Waddington’s epigenetic landscape is an intuitive metaphor for the developmental and evolutionary potential of biological regulatory processes. It emphasises time-dependence and transient behaviour. Nowadays, we can derive this landscape by modelling a specific regulatory network as a dynamical system and calculating its so-called potential surface. In this sense, potential surfaces are the mathematical equivalent of the Waddingtonian landscape metaphor. In order to fully capture the time-dependent (non-autonomous) transient behaviour of biological processes, we must be able to characterise potential landscapes and how they change over time. In this talk, I will present a methodological framework that I developed as part of my PhD project which allows us to classify different transient behaviours in non-autonomous systems. I will then briefly show how applying this framework to the gap gene network in flies is helping us understand the evolution of the different modes of segmentation in arthropods. I will use this work to argue that dynamical systems concepts are especially well-suited for the study of EvoDevo, and to try to illustrate the need for a primer bringing these two disciplines together.
Berta Verd holds a Bachelor´s degree in Mathematics from Polytechnic University of Catalonia (UPC), Barcelona and Master´s degrees from Kings College as well as Imperial College, London. She worked on her PhD thesis at the Centre for Genomic Regulation at the Pompeu Fabra University, Barcelona and at the Wissenschaftskolleg zu Berlin. She has recently completed her PhD and is now a Postdoctoral Fellow at the KLI.