A fast solver for modeling the evolution of virus populations

Solving Eigen's quasispecies model for the evolution of virus populations involves the computation of the dominant eigen vector of a matrix whose size N grows exponentially with the chain length of the virus to be modeled. Most biologically interesting chain lengths are so far well beyond the reach of existing algorithms and hardware. We show how to exploit the special properties of the problem under consideration and design a fast and accurate solver which reduces the complexity to Θ(N log2 N). Our solver is even faster than existing approximative strategies and contrary to those it can also be applied to more general formulations of the quasispecies model. Substantial further improvements and high parallelism can be achieved for special fitness landscapes in the evolution model. Beyond theoretical analysis, we evaluate the performance of our new solver experimentally on a GPU with an OpenCL implementation and illustrate that it achieves speedup factors of more than 107 over standard approaches.