In this talk I describe a mechanism for generating cycles in a large class of "mesoscale" biological populations (meaning populations composed of thousands to tens of thousands of units). Cycles are caused by a resonant amplification of the system dynamics triggered by internal noise. I will discuss this mechanism in the context of two classes of simple systems: ecological (e.g. predator-prey, host-pathogen) and biochemical (e.g. small gene regulation networks, modules of metabolic processes).