I was reading an article with title "birth-death models of information spread in structured populations" lately and have a few questions as the following. So, it is a discrete time process in which, at each iterate, a vertex is chosen, biased by fitness, to "reproduce". Then, an adjacent vertex is chosen to die and be replaced by a copy of the reproducing vertex. The edge from vertex i to vertex j is labeled with the probability that if vertex i is chosen for reproduction then vertex j is chosen for death. Then, what is the meaning of a single-vertex-fixation probability?