A mathematical framework for disentangling time-varying selection in HIV-1 evolution

Natural selection often acts on multiple traits simultaneously, with selection pressures that vary across environments and time. One example is provided by HIV-1 infection, as the virus must balance immune escape with maintaining replicative fitness - often through mutations that affect both traits. Temporal genetic data can help us to understand evolution quantitatively, but new methods are needed to extract such complex and time-varying features from data. Here we extend the marginal path likelihood method to disentangle the time-varying effects of escaping CD8⁺ T cell-mediated immunity, which we model as a binary trait, from other contributions to fitness. Our approach yields a screened Poisson-like equation describing the evolutionary dynamics. Applying this validated framework to clinical HIV-1 data reveals that selection for T cell epitope escape declines sharply with falling immune cell counts, alongside a broader trend toward weaker selection late in infection. This framework can be adapted to study time-varying selection on quantitative traits in other evolutionary systems.