Abstract
Viruses spread to give rise to epidemics and pandemics, and some key parameters that include virus and host population numbers determine virus persistence or extinction in nature. Viruses evolve at different rates of evolution depending on the polymerase copying fidelity during genome replication. Calculated rates of evolution in nature vary depending on the time interval between virus isolations. In particular, intra-host evolution is generally more rapid that inter-host evolution and several possible mechanisms for this difference are considered. The mechanisms by which the error-prone viruses evolve render very unlikely the operation of a molecular clock (constant rate of incorporation of mutations in the evolving genomes). Several computational methods are reviewed that permit the alignment of viral sequences and the establishment of phylogenetic relationships among viruses. The evolution of virus in the form of dynamic mutant clouds in each infected individual, together with multiple environmental influences, render the emergence and reemergence of viral pathogens an unpredictable event, another example of biological complexity.