Since a seminal paper by Jordan, Otto, and Kinderlehrer (98'), it is now well known that some evolution PDEs, such as diffusion and advection PDEs, can be interpreted as gradient flows with respect to the Wasserstein distance. Since then, there have been ongoing efforts to integrate various evolutionary processes into this framework. In this talk, I will introduce the Moran process and the Kimura equation. I will go through the main ideas of Wasserstein gradient flow theory and explain how it is related to the Moran process and the Kimura equation. Indeed, the key point here is to look at a conditioned version of the dynamics, called the Q-process. The resulting dynamics can then be seen as a Wasserstein gradient flow, with degenerate underlying geometry, involving the Shahshahani metric. Finally, we will see that the dissipation induced by the hidden gradient flow in the continuous setting is a good approximation of the dissipation in the discrete setting in its high population limit.