Fig. 6.

Fig. 6.

Quantitative study of how stochasticity in cell interactions affects wild-type and mutant zebrafish patterns. For each value of σ∈{0.01,0.05,0.1,0.2,0.3,0.5}, where σ times the default length scale is the SD of the noise that we include in the size of cellular interaction neighborhoods, we analyze 1,000 simulations for wild type and each mutant. (A–H) Summary of the patterns that emerge under stochasticity, as detected using our methods for (A and E) wild type, (B and F) nacre, (C and G) pfeffer, and (D and H) shady. In A–D, we highlight the range of σ values that retain at least 50% characteristic patterns under noise in gray. (We define “characteristic” for wild type as patterns having three unbroken interstripes and two unbroken stripes, and we define characteristic for mutants as patterns with spot size and spot number that fall within the baseline distributions in Fig. 5 A and B.) (I and J) Mean maximum stripe/interstripe width (I) and mean stripe curviness (J) for wild type for different noise strengths. (K and L) Spot spacing variance (K) and spot roundness (L) for mutants under different noise strengths. In I–L, the bars indicate SD and the shaded regions give the characteristic values (the mean ±1 SD) for the associated measurements from our default studies. Also see SI Appendix, Tables S2–S5.