Identification of ecosystem parameters by SDE-modelling

Stochastic differential equations (SDEs) for ecosystem modelling have attracted increasing attention during recent years. The modelling has mostly been through simulation experiments in order to analyse how system noise propagates through the ordinary differential equation formulation of ecosystem models. Estimation of parameters in SDEs is, however, possible by combining Kalman filter techniques and likelihood estimation. By modelling parameters as random walks it is possible to identify linear as well as non-linear interactions between ecosystem components. By formulating a simple linear SDE describing interactions between phytoplankton and water-column nitrogen with light as forcing, using data form a Danish estuary covering a 16 years period (1988-2003), and modelling primary production as a random walk, it is demonstrated how non-linear relationships between states can be identified by plotting the (random) production parameter as a function of the states in the system and global radiation. The resulting SDE model (that does not contain random walks), is analysed by simulation studies, to determine the properties of the seasonal distribution of phytoplankton.