A Model for Generating Aspects of Zebra and Other Mammalian Coat Patterns

Author(s)Jonathan B. L. Bard
Year Published1981
JournalJournal of Theoretical Biology
Page Numbers363-385
Size4.47 MB

A model is put forward which is capable of generating chemical maps whose concentration contours are similar to the patterns seen on the flanks of zebras, cats and other mammals. The model derives from the reaction diffusion kinetics invented by Turing (1952) and it is assumed that the necessary molecular apparatus is present in each cell of a two-dimensional array and that the cells are in diffusion contact. The model was expressed in differential equation form and solved digitally under a range of different initial, boundary and other conditions. The main forms of pattern that the model generated were spots of variable complexity, rings, and both vertical and horizontal stripes. If morphogen concentration levels are assumed to act as melanin-production switches, then a common basic mechanism is capable of generating a variety of skin patterns. Simple spots such as those found in the fallow deer or the serval, F. serval, are generated if the kinetics are initiated simultaneously in each cell and interpretation depends only on the presence or absence of morphogen, which is assumed for the deer to be an activator and for the cat a suppressor of pigment formation. The reticulated pattern of the giraffe is generated if there is a single high-value threshold. Complex spots typical of the leopards can be produced if there are different concentration thresholds for different colours. Rings of pattern typical of those found on cat tails are generated if the cellular array is a very narrow cylinder. Horizontal stripes are generated if the kinetics in each cell are initiated by a diffusion gradient whose source is the dorsal line of cells and these stripes may break up into spots to give a pattern very similar to that of, for example, the fishing cat, F. viverina. The vertical stripes of the caffre cat, F. cafra, or the zebras are formed if the kinetics are initiated by a vertically-moving constant-velocity wave which also allows morphogen diffusion between previously uncoupled cells. Thus far, the mechanism has generated neither the triradii that are commonly found on forelimbs nor the rings often observed on mammalian limbs. It does however incorporate the randomness that characterizes skin pattern, its operation is of the scale required in embryogenesis,it can be made stable to growth and it can explain certain degenerate patterns. Analysis of a spotted zebra in the light of the model provides evidence that zebra stripes arise from the inhibition rather than the stimulation of melanin; their pattern is thus of white stripes on a black background

Keywords: coat patterns, mammals, pigment formation, kinetics
Author: Jonathan B. L. Bard
Journal: Journal of Theoretical Biology

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