Complex dynamics in a carbon–nitrogen model of a grass–legume pasture

A physiologically based model of a grass-legume pasture is used to study the dynamics of these competing species. In our model, we consider carbon and nitrogen pools and fluxes, incorporating competition for light and soil mineral nitrogen, and including the processes of nitrogen fixation, nitrogen losses and dry matter allocation. First, the steadystate responses of each species to nitrogen deposition, to leaching rate, and to other nitrogen losses are examined. We then consider the dynamic behaviour of these species when there is no time delay for nitrogen cycled through the soil organic matter pool. Next, the effects of various time delays associated with the soil organic matter nitrogen pool on the system dynamics are examined: the behaviour becomes complex, non-linear and exhibits lightly or heavily damped oscillations at two frequencies. The high sensitivity of the system both to the initial value of the soil organic matter nitrogen pool, and to any photosynthetic competitive advantage, is investigated. The implications of these results in relation to observations and experiments on grass-legume pastures are discussed.