Invasion implications of environmental transmission. In A, we assume 104 susceptible migrants arriving at a lake of volume L (liters), containing V0 virus (measured in units of EID50 per liter). The color surface shows the cumulative fraction of birds infected, averaged over 1,000 stochastic realizations. The transparent mesh presents the outcome in the worst-case scenario (top 1% simulations). In B, we present a contour plot of the probability of an outbreak resulting in > 100 infections. As the contours demonstrate, the outcome is largely independent of initial virus concentration, suggesting virus in the environment could represent a long-term source of infections. Insets demonstrate, however, that changes in V0 affect the distribution of outbreak sizes. Model parameters were κ = 10, ω = 1012 per year, 1/η = 1 month, ρ = 104 liters per year, β = 7.8 × 10−3 per year per individual, 1/γ = 7 days. These parameters result in R0direct = 1.5. The sensitivity of these findings to changes in model parameter values are discussed in detail in the SI Appendix.