Snakes (order: squamata)—reptiles and amphibians in general, in fact—are numerous and highly diverse in their morphology and physiology. Snakes and lizards exhibit a particularly rich variety of patterns many of which are specific to snakes. The fascinating, and visually beautiful, book by Greene (2000) is a good place to start. He discusses their evolution, diversity, conservation, biology, venoms, social behaviour and so on. Another very good book, by Klauber (1998), is more specific and is essentially an encyclopedia on rattlesnakes.
Even within the same species there is often extreme pattern polymorphism. The common California king snake Lampropeltis getulus californiae is a very good example (Zweifel 1981). Pattern anomalies often occur even on an individual snake as illustrated in Figures 4.22(e) and (f). A browse through any field guide shows not only straightforward pattern elements such as lateral and longitudinal stripes and simple spots but
also a wide range of patterns based on various complex pattern elements which are not found on other animals. Figure 4.22 shows a few snake patterns, both regular and irregular. We saw in the case of butterfly wing patterns discussed in Chapter 3 that the seemingly complex patterns can be generated by a relatively small number of pattern elements. On the other hand, many of the common snake patterns do not seem to fall into any of the usual classes of patterns which can be generated by the usual reaction diffusion models unless they are modified by different boundary conditions, growing or changing domains, spatially varying parameters and so on. In the case of spatially varying parameters it is difficult to relate the results from these models to the biology.
The skin of reptiles is the largest organ in their bodies and poses many interesting developmental problems (see, for example, the review by Maderson 1985). The skin essentially consists of an external epidermis with an underlying dermis. Although we do not know the pattern formation mechanisms we do know that the pattern is fixed in the dermis. The basic skin pigment pattern remains the same after the periodic replacement of the epidermis—the well-known skin shedding exhibited by snakes and lizards. Pigment cell precursors, called chromatoblasts, migrate from the neural crest during development and more or less distribute themselves uniformly in the dermal skin. As with animal coat markings, whether or not the skin develops a pigmented patch depends on whether presumptive pigment cells produce pigment or remain quiescent. Interactions between these precursor cells and possibly directed movement may result in pigmented and unpigmented cells gathering in different regions to produce stripes or spots (Bag-nara and Hadley 1973) as we supposed in the above discussion on alligator stripes. It is not known when chromatoblasts become committed to producing pigment. From evidence from the studies on alligator development cells may be able to produce pigment long before it is actually seen. Cells which are committed to pigmentation can also divide for some time.
Experimental studies of pigment development and the migration of pigment cell precursors have been largely confined to amphibians, mammals and birds although there is a large body of work on the crocodilia as we described above. However, little has been done specifically on skin patterns on reptiles except for the alligator work described earlier. An underlying assumption there and here is that the basic processes of migration, division and differentiation will be the same in snakes and other reptiles as in other animals. Relatively little research has been done on snake embryology (a partial list is given by Hubert 1985; see also the rest of the edited volume of this series on reptilia in which this paper appears), ecology and evolutionary biology (the above-mentioned book by Greene (2000) is the most definitive). As we have noted, of course, extensive embryological studies have been carried out on alligators (Ferguson 1985, Deeming and Ferguson 1989a; see also earlier references in these papers).
Hubert and Dufaure (1968) mapped the development of the asp viper (Vipera as-pis). Pigmentation was first observed on the scales of the body, when the embryo was about 106 mm long, and extended to the head as development proceeded. The pattern is almost certainly laid down earlier in development than when it first becomes visible as was the case with the alligator. Zehr's (1962) observations of the development of the common garter snake (Thamnophis sirtalis sirtalis) suggest a similar developmental process. He noted that when the pigmentation pattern first appears it is not well formed but becomes more defined as development proceeds. (A similar progressive development of final pattern occurs on many butterfly wing patterns.) Treadwell (1962) noted that in embryos of the bullsnake (Pituophis melanoleucus sayi) three rows of spots appear on the sides of the embryo at 29 days and blotches appear on the dorsal midline at 31 days. The timing of developmental events in snakes should be regarded with caution since the rate of development is significantly affected by the temperature of incubation of the eggs or the body temperature of the mother in live-bearing species. In the case of the asp viper, for example, gestation periods from 90 to 110 days have been observed. In the case of the alligator we were able to get an estimate of when in development the stripe pattern was laid down; it was well before the pattern was visible. The cell-chemotaxis-diffusion mechanism considered there is the same as the one we use here. Recall that histological sections of the skin of the alligator embryo showed that there were melanocytes present in the white regions between the dark stripes but these did not appear to produce melanin. We suggested that one possible explanation for the lack of melanogenesis by these cells is that a threshold density of melanocytes could well be necessary before melanogenesis can take place. We noted that this could be responsible for the lighter shadow stripes observed on alligator bodies; these shadow stripes lie towards the ventral side of the body and lie between the distinct darker stripes on the dorsal side. Similar interdigitating stripes are found on certain fish patterns, specifically angelfish (Pomacanthus) a problem studied by Aragon et al. (1998), Painter et al. (1999) and Painter (2000). There are thus two potentially important implications relevant to snake integumental patterns which arise from the alligator studies. One is that potentially quite different patterns can be generated on an embryo when significant growth occurs during the patterning process. The other is that presumptive pigment cell patterns may be generated some time before they start to produce pigment and the pattern becomes discernable.
As in the above Sections 4.1-4.4 we are interested here in the patterns which can be formed by the mechanism when the integumental domain is growing during the patterning process. We find that the spatially heterogeneous solutions can be quite different from, and considerably more complex than those obtained by patterning mechanisms in a fixed domain. It is likely that many of the pattern forming mechanisms involved in embryogenesis are operative on a timescale commensurate with embryonic growth. Maini and his coworkers (for example, Aragon et al. 1998, Painter et al. 1999, Crampin et al. 1999) made a particular study of the interplay between growth and pattern formation in the case of reaction diffusion systems.
The surprising novelty and complexity of new patterns which are generated by this basic system as a consequence of domain growth are likely to occur with all other pattern forming mechanisms.
At this stage, because of the paucity of morphoglogical data on snake embryology it is not possible to suggest when in development of the snake embryo the mechanism is operative. Murray and Myerscough's (1991) purpose was to suggest how some of the diverse complex skin patterns on snakes could be generated. This is the usual necessary first requirement for any potential mechanism.
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