  Populations of swimming microorganisms produce fluid motions that lead to
dramatically enhanced diffusion of tracer particles. Using simulations of
suspensions of swimming particles in a periodic domain, we capture this effect
and show that it depends qualitatively on the mode of swimming: swimmers
``pushed'' from behind by their flagella show greater enhancement than swimmers
that are ``pulled'' from the front. The difference is manifested by an
increase, that only occurs for pushers, of the diffusivity of passive tracers
and the velocity correlation length with the size of the periodic domain. A
physical argument supported by a mean field theory sheds light on the origin of
these effects.
