Planarians grow when fed and shrink when starved, but how they maintain their body shape during these dramatic size changes is unclear. Here, Daniel Lobo and colleagues image planarians during periods of feeding or starvation to follow how their length and width vary over time. They use these data to generate a descriptive model of planarian shape and size dynamics and show that growing planarians are wider than shrinking planarians. To explore the mechanisms underpinning these differences between growth and shrinkage dynamics, they build a mechanistic model incorporating known morphogens that diffuse through the planarian body to influence growth or patterning. In turn, changes to body size and shape affect the diffusion of the morphogens, producing a feedback loop. To optimise the mechanistic model’s parameters, the authors take an evolutionary computational approach, defining the fitness of a given parameter set as the time that the model simulation can continue for before the shape difference between the mechanistic and descriptive models exceeds a certain threshold. The resulting parameter set closely recapitulates planarian growth dynamics and, when apoptosis and morphogen signalling at the body poles is increased, the calibrated model can also recapitulate planarian shrinkage dynamics. Overall, this work offers insight into how the mechanisms that regulate body shape change as planarians grow or shrink.