Recent cases of emergent diseases have renewed interest in the evolutionary and ecological mechanisms that promote parasite adaptation to novel hosts [1-6]. Crucial to adaptation is the degree of mixing of original, susceptible hosts, and novel hosts. An increase in the frequency of the original host has two opposing effects on adaptation: an increase in the supply of mutant pathogens with improved performance on the novel host [7-9]; and reduced selection to infect novel hosts, caused by fitness costs commonly observed to be associated with host switching [10-17]. The probability of disease emergence will therefore peak at intermediate frequencies of the original host. We tested these predictions by following the evolution of a virus grown under a range of different frequencies of susceptible (original) and resistant (novel) host bacteria. Viruses that evolved to infect resistant hosts were only detected when susceptible hosts were at frequencies between 0.1% and 1%. Subsequent experiments supported the predictions that there was reduced selection and mutation supply at higher and lower frequencies, respectively. These results suggest that adaptation to novel hosts can occur only under very specific ecological conditions, and that small changes in contact rates between host species might help to mitigate disease emergence.