Efficient parameter estimation for spatio-temporal models of pattern formation: case study ofDrosophila melanogaster

We show that parameter estimation for pattern formation models can be efficiently performed using an evolution strategy (ES). As a case study we use a quantitative spatio-temporal model of the regulatory network for early development in Drosophila melanogaster. In order to estimate the parameters, the simulated results are compared to a time series of gene products involved in the network obtained with immunohistochemistry. We demonstrate that a (mu,lambda)-ES can be used to find good quality solutions in the parameter estimation. We also show that an ES with multiple populations is 5-140 times as fast as parallel simulated annealing for this case study, and that combining ES with a local search results in an efficient parameter estimation method.