On the evolution of reproductive restraint in malaria

Abstract

Malaria is one of the leading causes of death among infectious diseases in the world, claiming over one million lives every year. By these standards, this highly complex parasite is extremely successful at generating new infections. Somewhat surprisingly, however, many malaria species seem to invest relatively little in gametocytes, converting only a small percentage of circulating asexual parasite forms into this transmissible form. In this article, we use mathematical models to explore three of the hypotheses that have been proposed to explain this apparent 'reproductive restraint' and develop a novel, fourth hypothesis. We find that only one of the previous three hypotheses we explore can explain such low gametocyte conversion rates, and this hypothesis involves a very specific form of density-dependent transmission-blocking immunity. Our fourth hypothesis also provides a potential explanation and is based on the occurrence of multiple infections and the resultant within-host competition between malaria strains that this entails. Further experimental work is needed to determine which of these two hypotheses provides the most likely explanation.

Figure 1

A particular optimal gametocyte production level can be obtained from multiple selectively neutral trait pairs. (a) Total gametocyte production as predicted by the within-host model described in the electronic supplementary material, appendix B at steady state (with θ=1, η=0.01, ζ=2 and φ₁ φ₂>φ₃). The total number of gametocytes, G, is the product of conversion rate, ϵ, and total RBCs infected, A(ϵ, ϕ). As conversion rate increases, fewer merozoites are available to infect RBCs, so A decreases with ϵ, resulting in the ‘hump’ shape of G. The total number of RBCs infected increases with ϕ. In response to selection pressures, evolution favours a certain optimal level of gametocyte production, G^*, denoted by the grey line. For each ϕ we see two values of ϵ that obtain G^* gametocytes. (b) Extending these results we find that a continuum of trait pairs give rise to G^* gametocytes.

Figure 2

The effect of multiple infections on the optimal conversion rate. Evolutionarily stable conversion rate strategies as predicted by the model of superinfection in the electronic supplementary material, appendix C assuming a steady-state gametocyte production as described in the electronic supplementary material, appendix B. (Here, μ(G)=μ₀+μ₁G, b(G)=λ(G/α+G), σ(κ_i−κ_j)=σ₁(1+tanh (h(κ_i−κ_j)))/2, m=1000, a=1000, p=1, μ₀=10⁻⁴, λ=1, α=1, T=10, r=0.01, d=0.001, θ=1, η=0.01, ζ=2, σ₁=1.) Under these conditions, selection always acts to increase ϕ. Therefore, the equilibrium value of ϕ will always be ϕ_max and here we have assumed ϕ_max=10. The parameter h describes the relationship between the likelihood of superinfection and the outcome of within-host competition. When h=0, superinfection occurs at a constant rate irrespective of the within-host growth factors of the competing strains. Superinfection in this case does not result in selection at the within-host level. As h increases, the likelihood of superinfection becomes increasingly dependent on the competing strains' within-host growth factors, generating selection at this level. The equilibrium conversion rate therefore decreases as h increases. Also, as the cost of gametocytes goes up, i.e. increased mosquito mortality μ₁, lower conversion rates are favoured by selection.