Plots (a–c) show proportion of occupied patches in the metapopulation model (1) with only environmental transmission, showing the effect of the clearance rate of contaminated patches (a) xZ = 0.0 (permanent persistence), (b) xZ = 0.2 (intermediate persistence), (c) xZ = 5.0 (short-term persistence), and the infection rate by free-living pathogen, = 0.01 (dotted line), = 0.2 (dashed line), = 0.5 (solid line). Curves have remaining parameters in common (). Plots (d–f) show proportion of occupied patches in the metapopulation model (1) with spillover transmission (dotted arrows in Fig. 1) being the only transmission mechanism (i.e., δ = 0.0, = 0.0). Spillover transmission rate is (d) g = 0.0, (e) g = 0.2, (f) g = 0.5. Unless stated otherwise, parameters in plots (d–f) are as in plots (a–c).