Table 1.
Variable and parameters descriptions for the within-host and between host models.
Fig 1.
Within-host model fitness and equilibrium viral load.
A) The relationship between the number of segregating sites and the fitness cost (synonymous with selection coefficient) associated with an additional mutation. We explore a range of values of m (ranging 10 to 400 in increments of 10), with the corresponding fitness cost of a mutation reducing on a log-linear scale as m increases. The six choices of m explored here are indicated by coloured points. B) The viral load at equilibrium of an infection with an increasing number of segregating sites. As the number of sites increase and the fitness costs decrease, the population at equilibrium is characterised by mutation-selection balance that maintains deleterious viral types in the population, thus lowering viral loads.
Fig 2.
Within host viral load trajectories.
The within-host viral load dynamics over time for 10, 50, 100, 150, 200 and 250 segregating sites, and varying initial numbers of mutations. The viral load of the equilibrium solution is shown by the black dashed horizontal line. The viral load changes as the virus population evolves over time, with new deleterious mutations appearing that are then lost due to purifying selection. When the cost of a mutation is high, viral loads climb to the maximum possible value. As we increase the number of segregating sites and reduce the fitness cost of a mutation, the selection against weaker virus types is balanced by the influx of mutations, and consequently the within-host dynamics are extremely slow relative to the typical duration of chronic infection.
Fig 3.
Between-host outcomes at endemic equilibrium.
A) The distribution of set-point viral loads (spVL) at the between-host equilibrium. The fittest virus type rapidly dominates within-host and short-sighted evolution dominates. Red dashed lines denote the average within-host viral load. B-F) Greater within-host diversity provides a larger pool of variants that can be transmitted and on which between-host selection can act. As the number of segregating sites increases, the within-host dynamics slow and the virus is better able to evolve between-host towards an intermediate spVL that maximises transmission potential.
Fig 4.
Between-host outcomes at equilibrium for an increasingly heterogenous host population.
Histograms of spVLs in heterogenous infected population for different maximum host effect size, e, for 250 segregating sites. To account for the effect that host genetics has on viral load, we introduced a host specific additive effect to viral load. The size of the host effect is discretely uniformly distributed between -e and e and there are 50 host types. A maximum effect size of e = 0.1 (A) results in a small increase in the range of viral loads observed, and as we increase e we observe a more realistic distribution of viral loads. Increasing the effect size towards e = 1 further flattens and skews the distribution. Corresponding results for other choices of m are present in supp. Fig 4.
Fig 5.
Average spVL over time in simulated epidemics.
For m = 10, short-sighted evolution leads to the rapid dominance of the fittest virus type as the single circulating variant within a few years of the epidemic. For m = 50 and m = 100, the within-host dynamics create a distinctive pattern at the population level. When epidemics start with lower viral load viruses that have a relatively long infection duration, within-host evolution leads to the emergence and transmission of fitter variants with higher viral loads. This process accelerates the population-level increase in average spVL. When we assume a large number of weakly deleterious mutations (m = 150,200,250) within-host dynamics are sufficiently slow for selection for transmission potential to influence the epidemiological dynamics and lower the average spVLs, despite the comparatively higher within-host equilibrium viral load. We observe slow cumulative changes in the average spVL, with over 100 years taken for convergence at higher values of m.
Fig 6.
Heritability is estimated by a parent-offspring regression of spVL in simulated source and recipient pairs. The error bars indicate the standard deviation of the estimates taken from 1000 sampled sets of 500 transmission pairs. The infection type of the source (number of deleterious mutations of infecting virus type) is determined based upon the population-level prevalence of viral types at the endemic steady state. The virus type transmitted from source to recipient is determine based upon the transmission potential of each virus type over the course of the source infection. In a homogenous population, heritability is high, and naturally as a host-effect is introduced the amount of variability in spVL explained by the virus type, i.e., heritability, falls to within the range reported in multiple studies.