The evolution of age-specific resistance to infectious disease

Abstract

Innate, infection-preventing resistance often varies between host life stages. Juveniles are more resistant than adults in some species, whereas the opposite pattern is true in others. This variation cannot always be explained by prior exposure or physiological constraints and so it has been hypothesized that trade-offs with other life-history traits may be involved. However, little is known about how trade-offs between various life-history traits and resistance at different life stages affect the evolution of age-specific resistance. Here, we use a mathematical model to explore how trade-offs with natural mortality, reproduction and maturation combine to affect the evolution of resistance at different life stages. Our results show that certain combinations of trade-offs have substantial effects on whether adults or juveniles are more resistant, with trade-offs between juvenile resistance and adult reproduction inherently more costly than trade-offs involving maturation or mortality (all else being equal), resulting in consistent evolution of lower resistance at the juvenile stage even when infection causes a lifelong fecundity reduction. Our model demonstrates how the differences between patterns of age-structured resistance seen in nature may be explained by variation in the trade-offs involved and our results suggest conditions under which trade-offs tend to select for lower resistance in juveniles than adults.

Keywords: adult; juvenile; parasite; pathogen; resistance; susceptibility.

Figure 1.

(a) Model schematic for the ecological model. (b–d) Examples of trade-off functions. Trade-offs are shown between: (b) adult resistance and birth rate (with a₀ = 5), (c) adult resistance and adult mortality (with b₀ = 1), and (d) both juvenile and adult resistance and the birth rate (with a₀ = 5). Trade-offs between juvenile resistance and the maturation or birth rate take the same form as (b) and the trade-off between juvenile resistance and juvenile mortality takes the same form as (c). Trade-off strength is controlled by the parameter $c_1^{\mathrm{i}}$; a relatively strong trade-off ($c_1^{\mathrm{A}}=0.5$, red curves) results in a much larger reduction in the birth rate for a given level of adult resistance than a relatively weak trade-off does ($c_1^{\mathrm{A}}=0.25$, blue curves). Trade-off curvature is controlled by the parameter $c_2^{\mathrm{i}}$; a relatively high curvature ($c_2^{\mathrm{A}}=10$, dashed lines) means that there is initially a low cost of increasing resistance but the cost eventually increases rapidly compared to a trade-off with lower curvature ($c_2^{\mathrm{A}}=3$, solid lines). (d) is shown only in the strong, low curvature case.

Figure 2.

The effects of varying sterility virulence, 1 − f, on juvenile resistance (solid red) and adult resistance (dashed blue), for six different combinations of trade-offs: (a)–(c) adult resistance with reproduction, (d)–(f) adult resistance with adult mortality; (a) and (d) juvenile resistance with maturation, (b) and (d) juvenile resistance with juvenile mortality, and (c) and (f) juvenile resistance with reproduction. The dotted grey line shows total population density and the solid grey line shows the density of infected hosts (both are non-dimensionalized). Parameter values are as in table 1 with β₀ = 8 and α = 0.

Figure 3.

Phase planes showing (a) a continuously stable strategy and (b) bistability, with the juvenile nullcline in red and the adult nullcline in blue. In (a), the host population will always evolve towards the continuously stable strategy (purple circle), no matter what the starting values of the juvenile and adult resistance traits. In (b), the host population will evolve towards one of the attractors (purple circles), depending on the starting values of the juvenile and adult resistance traits (basins of attraction are separated by the dashed line). Example trajectories are shown in green. In (a), juvenile resistance trades off with juvenile mortality, adult resistance trades off with reproduction and parameter values are as in table 1 with β₀ = 8, α = 0 and f = 0.1. In (b), juvenile resistance trades off with juvenile mortality, adult resistance trades off with adult mortality and parameter values are as in table 1 with β₀ = 1000 (high transmissibility), α = 0 and f = 0.5.

Figure 4.

The effect of varying baseline transmissibility, β₀, on juvenile resistance (solid red) and adult resistance (dashed blue), in the cases where juvenile resistance trades off with juvenile mortality and adult resistance trades off with adult mortality (a and c), and where both juvenile and adult resistance trade off with reproduction (b and d). The dotted grey line shows total population density and the solid grey line shows the density of infected hosts (both are non-dimensionalized). In the bistability region in panel (c), the higher total population density and the lower infected density correspond to the higher levels of resistance. Parameter values are as in table 1, with α = 0 and f = 0.5 (b and c) or f = 0.3 (a and d).

Figure 5.

The effect of varying mortality virulence, α, on juvenile resistance (solid red) and adult resistance (dashed blue), for six different combinations of trade-offs: (a)–(c) adult resistance with reproduction, (d)–(f) adult resistance with adult mortality; (a) and (d) juvenile resistance with maturation, (b) and (d) juvenile resistance with juvenile mortality, and (c) and (f) juvenile resistance with reproduction. The dotted grey line shows total population density and the solid grey line shows the density of infected hosts (both are non-dimensionalized). Parameter values are as in table 1 with β₀ = 8 and f = 1.