We build on a model of evolution and emergence originally presented by [10] in which a zoonotic pathogen infects humans, and initially has very poor onward transmissability. Thus for people who are infected by animals the average reproductive number, R 0 , is well below one (R 0 %1). We call this the first reproductive number a 1 for the wildtype strain. Occasionally, during such zoonotic infections, the pathogen acquires genetic changes that increase its ability to pass to other humans. During any chain of transmission the pathogen might adapt sufficiently that it achieves such ease of human-to-human transmission that R 0 w1 and an epidemic becomes possible. Such a process can be characterised by a vector of reproductive numbers (a i with i~1, . . . , n), and a vector of mutation probabilities (m i with i~1, . . . , n) where n{1 denotes the number of adaptive steps necessary to reach the fully adapted strain n.