Accumulation of somatic mutations in antibody variable regions is critical for antibody affinity maturation, with HIV-1 broadly neutralizing antibodies (bnAbs) generally requiring years to develop. We recently found that the rate at which mutations accumulate decreases over time, but the mechanism governing this slowing is unclear. In this study, we investigated whether natural selection and/or mutability of the antibody variable region contributed significantly to observed decrease in rate. We used longitudinally sampled sequences of immunoglobulin transcripts of single lineages from each of 3 donors, as determined by next generation sequencing. We estimated the evolutionary rates of the complementarity determining regions (CDRs), which are most significant for functional selection, and found they evolved about 1.5- to 2- fold faster than the framework regions. We also analyzed the presence of AID hotspots and coldspots at different points in lineage development and observed an average decrease in mutability of less than 10 percent over time. Altogether, the correlation between Darwinian selection strength and evolutionary rate trended toward significance, especially for CDRs, but cannot fully explain the observed changes in evolutionary rate. The mutability modulated by AID hotspots and coldspots changes correlated only weakly with evolutionary rates. The combined effects of Darwinian selection and mutability contribute substantially to, but do not fully explain, evolutionary rate change for HIV-1-targeting bnAb lineages.