Analytical model of stemwood growth in relation to nitrogen supply

We derived a simplified version of a previously published process-based model of forest productivity and used it to gain information about the dependence of stemwood growth on nitrogen supply. The simplifications we made led to the following general expression for stemwood carbon (c(w)) as a function of stand age (t), which shows explicitly the main factors involved: c(w)(t) = eta(w)G*/ micro (w)(1 - lambdae(- micro (w)t) - micro (w)e(-lambdat)/lambda - micro (w)), where eta(w) is the fraction of total carbon production (G) allocated to stemwood, G* is the equilibrium value of G at canopy closure, lambda describes the rate at which G approaches G*, and micro (w) is the combined specific rate of stemwood maintenance respiration and senescence. According to this equation, which describes a sigmoidal growth curve, c(w) is zero initially and asymptotically approaches eta(w)G*/ micro (w) with the rate of approach dependent on lambda and micro (w). We used this result to derive corresponding expressions for the maximum mean annual stem-wood volume increment (Y) and optimal rotation length (T). By calculating the quantities G* and lambda (which characterize the variation of carbon production with stand age) as functions of the supply rate of plant-available nitrogen (U(o)), we estimated the responses of Y and T to changes in U(o). For a plausible set of parameter values, as U(o) increased from 50 to 150 kg N ha(-1) year(-1), Y increased approximately linearly from 8 to 25 m(3) ha(-1) year(-1) (mainly as a result of increasing G*), whereas T decreased from 21 to 18 years (due to increasing lambda). The sensitivity of Y and T to other model parameters was also investigated. The analytical model provides a useful basis for examining the effects of changes in climate and nutrient supply on sustainable forest productivity, and may also help in interpreting the behavior of more complex process-based models of forest growth.