Cross-scale dynamics and the evolutionary emergence of infectious diseases

Sebastian J. Schreiber; Ruian Ke; Claude Loverdo; Miran Park; Priyanna Ahsan; James O. Lloyd-Smith

The importance of these frequency dynamics can be visualized via individual-based outbreak simulations, and cobwebbing diagrams summarizing the mean field dynamics. When the mutant reproductive number R m is greater than one but its cross-scale reproductive number α is less than one, mutant virions may be transmitted but the resulting mixed infections are invariably taken over by purely wild-type infections (Fig 3A) . Only pure mutant infections can escape this "relapse" to wild-type, and then only if the mutation rate µ is low enough that new wild-type virions are very slow to appear. When the within-host selective disadvantage is weak and the between-host selective advantage is strong, the cross-scale reproductive number α may be slightly greater than one and the mutant strain can drift to higher frequencies within the infected host population (Fig 3B) . For large within-host selective advantages, the cross-scale reproductive number α is large and the mutant strain can sweep rapidly to fixation in the infected host population ( Fig 3C) . Thus, in addition to revealing a new condition needed for evolutionary emergence, the cross-scale reproductive number α summarizes the conditions under which evolution occurs swiftly or gradually within chains of transmission.