Estimating relative fitness in viral competition experiments

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. Differences in the in vitro replication rate (or fitness) between viral variants can be estimated experimentally by pairwise competition experiments in tissue culture. The outcome of such an experiment is typically depicted in a logarithmic time plot of the ratio of the genotype or phenotype frequencies (7). On a logarithmic scale the ratio tends to change linearly in time, and the rate of change (i.e., the slope of the line) has previously been defined as the relative fitness (7). According to population genetics theory, the relative fitness (1 + s) of a variant represents its relative contribution to the next generation. The parameter s is defined as the coefficient of selection. The intertwined concepts of relative fitness (1 + s) and selection coefficients are traditionally employed in systems with discrete generations. They are equally valid for populations growing continuously, however, when time is scaled with respect to the generation time (11). Developing conventional population genetics models for pairwise competition experiments, we show that the above-mentioned slope in a logarithmic time plot provides the absolute fitness difference between the two variants rather than the generic relative fitness (1 +s) of one with respect to the other. As the fitness difference remains proportional to the replication rate realized in the particular experimental setup, viral strains having similar selection coefficients s may have large fitness differences. On the other hand, variants differing markedly in the selection coefficients will yield almost horizontal lines in logarithmic time plots when the realized replication rate in the experiment is sufficiently low. This has indeed caused confusion in the literature (see Discussion). Previous work on the fitness of human immunodeficiency virus type 1 (HIV-1) variants has indeed adopted the concept of a selection coefficient s from population genetics (2, 4). It is unfortunate, therefore, that the slope of the logarithmic time plot of the ratio of two variants in competition experiments has also been called a relative fitness. We here demonstrate that this slope gives the (absolute) fitness difference, and we develop a novel approach for estimating the generic relative fitness (1 +s) by competition experiments