The evolutionary dynamics of within-generation immune priming in invertebrate hosts

Abstract

While invertebrates lack the machinery necessary for 'acquired immunity', there is increasing empirical evidence that exposure to low levels of disease may 'prime' an invertebrate's immune response, increasing its defence to subsequent exposure. Despite this increasing empirical data, there has been little theoretical attention paid to immune priming. Here, we investigate the evolution of immune priming, focusing on the role of the unique feedbacks generated by a newly developed susceptible-primed-infected epidemiological model. Contrasting our results with previous models on the evolution of acquired immunity, we highlight that there are important implications to the evolution of immunity through priming owing to these different epidemiological feedbacks. In particular, we find that in contrast to acquired immunity, priming is strongly selected for at high as well as intermediate pathogen virulence. We also find that priming may be greatest at either intermediate or high host lifespans depending on the severity of disease. Furthermore, hosts faced with more severe pathogens are more likely to evolve diversity in priming. Finally, we show when the evolution of priming leads to the exclusion of the pathogens or hosts experiencing population cycles. Overall the model acts as a baseline for understanding the evolution of priming in host-pathogen systems.

Figure 1.

Two example pairwise invasion plots (PIPs). Resident trait values form the x-axis and mutant trait values the y-axis. Black regions denote areas of positive mutant invasion fitness, white regions areas of negative invasion fitness. The black arrows indicate the direction of selection along the main diagonal (i.e. small mutational steps), with grey dots marking evolutionary singularities and the grey arrows indicating whether selection near the singular point is in towards the singular point (a) or away from it (b). (a) A continuously stable strategy (CSS): a_max = 2.133, a_min = 1.842, λ =−0.159; (b) an evolutionary branching point: a_max = 2.750, a_min = 1.612 and λ = 0.931. Other parameter values: α = 1, q = 0.5, f_I = 1, β = 2, b = 1 and c = 0.

Figure 2.

Evolutionary outcome at the singular point (p,a(p)) = (0.5,2) as a function of the trade-off curvature a″(p) for varying (a) virulence, α, (b) infected reproduction (sterility, f_I) and (c) reinfection (immune protection, q). Solid lines mark the boundary of ES, and dashed lines the boundary of CS. ‘CSS’ denotes continuously stable strategy and ‘GoE’ denotes Garden of Eden. Default parameter values are as of figure 1.

Figure 3.

CSS levels of priming as functions of (a) virulence, α, (b) infected reproduction (sterility, f_I), (c) reinfection (immune protection, q), and (d,e) lifespan, 1/b. The plots are divided in to regions of underlying population dynamics as annotated. Shaded regions mark areas of bistability in the population dynamics—light shading for bistability between disease-free (D.F.) and an endemic equilibrium (Eq.), dark shading for bistability between disease-free and endemic cycles (Cy.). Default parameter values in (a–d) are as of figure 1, with a_max = 2.133, a_min = 1.842 and λ =−0.159. In (e), α = 2 and f_I = 0.25.

Figure 4.

Simulated evolutionary dynamics of immune priming when the singular point is a branching point, alongside the densities of the resident susceptible strain(s) at regular evolutionary time points (in the density plots, solid lines denote equilibrium points, dots the upper and lower limits of cycles). The dashed line marks the point where two coexisting strains first emerge. The small insets show sample population dynamics of the two resident strains, with black curves for densities and grey curves for densities, at (a) evolutionary time = 300 and 600, and (b) evolutionary time = 800 and 1500. Parameter values as of figure 1, with f_I = 0. (a) Singular point at (p,a(p)) = (0.5,2), curvature a″(p) = 1.3; a_max = 2.750, a_min = 1.612 and λ = 0.931. (b) Singular point at (p,a(p)) = (0.8,1.8), curvature a″(p) = 0.68; a_max = 2.711, a_min = 1.675 and λ = 0.815.

Figure 5.

Simulated evolutionary dynamics of immune priming when the singular point at (p,a(p)) = (0.5,2) is a repeller, alongside the resident population densities for the resident strain at regular evolutionary time steps (in (b), the dashed line marks the point where two coexisting strains first emerge). The small insets show PIPs for the two systems (in (a) the grey region denotes where the underlying population dynamics are purely disease-free). Parameter values as of figure 1, with (a) q = 0.2, curvature a″(p) = 0.75; a_max = 2.384, a_min = 1.845 and λ = 1.480; (b) q = 0.1, curvature a″(p) = 0.75; a_max = 2.410, a_min = 1.805 and λ = 1.098.