Analysis of nutrient-cycling dynamics, for predicting sustainability and CO 2-response of nutrient-limited forest ecosystems

Abstract

The dynamics of nutrient cycling within a forest system involve processes operating on many different timescales, ranging from seconds to thousands of years. In their response to environmental change, trees can respond initially in one direction and then later reverse the response due to a process acting on a longer time scale. Thus, theoretical models are required for the interpretation of short-term experiments where CO 2 concentration or nutrient availability are modified. Comins and McMurtrie (1993) delineate the G'DAY plant-soil model, which attempts to incorporate nutrient cycling responses on various time scales in a model of moderate complexity, using the Century model of soil nutrient dynamics coupled with a simple model of tree growth. The model shows a complex response to doubling CO 2 under nitrogen-limited conditions; large or small short-term responses can be independently combined with either large or small long-term responses, depending on certain details of plant and soil dynamics. Comins and McMurtrie describe the long-term behaviour of the system by calculating the equilibrium of the model, excluding the passive soil organic matter pool. This analytical result makes clear which parameters of the model determine the long-term dynamics. Subsequently it has been found that a more general description of long-term dynamics requires understanding both the equilibrium pool sizes and the equilibration time of the system. This paper derives an analytical expression for the equilibration time, again permitting the important parameters of the model to be identified. It also describes an intermediate level of approximation, using differential equations for slow soil organic matter carbon and nitrogen pools. This is useful for generalisations of the model, and for describing the long-term dynamics in a gradually changing environment, as opposed to the dynamics following a step change. It is found that most parametrisations of G'DAY which have low nitrogen loss rates also have relatively long equilibration times. The equilibration time is approximately predicted by the slow pool decay time divided by the ‘slow nitrogen loss fraction’ (defined as the fraction of nitrogen released from the slow soil organic matter pool which leaves the system without ever re-entering the slow pool). In a slowly changing environment, the response of G'DAY can be approximately predicted using equilibrium analysis and a time lag, where the appropriate time lag is equal to the predicted equilibration time.