Training data is an essential input into creating competent artificial intelligence (AI) models. AI models for biology are trained on large volumes of data, including data related to biological sequences, structures, images, and functions. The type of data used to train a model is intimately tied to the capabilities it ultimately possesses--including those of biosecurity concern. For this reason, an international group of more than 100 researchers at the recent 50th anniversary Asilomar Conference endorsed data controls to prevent the use of AI for harmful applications such as bioweapons development. To help design such controls, we introduce a five-tier Biosecurity Data Level (BDL) framework for categorizing pathogen data. Each level contains specific data types, based on their expected ability to contribute to capabilities of concern when used to train AI models. For each BDL tier, we propose technical restrictions appropriate to its level of risk. Finally, we outline a novel governance framework for newly created dual-use pathogen data. In a world with widely accessible computational and coding resources, data controls may be among the most high-leverage interventions available to reduce the proliferation of concerning biological AI capabilities.