Mathematical Analysis of Melanocyte Patterns on Danio rerio

The study of zebrafish skin pattern development could lead to a better understanding of how these patterns are generated and how they evolved. To compare and contrast wild-type (WT) striped and leopard mutant spotted patterns, photographs were taken of the developing fish. Initial observations led to the hypothesis that the black melanocyte spots in leopard mutants were not randomly distributed, but rather were located in "dashed" stripes. To test this, melanocyte-spot-sized transparent grids were overlaid onto photographs and the location of melanocyte clusters was recorded. The grid maps were used to identify whether a black, melanocyte positive, grid area was present adjacent to each melanocyte cluster in each cardinal and intercardinal direction. In addition, Python-based computer programs were used to analyze the photographs at the pixel level. When analyzed using analysis of variance and logistic regression models, the striped and spotted patterns expressed more similarities than expected. In the leopard zebrafish, the spots were organized into dashed stripes that had similar locations to the WT stripes. This research suggests that spotted and striped patterns are related. Further, the leopard spots were farther apart along the dorsal-ventral axis than in the anterior-posterior direction, suggesting that different mechanisms control spacing along these two axes.