurrence. An indirect reinnervation by collateral sprouting of the remaining spinal nerves 3 and 5 could have taken place over the 3 –4 weeks duration of the experiment. Alternatively, the regenerates could have recovered from the denervation and loss of trophic factor either by starting to synthesize their own trophic factor or by gradually becoming independent of trophic factor. The latter seems to be the most likely case since total denervation at progressively later stages of blastemal development reveals just this phenomenon - a gradual appearance of resistance to the debilitating effects of denervation (Schotté & Butler, 1944). Indeed, total denervation after day 13 of regeneration in adult newts prevents any further growth in volume, but growth in length continues (Singer & Craven, 1948).

Relevance to theories of pattern formation

It is clear from the above results that growth and pattern formation in the regenerating limb are not strictly linked since elements of varying sizes can be produced by disturbing the growth rate. If the two were totally dependent upon each other then such a disturbance should not affect element size, instead it would simply take longer (or shorter) to reach the prescribed size. Thus, size independence has been demonstrated in an epimorphic system, a previously unrecognized behaviour which calls for a re-evaluation of contemporary theories of pattern formation (see Introduction).

What then controls the size of elements in the regeneration blastema? Although distal blastemas are smaller than proximal blastemas (Maden, 1976), the above experiments show it is not tissue mass which controls the size. One idea which would predict variable size elements is if redifferentiation occurred at a fixed absolute time after amputation. Slower growing blastemas would then have less tissue after this fixed time. However, this can be immediately dismissed since slower growing blastemas (after partial denervation or those on older animals) redifferentiate much later than normal (see Results).

Neither can size control be exerted by the ticks of a cell-cycle clock as proposed in the progress zone theory (Summerbell et al. 1973) as this again would predict size-dependent behaviour. Nevertheless, there are many similarities between chick limb-bud growth and that described here. For instance, the size of elements when they first redifferentiate is the same even though the size of elements in the final form is grossly different due to variable intrinsic growth rates. In both systems these growth rates are tightly controlled since the variation in the size of the final form is extremely small ( ± 5%). These coincidences between a regulative system (regeneration) and a mosaic system (chick limb bud) imply a similarity of growth control and pattern formation mechanisms despite their apparent differences in response to experimental manipulation (Maden, 1981).

Not only are the similarities between development and regeneration now apparent but also those between epimorphosis and morphallaxis since both show size-independent behaviour. It seems probable, therefore, that during the evolutionary change from morphallaxis to epimorphosis, the same basic mechanisms of pattern formation were preserved, and growth was just added on top as a complicating factor. Growth did not therefore replace already existing mechanisms of pattern formation. Similarly, the progression during embryonic development from the morphallactic behaviour of the primary field (Cooke, 1979) to the epimorphic behaviour of secondary fields such as the limb is unlikely to involve a sudden and complete change of pattern-forming mechanisms. Rather it is more likely to produce the pattern by the same process, but now in a system which is growing. This is precisely the mode of operation of one theory already proposed for the regenerating limb (Maden, 1977) in which an early phase of morphallactic change of positional value occurs before growth begins. Hopefully this approach can be extended in the future to produce theories of pattern formation which highlight the similarities between and are relevant to development, regeneration, morphallaxis and epimorphosis.

I should like to thank Katriye Mustafa for excellent technical assistance in all aspects of this work.

Cooke
,
J.
(
1979
).
Cell number in relation to primary pattern formation in the embryo of Xenopus laevis
.
J. Embryol. exp. Morph
.
51
,
165
182
.
Cooke
,
J.
&
Summerbell
,
D.
(
1980
).
Cell cycle and experimental pattern duplication in the chick wing during embryonic development
.
Nature
287
,
697
701
.
Faber
,
J.
(
1971
).
Vertebrate limb ontogeny and limb regeneration: morphogenetic parallels
.
Advances in Morphogenesis
9
,
127
147
.
Faber
,
J.
(
1976
).
Positional information in the amphibian limb
.
Acta biotheor
.
25
,
44
65
.
French
,
V.
,
Bryant
,
P. J.
&
Bryant
,
S. V.
(
1976
).
Pattern regulation in epimorphic fields
.
Science
193
,
969
981
.
Hinchliffe
,
J. R.
&
Johnson
,
D. R.
(
1980
).
The Development of the Vertebrate Limb
.
Oxford Univ. Press
.
Karczmar
,
A. G.
(
1946
).
The role of amputation and nerve resection in the regressing limbs of Urodele larvae
.
J. exp. Zool
.
103
,
401
427
.
Lauthier
,
M.
(
1971
).
Étude descriptive d’anomalies spontanées des membres postérieurs chez Pleurodeles waltlii Michah
.
Ann. d’Embryol. Morphog
.
4
,
65
78
.
Maden
,
M.
(
1976
).
Blastemal kinetics and pattern formation during amphibian limb regeneration
.
J. Embryol. exp. Morph
.
36
,
561
574
.
Maden
,
M.
(
1977
).
The regeneration of positional information in the amphibian limb
.
J. theor. Biol
.
69
,
735
753
.
Maden
,
M.
(
1981
).
Experiments on Anuran limb buds and their significance for principles of vertebrate limb development
.
J. Embryol. exp. Morph
.
63
,
243
265
.
Morgan
,
T. H.
(
1901
).
Regeneration
.
MacMillan
.
Neufeld
,
D. A.
&
Settles
,
H. E.
(
1981
).
The pattern of mesenchymal condensations prior to chondrogenesis in regenerating forelimbs of the adult newt, Notophthahnus viridescens
.
Am. Zool. (abstract) (in press)
.
Schotté
,
O. E.
(
1923
).
La suppression partielle de l’innervation et la régénération des pattes chez les Tritons
.
C. R. Seanc. Soc. Phys. Hist. Nat. Genève
40
,
160
164
.
Schotté
,
O. E.
&
Butler
,
E. G.
(
1944
).
Phases in regeneration of the Urodele limb and their dependence upon the nervous system
.
J. exp. Zool
.
97
,
95
121
.
Settles
,
H. E.
&
Neufeld
,
D. A.
(
1981
).
Morphogenesis of cartilaginous skeletal elements in regenerating forelimbs of adult newt, Notophthalmus viridescens
.
Am. Zool. (abstract) (in press)
.
Singer
,
M.
(
1946
).
The influence of number of nerve fibres, including a quantitative study of limb innervation
.
J. exp. Zool
.
101
,
299
337
.
Singer
,
M.
(
1974
).
Neurotrophic control of limb regeneration in the newt
.
Ann. N. Y. Acad. Sci
.
228
,
308
322
.
Singer
,
M.
&
Craven
,
L.
(
1948
).
The growth and morphogenesis of the regenerating forelimb of adult Trituras following denervation at various stages of development
.
J. exp. Zool
.
108
,
279
308
.
Singer
,
M.
&
Egloff
,
F. R. L.
(
1949
).
The effect of limited nerve quantities on regeneration
.
J. exp. Zool
.
III
,
295
314
.
Slack
,
J. M. W.
(
1976
).
Determination of polarity in the amphibian limb
.
Nature
261
,
44
46
.
Slack
,
J. M. W.
(
1977
).
Determination of anteroposterior polarity in the axolotl forelimb by an interaction between limb and flank rudiments
.
J. Embryol. exp. Morph
.
39
,
151
168
.
Smith
,
A. R.
(
1978
).
Digit regeneration in the amphibian - Triturus cristatus
.
J. Embryol. exp. Morph
.
44
,
105
112
.
Stenhouse
,
F. O.
&
Williams
,
K. L.
(
1977
).
Patterning in Dictyostelium discoideunv. the properties of three differentiated cell types (spore, stalk and basal disk) in the fruiting body
.
Devi Biol
.
59
,
140
152
.
Stocum
,
D. L.
(
1979
).
Stages of forelimb regeneration in Ambystoma maculatum
.
J. exp. Zool
.
209
,
395
416
.
Summerbell
,
D.
(
1976
).
A descriptive study of the rate of elongation and differentiation of the skeleton of the developing chick wing
.
J. Embryol. exp. Morph
.
35
,
241
260
.
Summerbell
,
D.
(
1981
).
Evidence for growth control in the chick limb bud
.
J. Embryol. exp. Morph
.
65
(Supplement)
129
150
.
Summerbell
,
D.
&
Wolpert
,
L.
(
1973
).
Precision of development in chick limb morphogenesis
.
Nature
244
,
228
230
.
Summerbell
,
D.
,
Lewis
,
J. H.
&
Wolpert
,
L.
(
1973
).
Positional information in chick limb morphogenesis
.
Nature
244
,
492
496
.
Tank
,
P. W.
,
Carlson
,
B. M.
&
Connelly
,
T. G.
(
1976
).
A staging system for forelimb regeneration in the axolotl, Ambystoma mexicanum
.
J. Morph
.
150
,
117
128
.
Tarin
,
D.
&
Sturdee
,
A. P.
(
1971
).
Early limb development of Xenopus laevis
.
J. Embryol. exp. Morph
.
26
,
169
179
.
Taylor
,
A. C.
&
Kollros
,
J. J.
(
1946
).
Stages in the normal development of Rana pipiens larvae
.
Anat. Rec
.
94
,
7
23
.
Thornton
,
C. S.
(
1968
).
Amphibian limb regeneration
.
Adv. in Morphog
.
7
,
205
249
.
Wolpert
,
L.
(
1969
).
Positional information and the spatial pattern of cellular differentiation
.
J. theor. Biol
.
25
,
1
47
.
Wolpert
,
L.
,
Hornbruch
,
A.
&
Clarke
,
M. R. B.
(
1974
).
Positional information and positional signalling in Hydra
.
Am. Zool
.
14
,
647
663
.