  We analyze plankton-nutrient food chain models composed of phytoplankton,
herbivorous zooplankton and a limiting nutrient. These models have played a key
role in understanding the dynamics of plankton in the oceanic layer. Given the
strong environmental and seasonal fluctuations that are present in the oceanic
layer, we propose a stochastic model for which we are able to fully classify
the longterm behavior of the dynamics. In order to achieve this we had to
develop new analytical techniques, as the system does not satisfy the regular
dissipativity conditions and the analysis is more subtle than in other
population dynamics models.
