In suspensions of microorganisms, pattern formation can arise from the interplay of chemotaxis and the fluid flows collectively generated by the organisms themselves. Here we investigate the resulting pattern formation in square and elongated domains in the context of two distinct models of locomotion in which the chemoattractant dynamics is fully coupled to the fluid flows and swimmer motion. Analyses for both models reveal an aggregative instability due to chemotaxis, independent of swimmer shape and type, and a hydrodynamic instability for "pusher" swimmers. We discuss the similarities and differences between the models. Simulations reveal a critical length scale of the swimmer aggregates and this feature can be utilized to stabilize swimmer concentration patterns into quasi-one-dimensional bands by varying the domain size. These concentration bands transition to traveling pulses under an external chemoattractant gradient, as observed in experiments with chemotactic bacteria.E.L. acknowledges a New Jersey Institute of Technology faculty seed grant award. R.E.G. was supported in part by Established Career Fellowship EP/M017982/1 from the Engineering and Physical Sciences Research Council and the Schlumberger Chair Fund. M.J.S. acknowledges support from NSF Grants No. DMS-1463962 and No. DMS-1620331, as well as the NSF Grant No. DMR-1420073 awarded to the MRSEC at NYU
