This paper studies the interaction between two dynamic domains, (1) an evolutionary biological system (‘the environment’) whose behaviour determines the availability of a resource stock, and (2) an industry where access to the resource stock is determined by the outcome of a patent race. The specific setting of the model is that of managing microbial resistance to antibiotics. Here, resistance develops in response to the use of antibiotics above a threshold level. We show that the optimal policy from society’s point of view is to generate through R&D a diversified portfolio of antibiotics that maintains a steady-state of resistance. In practice, however, the management of the resistance stock is left to an industry operating under a system of intellectual property rights (IPR). There, firms are involved in a sequence of patent races to supply the antibiotic with the best cost-effectiveness ratio. The paper studies the structure of the patent race within the industry against the background of pathogen evolution. We show that a multi-firm industry operating under an IPR-based incentive mechanism is unlikely to generate the socially optimal number of antibiotics because IPR systems (1) create incentives for sequential rather than simultaneous innovation; (2) generate incentives that decline with the number of previous (shelved) discoveries; and (3) generate incentives that respond perversely to increases in biological system velocity. These results highlight the importance of well-designed dynamic incentives for managing resource stock dynamics.