  In Nature there are significant relationships known between microorganisms
from two kingdoms of life, as in the supply of vitamin B$_{12}$ by bacteria to
algae. Such interactions motivate general investigations into the
spatio-temporal dynamics of metabolite exchanges. Here we study by experiment
and theory a model system: a coculture of the bacterium $B. subtilis$, an
obligate aerobe that is chemotactic to oxygen, and a nonmotile mutant of the
alga $C. reinhardtii$, which photosynthetically produces oxygen when
illuminated. Strikingly, when a shaft of light illuminates a thin, initially
uniform suspension of the two, the chemotactic influx of bacteria to the
photosynthetically active region leads to expulsion of the algae from that
area. This effect arises from algal transport due to spatially-varying
collective behavior of bacteria, and is mathematically related to the
``turbulent diamagnetism" associated with magnetic flux expulsion in stars.
