Marine plankton ecosystems exert a profound influence on climate through processes such as their drawdown of carbon dioxide from the atmosphere and their production and emission to the atmosphere of dimethylsulphide. Similarly, marine plankton ecosystems are sensitive to changes such as ocean acidification and stratification associated with a warming climate. In order to understand the importance and consequences of plankton-climate interactions we first need to understand and reliably predict the dynamics of plankton ecosystems. While the physical and chemical constraints on plankton systems are reasonably well understood, the dynamics that result from population interactions lack a complete and robust theoretical basis. The demonstrated potential for plankton systems to exhibit stable, chaotic and catastrophic behaviour suggests that a better understanding of these systems may be fundamental to predicting future climates.

We set out a theoretical framework for modelling plankton ecosystems. This reproduces the classic results for simple trophic interactions such as competition and predation but also allows us to define and model more complex interactions such as mixotrophy and facultative and obligate mutualism. We show that a complete theory of trophic interactions may be developed within a simple framework, and demonstrate the practical benefits of the approach for constructing and parameterising complex ecosystem models.