Fig. 1: The interplay between evolutionary and epidemiological dynamics.

a Host i contracts a pathogen (orange) with initial fitness φ(i, 0), ψ(i, 0). b Within i the pathogen replicates, undergoing mutation and selection. The potential transitions between strains μ → ν is governed by M_μν. Strains with higher intra-host fitness (φ_μ(i)) replicate at a higher rate. After ρ replication cycles the pathogen population within i takes the form of a multistrain \({{{{{{{{\mathcal{Z}}}}}}}}}_{i}\), in which there is a fraction Z_μ(i) of the strain μ. c Upon transmission i → j, a single (or few) individual pathogens are sampled from \({{{{{{{{\mathcal{Z}}}}}}}}}_{i}\), instigating again, j's intra-host dynamics, this time staring from initial fitness φ(j, 0), ψ(j, 0). d The transition matrix M_μν. Mutations enable transition with probability 0 ≤ p ≤ 1 between adjacent strains. The larger is p, the less stable is the pathogen. e The fitness distribution f_i(φ, ψ) in (1) following ρ = 25, 000 replication/mutation cycles initiated at an arbitrary φ(i, 0), ψ(i, 0) (grey dot). Each lineage captures a random walk in fitness space (black path), resulting in the density function f_i(φ, ψ), describing i's multistrain \({{{{{{{{\mathcal{Z}}}}}}}}}_{i}\). The intra-host fitness distribution f_i(φ) (top, blue) is skewed in favor of fitter strains, which replicate more efficiently within i. The inter-host distribution, f_i(ψ) (right, green), on the other hand follows a zero-mean normal distribution, as, indeed, there is no intra-host selection for high ψ_μ. During infection the fitness of the transmitted pathogen ψ(j, 0) (green) is extracted from f_i(ψ). The variance σ² determines the size of the evolutionary gap Δψ of Eq. (10) between infection and transmission. f The inter-host dynamics is captured by network epidemic spreading, starting from an infection at node o by the wild-type μ = 0. As the pathogen propagates along the network A_ij it undergoes random shifts in its observed inter-host fitness ψ_μ. g The network spreading dynamics give rise to selection for higher ψ_μ. Here, strain 1 (green), the fittest of the three, is more transmissible, and therefore, exhibits an exponentially growing dominance over the observed pathogen population.