We provide the link between population dynamics and the dynamics of Darwinian evolution via studying the joint population dynamics of "similar" populations. Similarity implies that the "relative" dynamics of the populations is slow compared to, and decoupled from, their "aggregated" dynamics. The relative dynamics is simple, and captured by a Taylor expansion in the difference between the populations. The emerging evolution is directional, except at the "singular" points of the evolutionary state space, where "evolutionary branching" may happen
