Error Thresholds on Correlated Fitness Landscapes

Abstract

The evolution of molecular quasispecies on two different complex fitness landscapes, the Sherrington Kirkpatrick spin glass and the Graph Bipartitioning landscape, is investigated in dependence on replication fidelity and population size. Three different regimes of replication fidelity are detected. At high copying fidelity one obtains a population with high mean fitness localized around a time-independent consensus sequence. For large mutation frequencies the population is spread over the entire sequence space and the average fitness vanishes. In the intermediate regime the population is centered around a consensus sequence which moves in sequence space. Although the genetic information is lost over time, the population maintains an average fitness significantly above zero. A theoretical approximation is derived for the error threshold as a function of the sequence length.