  While the role of local interactions in nonequilibrium phase transitions is
well studied, a fundamental understanding of the effects of long-range
interactions is lacking. We study the critical dynamics of reproducing agents
subject to autochemotactic interactions and limited resources. A
renormalization group analysis reveals distinct scaling regimes for fast
(attractive or repulsive) interactions; for slow signal transduction, the
dynamics is dominated by a diffusive fixed point. Furthermore, we present a
correction to the Keller-Segel nonlinearity emerging close to the extinction
threshold and a novel nonlinear mechanism that stabilizes the continuous
transition against the emergence of a characteristic length scale due to a
chemotactic collapse.
