Choice of traits defines the scope for assisted evolution of corals under climate change.

Marine heatwaves, exacerbated by climate change, are causing widespread coral mortality. Novel host-associated assisted evolution interventions, such as selective breeding, are now being considered to enhance coral heatwave tolerance and promote population persistence. Yet the evolutionary constraints associated with targeting different heat tolerance traits and the risks of unintended fitness costs remain uncertain. Here, we quantify key life history traits for Acropora aff. digitifera corals in a pedigree-tracked managed population. We find weak-to-moderate positive genetic correlations among coral's tolerance to a 1-month 32.5°C heatwave and shorter acute exposures-1-2 weeks at 34.5°C and 6 days of 36°C daily pulses-suggesting a partially shared genetic architecture. However, photo-symbiont efficiency loss under a rapid heat shock assay (38.5°C) was genetically uncorrelated with bleaching and mortality-based heatwave tolerance, indicating that such widely used assays may not reliably identify tolerant coral genotypes for breeding and conservation. Encouragingly, we detected no genetically based trade-offs between heat tolerance and other fitness traits-reproduction, growth, tissue biomass, and symbiont flexibility-and a weak positive correlation with calcification. Evolutionary simulations show that achieving the tolerance levels required to withstand future heatwaves is theoretically possible but requires extremely strong selection, which introduces additional challenges and risks. Alongside rapid emissions reductions, reef management, and restoration interventions will need to carefully consider trait selection to fully harness the evolutionary potential of corals under climate change.