Recent imaging studies of mitochondrial dynamics have implicated a cycle of fusion, fission, and autophagy in the quality control of mitochondrial function by selectively increasing the membrane potential of some mitochondria at the expense of the turnover of others. This complex, dynamical system creates spatially distributed networks that are dependent on active transport along cytoskeletal networks and on protein import leading to biogenesis. To study the relative impacts of local interactions between neighboring mitochondria and their reorganization via transport, we have developed a spatiotemporal mathematical model encompassing all of these processes in which we focus on the dynamics of a health parameter meant to mimic the functional state of mitochondria. In agreement with previous models, we show that both autophagy and the generation of membrane potential asymmetry following a fusion/fission cycle are required for maintaining a healthy mitochondrial population. This health maintenance is affected by mitochondrial density and motility primarily through changes in the frequency of fusion events. Health is optimized when the selectivity thresholds for fusion and fission are matched, providing a mechanistic basis for the observed coupling of the two processes through the protein OPA1. We also demonstrate that the discreteness of the components exchanged during fusion is critical for quality control, and that the effects of limiting total amounts of autophagy and biogenesis have distinct consequences on health and population size, respectively. Taken together, our results show that several general principles emerge from the complexity of the quality control cycle that can be used to focus and interpret future experimental studies, and our modeling framework provides a road-map for deconstructing the functional importance of local interactions in communities of cells as well as organelles.