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Our goal is to automatically identify which species of bird is present in an audio recording using supervised learning. Devising effective algorithms for bird species classification is a preliminary step toward extracting useful ecological data from recordings collected in the field. We propose a probabilistic model for audio features within a short interval of time, then derive its Bayes risk-minimizing classifier, and show that it is closely approximated by a nearest-neighbor classifier using Kullback-Leibler divergence to compare histograms of features. We note that feature histograms can be viewed as points on a statistical manifold, and KL divergence approximates geodesic distances defined by the Fisher information metric on such manifolds. Motivated by this fact, we propose the use of another approximation to the Fisher information metric, namely the Hellinger metric. The proposed classifiers achieve over 90% accuracy on a data set containing six species of bird, and outperform support vector machines.