Some zoonotic pathogens cause sporadic infection in humans but rarely propagate further, while others have succeeded in overcoming the species barrier and becoming established in the human population. Adaptation, driven by selection pressure in human hosts, can play a significant role in allowing pathogens to cross this species barrier. Here we use a simple mathematical model to study potential epidemiological markers of adaptation. We ask: under what circumstances could ongoing adaptation be signalled by large clusters of human infection? If a pathogen has caused hundreds of cases but with little transmission, does this indicate that the species barrier cannot be crossed? Finally, how can case reports be monitored to detect an imminent emergence event? We distinguish evolutionary scenarios under which adaptation is likely to be signalled by large clusters of infection and under which emergence is likely to occur without any prior warning. Moreover, we show that a lack of transmission never rules out adaptability, regardless of how many zoonoses have occurred. Indeed, after the first 100 zoonotic cases, continuing sporadic zoonotic infections without onward, human-to-human transmission offer little extra information on pathogen adaptability. Finally, we present a simple method for monitoring outbreaks for signs of emergence and discuss public health implications.