  The evolution of two species with different fitness is investigated on
degree-heterogeneous graphs. The population evolves either by one individual
dying and being replaced by the offspring of a random neighbor (voter model
(VM) dynamics) or by an individual giving birth to an offspring that takes over
a random neighbor node (invasion process (IP) dynamics). The fixation
probability for one species to take over a population of N individuals depends
crucially on the dynamics and on the local environment. Starting with a single
fitter mutant at a node of degree k, the fixation probability is proportional
to k for VM dynamics and to 1/k for IP dynamics.
