Fig. 3.

The effect of effective fecundity on the equilibrium infection frequency of CI (a) and MK (b). a Due to frequency-dependent selection, CI dynamics exhibit cβ if F _CI t _CI < 1. In this case, an unstable equilibrium, which defines the CI threshold frequency $p_{\mathrm{C}I}^{\mathrm{t}hr}$, separates two stable equilibria, one at 0 and the other defining the CI equilibrium frequency ${\widehat{p}}_{\mathrm{C}I}$. Invasion is possible only if the initial frequency exceeds the threshold frequency. At F _CI t _CI = 1, there is a fold bifurcation. If F _CI t _CI > 1, there is only one stable equilibrium $\left({\widehat{p}}_{\mathrm{C}I}\right)$ so that invasion is possible for arbitrarily low initial frequencies. Parameters take the values t _CI = 0.99 and l _CI = 0.5. b MK dynamics lack frequency-dependent selection, and hence do not exhibit bistability. The critical resource reallocation efficiency β ^crit (below which invasion is not possible) exists whenever F _MK t _MK < 1. At F _MK t _MK = 1, there is a transcritical bifurcation. However, the fact that the bifurcation point lies at F _MK t _MK = 1 only becomes obvious for very small β values, because β ^crit is easily exceeded if β values are larger (see inset). Parameters take the values t _MK = 0.99, β = 0.001, and v = 0