During insect development, segments either form sequentially (short germ-band) or simultaneously (long germ-band). In depteran insects (flies, midges, and mosquitoes), where the long germ-band mode of segmentation is used, the gap genes are activated by maternal gradients and cross regulate each other to form the first zygotic regulatory layer of the segmentation gene hierarchy. A precise data-driven mathematical model revealed that two distinct dynamical regimes govern anterior and posterior trunk gap gene patterning in Drosophila melanogaster. Stationary domain boundaries in the anterior rely on multi-stability whilst the observed anterior shifts of posterior gap gene domains can be explained as an emergent property of an underlying regulatory mechanism implementing a damped oscillator. Major features of both regimes are recovered by a three-gene motif embedded in the gap gene regulatory network. Interestingly, this sub-network, known as the AC/DC motif, can also sustain oscillations. Oscillations are not found in the gap gene system, but are characteristic of short germ-band segmentation, suggesting that both modes share more than previously thought. Studying the evolution of gene regulatory networks can help us understand how oscillations arise or cease, and this will shed some light on how long germ-band segmentation could have repeatedly and independently evolved from the ancestral short germ-band mode. In order to address the evolvability of segment determination dynamics I propose the following three-part project. The first step will be to perform a comparative analysis of the dynamics of gap gene pattern formation using data-driven models of gap gene regulatroy network in three species of dipteran flies (Drosophila melanogaster, Megaselia abdita, and Clogmia albipunctata) wher gap gene expression order is conserved but dynamcis differ. Next, I will characterize intermediate gap gene regulatory networks obtained from in silico evolutionary simulations where the gap gene network in the more basal species C. albipunctata has been used as the starting point. These first two parts will help us understand how different expression dynamics arise from different network architectures within the same dynamic mode of segmentation, as well as reveal how these evolutionary changes might be shaped. On a more theoretical level, I plan to explore how the evolutionary trajectories between both dynamic modes of segmentation are constrained in parameter space by considering the AC/DC circuit as a basic dynamical module driving segmentation processes.