Conceptual or explanatory models are a key element in the process of complex system modelling. They not only provide an intuitive way for modellers to comprehend and scope the complex phenomena under investigation through an abstract representation but also pave the way for the later development of detailed and higher-resolution simulation models. An evolutionary echo state network-based method for supporting the development of such models, which can help to expedite the generation of alternative models for explaining the underlying phenomena and potentially reduce the manual effort required, is proposed. It relies on a customised echo state neural network for learning sparse conceptual model representations from the observed data. In this paper, three evolutionary algorithms, a genetic algorithm, differential evolution and particle swarm optimisation are applied to optimize the network design in order to improve model learning. The proposed methodology is tested on four examples of problems that represent complex system models in the economic, ecological and physical domains. The empirical analysis shows that the proposed technique can learn models which are both sparse and effective for generating the output that matches the observed behaviour.