Taylor's Power Law rules the dynamics of allele frequencies during viral evolution in response to host changes.

Sudden and gradual changes from permissive to resistant hosts affect viral fitness, virulence and rates of molecular evolution. We analysed the roles of stochasticity and selection in evolving populations of Sindbis virus under different rates of host replacement. First, approximate Markov models within the Wright-Fisher diffusion framework revealed a reduction in effective population size by approximately half under sudden host changes. These scenarios were also associated with fewer weak beneficial mutations. Second, genetic distance between populations at consecutive time points indicated that populations undergoing gradual host changes evolved steadily until the original host disappeared. Distances to the ancestral sequence in these cases exhibited occasional leapfrog phenomena, where the rise of certain haplotypes is not predictable based on their relatedness to previously dominant ones. In contrast, populations exposed to sudden changes exhibited less-stable compositions and diverged from the ancestral sequence at a consistent rate. Third, we observed that the distribution of allele frequencies followed Taylor's Power Law. Both treatments exhibited high levels of allele aggregation and significant fluctuations, with neutral, beneficial and deleterious alleles distinguishable by their behaviour and position on Taylor's plot. Finally, we found evidence that the host replacement regime influences the temporal distribution of mutations across the genome.