New sublineages of SARS-CoV-2 variants-of-concern (VOCs) continuously emerge with mutations in the spike glycoprotein. In most cases, the sublineage-defining mutations vary between the VOCs. It is unclear whether these differences reflect lineage-specific likelihoods for mutations at each spike position or the stochastic nature of their appearance. Here we show that SARS-CoV-2 lineages have distinct evolutionary spaces (a probabilistic definition of the sequence states that can be occupied by expanding virus subpopulations). This space can be accurately inferred from the patterns of amino acid variability at the whole-protein level. Robust networks of co-variable sites identify the highest-likelihood mutations in new VOC sublineages and predict remarkably well the emergence of subvariants with resistance mutations to COVID-19 therapeutics. Our studies reveal the contribution of low frequency variant patterns at heterologous sites across the protein to accurate prediction of the changes at each position of interest.We describe a systematic approach to identify "clues" that can predict the mutational profiles of SARS-CoV-2 subvariants at early stages after emergence of their parental lineages. We found that the likelihood for mutations at each position of spike is lineage-specific, and is estimated well by the mutational patterns at all positions of the protein. As examples, we apply the model to forecast emergence of resistance to the antibody therapeutics Bebtelovimab and Cilgavimab, which appeared in sublineages of VOCs BA.5 and BA.4, respectively. Emergence of these subvariants required changes in treatment protocols of COVID-19 patients. In both cases, the escape mutations were predicted well by the mutational profiles at all positions of spike at early time points after emergence of the parental VOCs. Accurate estimations of the imminent changes in SARS-CoV-2 lineages can contribute to design and selection of therapeutics that maintain their efficacy against future forms of this virus.