The Common Developmental Origin of Eyespots and Parafocal Elements and a New Model Mechanism for Color Pattern Formation

Abstract

The border ocelli and adjacent parafocal elements are among the most diverse and finely detailed features of butterfly wing patterns. The border ocelli can be circular, elliptical, and heart-shaped or can develop as dots, arcs, or short lines. Parafocal elements are typically shaped like smooth arcs but are also often "V," "W," and "M" shaped. The fusion of a border ocellus with its adjacent parafocal element is a common response to temperature shock and treatment with chemicals such as heparin and tungstate ions. Here I develop a new mathematical model for the formation of border ocelli and parafocal elements. The models are a reactiondiffusion model based on the well-established gradient-threshold mechanisms in embryonic development. The model uses a simple biochemical reaction sequence that is initiated at the wing veins and from there spreads across the field in the manner of a grass-fire. Unlike Turing-style models, this model is insensitive to the size of the field. Like real developmental systems, the model does not have a steady state, but the pattern is "read out" at a point in development, in response to an independent developmental signal such as a pulse of ecdysone secretion, which is known to regulate color pattern in butterflies. The grass-fire model reproduces the sequence of Distal-less expression that determines the position of eyespot foci and also shows how a border ocellus and its neighboring parafocal element can arise from such a single focus. The grass-fire model shows that the apparent fusion of ocellus and parafocal element is probably due to a premature termination of the normal process that separates the two and supports the hypothesis that the parafocal element is the distal band of the border symmetry system.

Butterfly eyespot color pattern formation requires physical contact of the pupal wing epithelium with extracellular materials for morphogenic signal propagation

“…TS-type modifications occur due to temperature shock [15] or the injection of chemicals such as tungstate [16], molsin [17], or heparin and other sulfated proteoglycans [23]. The modifications of PFEs should be incorporated in the model of eyespot formation [33][34][35][36]72]. A minor but interesting finding of the present study was that SMBs were also affected in response to eyespot-reducing contact materials, but SMBs did not appear to be dislocated toward the proximal side.…”

Morphological and Spatial Diversity of the Discal Spot on the Hindwings of Nymphalid Butterflies: Revision of the Nymphalid Groundplan

“…Some minor modifications of the nymphalid groundplan have been introduced [ 7 , 8 ] since Nijhout (1991) [ 5 ]. First, the status of the parafocal element (PFE) has been established as a part of the border symmetry system [ 12 , 13 , 14 , 15 , 16 , 17 ]. Second, the proximal parafocal element (pPFE) in addition to the distal parafocal element (dPFE) has been identified [ 7 , 12 ].…”

Synergistic Damage Response of the Double-Focus Eyespot in the Hindwing of the Peacock Pansy Butterfly

“…Among these elements, eyespots that belong to the border symmetry system are probably most conspicuous, at least to human eyes, and developmental mechanisms of eyespots have been studied relatively well. The initial specification of the central location of an eyespot has been successfully described by an RD model based on signals from wing veins in developing wing disk [8], although this model may be too fine-tuned to explain the developmental robustness of actual eyespots [15]. Interestingly, the subsequent determination process of an eyespot after the determination of its central location has been explained by a concentration gradient model, a non-RD model [8,16,17].…”

“…Furthermore, the status of parafocal elements as a part of the border symmetry system [10,11,22,23] has not been explained by the previous models. Nijhout [15] recently proposed the grass fire model, in which parafocal elements can be produced together with eyespots by a simple RD system. It would not be surprising for the entire process of the butterfly eyespot determination to be solely based on RD mechanisms.…”