Evolution of fitness values upon replication of viral populations is strongly influenced by the size of the virus population that participates in the infections. While large population passages often result in fitness gains, repeated plaque-to-plaque transfers result in average fitness losses. Here we develop a numerical model that describes fitness evolution of viral clones subjected to serial bottleneck events. The model predicts a biphasic evolution of fitness values in that a period of exponential decrease is followed by a stationary state in which fitness values display large fluctuations around an average constant value. This biphasic evolution is in agreement with experimental results of serial plaque-to-plaque transfers carried out with foot-and-mouth disease virus (FMDV) in cell culture. The existence of a stationary phase of fitness values has been further documented by serial plaque-to-plaque transfers of FMDV clones that had reached very low relative fitness values. The statistical properties of the stationary state depend on several parameters of the model, such as the probability of advantageous versus deleterious mutations, initial fitness, and the number of replication rounds. In particular, the size of the bottleneck is critical for determining the trend of fitness evolution.The initial steps in virus evolution are generation of diversity (through mutation, recombination, and genome segment reassortment in multipartite genomes), competition among the generated variants, and selection of those mutants showing the largest phenotypic advantage in a given environment (see overviews in references 9, 14, 17, 28, 30, and 40). Because of high mutation rates during viral RNA biosynthesis (2, 18), RNA viruses replicate as complex mutant swarms termed viral quasispecies (14,(21)(22)(23)(24). The degree of adaptation of a viral quasispecies to a given environment is often quantitated by a relative fitness value, which measures the replication capacity of a viral population relative to a reference mutant distinguishable either genotypically or phenotypically (15,26,33,37). The long-term survival probability of a virus should consider parameters other than replication capacity (such as particle stability, transmissibility, etc. [11,12,15]). Despite their limitations, relative fitness values, determined by growth competition experiments between two viral populations in cell culture and in vivo, are providing insights into basic features of quasispecies evolution as well as viral disease progression (5,15,49).Because of the large variations in viral population size during infections in vivo, a focus of interest has been the study of the influence of virus population size on the evolution of fitness values (reviewed in reference 15). Experimental results with several RNA viruses have documented that large population passages often result in fitness gains (7,26,43,45,58) while repeated bottleneck events (serial plaque-to-plaque transfers being an extreme example) lead to average fitness losses (6,19,25,27,59,60),...