A comprehensive model for colour pattern formation in butterflies

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Abstract
This paper presents an attempt to construct a single model that can account for pattern formation in a very broad diversity of Lepidoptera. A pattern database is developed for 330 genera and 2208 species in the family Nymphalidae. It is argued that because of the close taxonomic relation between these species, and that all have patterns that are readily derived from the homology system known as the nymphalid ground-plan, the whole diversity of patterns in the database should emerge from a single model mechanism, and that most of this diversity should emerge from simple quantitative variations of the parameters of that model. A formal list of desiderata and constraints on any model for colour pattern formation is developed and used as the basis for the present modelling effort. Based on the assumptions of simple diffusion and threshold mechanisms, a pattern of source--sink distributions is deduced that can generate the diversity of patterns in the database. The adequacy of this source--sink `toolbox' is tested by computer simulation; it is shown that a two-gradient model with a simple additive relation between the two gradients suffices to generate nearly the entire diversity of patterns observed. The requisite positions of the sources and sinks of the toolbox, in turn, emerge readily from Meinhardt's lateral inhibition model for reaction diffusion. Thus a two step model, consisting first of a reaction-diffusion system that sets up a source-sink pattern and is followed by simple diffusion of a morphogen from those sources, appears to be able to generate nearly the entire diversity of colour patterns seen in the Nymphalidae.

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