The spectre of anthropogenic global climate change has focused attention on biogeochemical cycling in the oceans as marine plankton ecosystems are involved in the cycling of several compounds thought to have significant implications for climate. To better understand these processes, modellers are developing plankton functional type (PFT) models that group plankton according to their biogeochemical properties. There is some debate as to whether our understanding of plankton ecosystems is sufficiently well developed for PFT models to be reliable and for their predictions to be treated with confidence. In this paper, we examine the dynamical properties of a generic predator-prey-prey PFT model, then apply these analysis techniques to a simple example PFT model with two phytoplankton and one zooplankton in order to explore its parameter space. We find that parameter combinations for which all PFTs stay extant for all time appear rare, but develop a simple heuristic that allows such parameter sets to be identified relatively easily for many PFT models. We observe that such systems often have phytoplankton with similar growth rates, but that differ in other properties such as differing nutrient utilisation strategies or different susceptibilities to grazing. We also note that persistent PFT systems are more likely if neither phytoplankton have a low specific mortality rate or is a highly nutritious food for the grazer.