We also find that the waiting time for an outcome of a novel pathogen's introduction is highly unpredictable, even if the probability for such an event is known. Conversely, this means that an estimate of the underlying epidemiological parameters from observed data will be highly uncertain. Unfortunately, a large number of observations will be necessary to achieve confidence in the parameters, and even a large number of introductions gone extinct do not rule out the possibility of emergence for a pathogen. We came to a similar result [11] using a measurement on the upper bound of the probability of emergence. Moreover, the probability of emergence given a certain number of infectious hosts can be surprisingly low. Even a comparatively large number of infectious hosts can end in extinction, especially for low mutation rates and intermediate-stage average reproductive numbers just below one. Figure 5 . Data of commuting patterns in different parts of the world. Shown is the cumulative fraction of all communities with equal or less than the specified number of commuters. The data was mostly collected by the National Statistical Offices of the respective countries. The gold line represents commuting data from Brazil [21] , the red line data from the USA [22], the blue line data from the UK [23] , the brown line data from Japan [25], the cyan line data from Hong Kong [24] , and the green line data from two independent sources. The green line has orange [27] and pink data points [26] , corresponding to its data sources. Our data represents the commuting flows between administrative units. The definition of administrative units varies highly between countries. For example, the US data is on a granularity of 3,141 counties, while the data from Japan is based on its 47 prefectures. However, heterogeneity can also be found within countries datasets. The Brazilian data is on a level of 5,507 municipalities with resident sizes ranging from 1,166 to 10, 435, 548. doi:10.1371/journal.pcbi.1000947.g005 Figure 6 . Deviation between simulated and analytical predicted probability of emergence. The deviation is a function of the average number of commuters vcw. The deviation is defined as Dp (ana) em {p (sim) em D=p (ana) em . The analytical probability of emergence p (ana) em is for an infinite ulation without spatial structure. The simulated probability of emergence p (sim) em is for short-term commuting with the blue data points representing the gradual route (II) of adaptation, and the orange data points representing the punctuated route (I). The solid black line is 1{H spatial (1=a 3 ) vcwf , as defined in equation 12 in the main text. It is the analytical expected deviation for spatial heterogeneity as a function of the spatial homogeneity coefficient. The simulations agree very well with the analytical expected deviation. The gradual route (II) is slightly more off from the theoretical prediction as a result of the small but significant number of infected with the intermediate strain. Effectively, it lowers the number of commuters infected with the fully adapted strain and therefore the probability of transmission from the village to the city. Nevertheless, the analytical prediction as well as the simulations show no significant impact of spatial heterogeneity from a critical commuter threshold of vcw~10. doi:10.1371/journal.pcbi.1000947.g006 Figure 7 . Impact of spatial heterogeneity on disease transmission between communities (I). The impact is measured with the spatial homogeneity coefficient with 0ƒH spatial ƒ1. Given H spatial~1 every emergence in the village automatically leads to an emergence in the city, and H spatial~0 represents no chance of successfully transmitting the pathogen into the city. The figure reveals that spatial structure becomes especially important for small average reproductive numbers. In addition, the average number of commuters needed to show an effect of spatial heterogeneity is surprisingly small. doi:10.1371/journal.pcbi.1000947.g007