Effect of the fraction of resistant hosts, host resistance diversity (<i>n</i>), and spatial structure (<i>ϕ</i>) on pathogen emergence.

(A) Probability of pathogen emergence without (u0,n = 0, dashed curve) or with (u0,n = 5 * 10−3, full curve) mutations (note the logarithmic scale) when n = 4 and for increasing values of the fraction of resistant hosts in the absence of spatial structure (i.e., ϕ = 0). The shaded area illustrates the fraction of pathogen emergence caused by pathogen adaptation. The dotted curves indicate the probability of emergence for lower levels of host diversity. In (B), the probability of pathogen emergence is shown for increasing values of ϕ (i.e., spatial structure) when fR = 0.88. Other parameter values: b = 2.5, d = 1, c = 0.05.