The deployment of acoustic sensor networks in a natural environment contributes to the understanding and the conservation of biodiversity. Yet, the sheer size of audio data which result from these recordings prevents listening them in full. In order to skim through an ecoacoustic corpus, one may typically draw K snippets uniformly at random. In this article, we present an alternative method, based on K-determinantal point processes (K-DPP). This method weights the sampling of K-tuples according to a twofold criterion of relevance and diversity. To study the eco-acoustics of a tropical dry forest in Colombia, we define relevance in terms of time-frequency second derivative (TFSD) and diversity in terms of scattering transform. Hence, we show that K-DPP offers a better tradeoff than K-means clustering. Furthermore, we estimate the species richness of the K selected snippets by means of the BirdNET birdsong classifier, which is based on a deep neural network. We find that, for K > 10, K-DPP and K-means tend to produce a species checklist that is richer than sampling K snippets independently without replacement.