This work presents the design of a directed acyclic graph (DAG) scheme, the nodes of which incorporate hidden Markov models (HMMs) for classifying insect species. Such a DAG scheme is able to limit the problem space, while having the HMMs capture the temporal evolution of Mel-scaled spectrograms extracted out of wingbeat sounds. Interestingly, the proposed approach offers interpretability of the classification process by inspecting the sequence of edges activated in the DAG (path). The dataset encompasses 50 000 wingbeat sounds representing six species, i.e., Ae. aegypti (male and female), Cx. quinquefasciatus (male and female), Cx. stigmatosoma (male and female), Cx. tarsalis (male and female), Musca domestica, and Drosophila simulans, and is publicly available at https://sites.google.com/site/insectclassification/. Thorough species classification experiments showed that the proposed solution outperforms state-of-the-art approaches.