  We consider the dynamics of a three-species system incorporating the Allee
Effect, focussing on its influence on the emergence of extreme events in the
system. First we find that under Allee effect the regular periodic dynamics
changes to chaotic. Further, we find that the system exhibits unbounded growth
in the vegetation population after a critical value of the Allee parameter. The
most significant finding is the observation of a critical Allee parameter
beyond which the probability of obtaining extreme events becomes non-zero for
all three population densities. Though the emergence of extreme events in the
predator population is not affected much by the Allee effect, the prey
population shows a sharp increase in the probability of obtaining extreme
events after a threshold value of the Allee parameter, and the vegetation
population also yields extreme events for sufficiently strong Allee effect.
Lastly we consider the influence of additive noise on extreme events. First, we
find that noise tames the unbounded vegetation growth induced by Allee effect.
More interestingly, we demonstrate that stochasticity drastically diminishes
the probability of extreme events in all three populations. In fact for
sufficiently high noise, we do not observe any more extreme events in the
system. This suggests that noise can mitigate extreme events, and has
potentially important bearing on the observability of extreme events in
naturally occurring systems.
