  We present a nonlinear and non-Markovian random walk model for stochastic
movement and the spatial aggregation of living organisms that have the ability
to sense population density. We take into account social crowding effects for
which the dispersal rate is a decreasing function of the population density and
residence time. We perform stochastic simulations of random walk and discover
the phenomenon of self-organized anomaly (SOA) which leads to a collapse of
stationary aggregation pattern. This anomalous regime is self-organized and
arises without the need for a heavy tailed waiting time distribution from the
inception. Conditions have been found under which the nonlinear random walk
evolves into anomalous state when all particles aggregate inside a tiny domain
(anomalous aggregation). We obtain power-law stationary density-dependent
survival function and define the critical condition for SOA as the divergence
of mean residence time. The role of the initial conditions in different SOA
scenarios is discussed. We observe phenomenon of transient anomalous bi-modal
aggregation.
