| Abstract | Evolution of viral proteins involved in immune escape typically exhibits one of two strikingly different dynamical regimes: either lineage turnover with limited genetic diversity (cactus-like dynamics) or evolutionary branching with increasing genetic diversity (acacia-like dynamics). For example, the evolutionary dynamics of influenza A in humans is cactus-like, while in pigs it is acacia-like. Understanding why viral proteins exhibit cactus-like versus acacia-like dynamics will lead to better disease prediction and control, especially of new pandemic strains. To this end, we propose to distinguish between cactus-like and acacia-like evolution using a dimensionless number. The proposed number is given by the ratio of the time to extinction of the original variant to the time to generation of a second variant by the original variant. We expect this number to be < 1 for cactus-like viruses and >1 for acacia-like viruses and to depend on properties of the host as well as the virus. We present an analytic function, derived using the Moran model, for the numerator, the time to extinction of the original variant. This function depends on the selective advantage of a novel variant and on the population size of infected individuals. We use numerical simulations based on two epidemiological multi-strain models to address the relevance of this function. In spite of the assumptions inherent to the Moran model (namely, a constant selective advantage and a constant population size), the analytic expression matches the simulation results remarkably well. We also present simulations for the denominator of the dimensionless number and end with work in progress towards an analytic expression for this quantity. |
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