  We consider a size-structured aggregation and growth model of phytoplankton
community proposed by Ackleh and Fitzpatrick [2]. The model accounts for basic
biological phenomena in phytoplankton community such as growth, gravitational
sedimentation, predation by zooplankton, fecundity, and aggregation. Our
primary goal in this paper is to investigate the long-term behavior of the
proposed aggregation and growth model. Particularly, using the well-known
principle of linearized stability and semigroup compactness arguments, we
provide sufficient conditions for local exponential asymptotic stability of
zero solution as well as sufficient conditions for instability. We express
these conditions in the form of an easy to compute characteristic function,
which depends on the functional relationship between growth, sedimentation and
fecundity. Our results can be used to predict long-term phytoplankton dynamic
