This study introduces a quantum-inspired spiking neural network (QiSNN) as an integrated connectionist system, in which the features and parameters of an evolving spiking neural network are optimized together with the use of a quantum-inspired evolutionary algorithm. We propose here a novel optimization method that uses different representations to explore the two search spaces: A binary representation for optimizing feature subsets and a continuous representation for evolving appropriate real-valued configurations of the spiking network. The properties and characteristics of the improved framework are studied on two different synthetic benchmark datasets. Results are compared to traditional methods, namely a multi-layer-perceptron and a naïve Bayesian classifier (NBC). A previously used real world ecological dataset on invasive species establishment prediction is revisited and new results are obtained and analyzed by an ecological expert. The proposed method results in a much faster convergence to an optimal solution (or a close to it), in a better accuracy, and in a more informative set of features selected.