Emergent individuals are often characterized with respect to their viability: their ability to maintain themselves and persist in variable environments. As such individuals interact with an environment, they undergo sequences of structural changes that correspond to their ontogenies. Ultimately, individuals that adapt to their environment, and increase their chances of survival, persist. This article provides an initial step towards a more formal treatment of these concepts. A network of possible ontogenies is uncovered by subjecting a model protocell to sequential perturbations and mapping the resulting structural configurations. The analysis of this network reveals trends in how the protocell can move between configurations, how its morphology changes, and how the role of the environment varies throughout. Viability is defined as expected life span given an initial configuration. This leads to two notions of adaptivity: a local adaptivity that addresses how viability changes in plastic transitions, and a global adaptivity that looks at longer-term tendencies for increased viability. To demonstrate how different protocell-environment pairings produce different patterns of ontogenic change, we generate and analyze a second ontogenic network for the same protocell in a different environment. Finally, the mechanisms of a minimal adaptive transition are analyzed, and it is shown that these rely on distributed spatial processes rather than an explicit regulatory mechanism. The combination of this model and analytical techniques provides a foundation for studying the emergence of viability, ontogeny, and adaptivity in more biologically realistic systems.