Mother cell-specific ageing is a well-known phenomenon in budding yeast Saccharomyces cerevisiae. Asymmetric segregation of damage and its accumulation in the mother cell has been proposed as one important mechanism. There are, however, unicellular organisms such as the fission yeast Schizosaccharomyces pombe, which replicates with almost no asymmetry of segregation of damage and the pathogenic yeast Candida albicans, which falls around the middle of the segregation spectrum far from both complete symmetry and complete asymmetry. The ultimate evolutionary cause that determines the way damage segregates in a given organism is not known. Here we develop a mathematical model to examine the selective forces that drive the evolution of asymmetry and discover the conditions in which symmetry is the optimal strategy. Three main processes are included in the model: protein synthesis (growth), protein damage, and degradation of damage. We consider, for the first time, the costs to the cell that might accompany the evolution of asymmetry and incorporate them into the model along with known trade-offs between reproductive and maintenance investments and their energy requirements. The model provides insight into the relationship between ecology and cellular trade-off physiology in the context of unicellular ageing, and applications of the model may extend to multicellular organisms.