Patient-derived xenografts (PDXs) are currently promoted as new translational models in precision oncology. PDXs are immunodeficient mice with human tumors that are used as surrogate models to represent specific types of cancer. By accounting for the genetic heterogeneity of cancer tumors, PDXs are hoped to provide more clinically relevant results in preclinical research. Further, in the function of so-called "mouse avatars", PDXs are hoped to allow for patient-specific drug testing in real-time (in parallel to treatment of the corresponding cancer patient). This paper examines the circulation of knowledge and bodily material across the species boundary of human and personalized mouse model, historically as well as in contemporary practices. PDXs raise interesting questions about the relation between animal model and human patient, and about the capacity of hybrid or interspecies models to close existing translational gaps. We highlight that the translational potential of PDXs not only depends on representational matching of model and target, but also on temporal alignment between model development and practical uses. Aside from the importance of ensuring temporal stability of human tumors in a murine body, the mouse avatar concept rests on the possibility of aligning the temporal horizons of the clinic and the lab. We examine strategies to address temporal challenges, including cryopreservation and biobanking, as well as attempts to speed up translation through modification and use of faster developing organisms. We discuss how featured model virtues change with precision oncology, and contend that temporality is a model feature that deserves more philosophical attention.