Estimating Relative Fitness in Viral Competition Experiments

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Abstract
The relative fitness of viral variants has previously been defined as the slope of the logarithmic ratio of the genotype or phenotype frequencies in time plots of pairwise competition experiments. Developing mathematical models for such experiments by employing the conventional coefficient of selection s, we demonstrate that this logarithmic ratio gives the fitness difference, rather than the relative fitness. This fitness difference remains proportional to the actual replication rate realized in the particular experimental setup and hence cannot be extrapolated to other situations. Conversely, the conventional relative fitness (1 + s) should be more generic. We develop an approach to compute the generic relative fitness in conventional competition experiments. This involves an estimation of the total viral replication during the experiment and requires an estimate of the average lifetime of productively infected cells. The novel approach is illustrated by estimating the relative fitness, i.e., the relative replication rate, of a set of zidovudine-resistant human immunodeficiency virus type 1 variants. A tool for calculating the relative fitness from observed changes in viral load and genotype (or phenotype) frequencies is publically available on the website athttp://www-binf.bio.uu.nl/∼rdb/fitness.html.