Butterfly wing patterns: how good a determining mechanism is the simple diffusion of a single morphogen?

The formation of the wing pigmentation patterns of three species of butterflies has been modelled using a mechanism based on a tripod of assumptions. First, that there may be morphogen sources in the foci of eyespots and morphogen sinks at some parts of the wing margin, all other cells being passive. Second, that the morphogen has a finite half life and diffuses simply and freely away from the sources throughout a wing of hexagonally packed cells. Third, that the overt pattern derives from cells interpreting the local morphogen concentration with respect to thresholds which determine scale colours. The final pattern thus follows lines of constant morphogen concentration and may, depending on the distribution of sources, comprise rings, curves or bands. With such a model, we have been able to compute stable patterns having the essential topology of the compound spots of Tenaris domitilla, the large rings of Diaethria marchalii and the pattern of eyespots, rings and asymmetric bands of Ragadia minoa. Quantitative analysis of the pattern-forming process shows that, with a biologically realistic diffusion constant (approximately 5.10(-7) cm2 sec-1) and a morphogen half life less than 6h, the patterns form within approximately 12h over a wing of approximately 1000 cells in length. The limitations of the model are that the exact morphology of the eyespots and bands do not match precisely those of the original wings, that there are edge distortions and that optimal patterns may be critically dependent on the exact positions of sources and sinks. An explanation for part of the discrepancy is that we have assumed an adult wing shape and foci coordinates in modelling a process that took place earlier in development. Nevertheless, the limitations of the model argue against a mechanism based on a single morphogen operating in vivo. However, as the model can generate many features of butterfly wing patterns, it may be considered as a degenerate case of that mechanism.