Evolutionary stable investment in maternal transfer of immunity θ (when θP = θD) with or without cross-immunity: χ = 0.5 (dashed line) and χ = 0 (full line) against (a) the longevity of the host, (b) the dispersal of the host. Default parameter values (see the electronic supplementary material for more details on the model): r0 = 1.5, cθ = 0.1, k = 1.1, η = 0.3, K = 20, h = 1.1, α = 3, δM = 1, μ = 0.02.