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Many species of phytoplankton migrate vertically near the surface of the ocean, in search of either light or nutrients. These motile organisms are affected by ocean surface waves. We derive a set of wave-averaged equations to describe the motion of microswimmers with spheroidal body shapes that includes several additional effects, such as gyrotaxis, settling and wind-driven shear. In addition to the well-known Stokes drift, the microswimmer trajectories depend on their orientation in a way that can lead to trapping at a particular depth; this in turn can affect transport of organisms, and may help explain observed phytoplankton layers in the ocean. [ABSTRACT FROM AUTHOR]