While monitoring biodiversity through camera traps has become an important endeavor for ecological research, identifying species in the captured image data remains a major bottleneck due to limited labeling resources. Active learning -- a machine learning paradigm that selects the most informative data to label and train a predictive model -- offers a promising solution, but typically focuses on uncertainty in the individual predictions without considering uncertainty across the entire dataset. We introduce a new active learning policy, Vendi information gain (VIG), that selects images based on their impact on dataset-wide prediction uncertainty, capturing both informativeness and diversity. We applied VIG to the Snapshot Serengeti dataset and compared it against common active learning methods. VIG needs only 3% of the available data to reach 75% accuracy, a level that baselines require more than 10% of the data to achieve. With 10% of the data, VIG attains 88% predictive accuracy, 12% higher than the best of the baselines. This improvement in performance is consistent across metrics and batch sizes, and we show that VIG also collects more diverse data in the feature space. VIG has broad applicability beyond ecology, and our results highlight its value for biodiversity monitoring in data-limited environments.