Fig. 8.

Variability in pattern formation. Dynamics of our simplified model with certain iridophore pathways removed are consistent with other Danio fish. a Danio albolineatus features a nearly uniform pattern, with a central light stripe near the tailfin. b Our model suggests D. albolineatus patterns differ from zebrafish stripes in a critical loss of long-range promotion of I^d by X^d: in particular, the absence of X^d at long range fails to induce I^l to become dense (in other words, we obtain D. albolineatus patterns when we simplify our loose-to-dense iridophore transition rule from [$\tilde{\mathrm{A}}$&$\left(\tilde{\mathrm{B}}\mid \mid \tilde{\mathrm{C}}\right)$] to $\left[\tilde{\mathrm{A}}\&\tilde{\mathrm{C}}\right]$, see Supplementary Fig. 3a). Note we assume D. albolineatus contains both X^d and X^l; if only one type of xanthophore is present (e.g., refs. ^28,39 suggest that the xanthophores on this fish have some characteristics in common with X^d), we predict D. albolineatus pattern evolution involved additional changes to xanthophore form behavior. d D. margaritatus is characterized by light spots; e our model indicates the I^d on this fish are not sensitive to local support signals from X^d that are crucial in zebrafish (this means we simplify our rule for dense-to-loose transitions from [A||(B&C)] to [A||B]; see Supplementary Fig. 3b). Notably, c, f may suggest why these altered patterns evolved as part of robust Danio species, rather than through fragile mutations: when we further reduce the iridophore pathways in our model by removing M signaling to iridophores (by using mechanism [$\tilde{\mathrm{C}}$] in place of [$\tilde{\mathrm{A}}$&$\tilde{\mathrm{C}}$] or [B] in place of [A||B], respectively), we obtain the same patterns, suggesting that these fish are robust themselves. We do not know of mutant phenotypes lacking cell types for these Danio fish but provide what our model predicts D. albolineatus and D. margaritatus g, h without melanophores or i-k without xanthophores, respectively, would look like as a means of future model testing. See Supplementary Methods for the parameter values altered to create these simulations. Simulation scale bars are 500 μm. Empirical images a, d reproduced from Singh and Nüsslein-Volhard² with permission from Elsevier; Copyright (2015) Elsevier Ltd