Skip to page navigation menu Skip entire header
Brown University
Skip 13 subheader links

Quantitative Comparison of agent-based Zebrafish Models


During their early development, zebrafish (Danio rerio) develop stripes on their skin through complex interactions between different pigment cell types. Zebrafish are a model organism commonly studied in developmental biology, as their skins are translucent, the embryos develop outside of the mother, and their genome has been sequenced. Interactions between pigment cells are now understood to govern zebrafish stripe formation. Alexandria Volkening and our faculty mentor, Björn Sandstede, designed a mathematical model of zebrafish pattern development (the ‘VS’ model) to explain which pigment cell interactions are essential for stripes to form. A second team of researchers at Bath, including Jennifer Owen, recently proposed a different model for zebrafish patterns (the ‘Owen’ model). Our UTRA aimed to compare the two models to each other and to empirical measurements from real zebrafish using quantitative techniques. We thus sought to establish the biological accuracy of each model and identify potential areas of improvement. Both models treat cells as agents and describe their positions as a function of time using stochastic differential equations, supplemented by discrete rules for cell birth, differentiation, death, and shape change. The models also have fundamental differences in their design: the Owen model structures its cells on a lattice and simulates time continuously using a Gillespie algorithm. In contrast, the VS model is off-lattice and relies on discrete time steps, updating the simulation once per day. Björn Sandstede’s lab recently developed the first methodology to quantitatively compare the outputs of agent-based models. This new technique relies on topological data analysis to assess each simulation across a range of measures, including cell densities, stripe width, straightness, and number of breaks. Our UTRA project entailed optimizing this technique for both models. We then used it to obtain a statistical assessment of 1000 simulations of each model. This work constituted the first quantitative comparison of agent-based models. Both models properly simulate the development of two stripes and three interstripes, as in real zebrafish. However, the two models differ significantly in their average number of stripe and interstripe breaks, stripe straightness, cell-to-cell spacing, and cell densities. To determine the biological accuracy of the models, we compared their simulated cell densities and cell-to-cell spacings to published empirical measurements from real zebrafish. The VS model was thus found to simulate zebrafish pattern development more accurately than the Owen model under the published wild-type parameter settings.

Access Conditions

Use and Reproduction
Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)
In Copyright
Restrictions on Use
All Rights Reserved


Cleveland, Electa, Zhu, Angela, and Sandstede, Björn, "Quantitative Comparison of agent-based Zebrafish Models" (2021). Summer Research Symposium. Brown Digital Repository. Brown University Library.



  • Summer Research Symposium

    Each year, Brown University showcases the research of its undergraduates at the Summer Research Symposium. More than half of the student-researchers are UTRA recipients, while others receive funding from a variety of Brown-administered and national programs and fellowships and go …