Nonlinearity and noise interaction in a model of forest growth

A deterministic nonlinear matrix growth model of naturally regenerated loblolly pine (Pinus taeda L.) stands (Lin, C.-R., Buongiorno, J., Prestemon, J., Skog, K., 1998. Growth model for uneven-aged Loblolly pine stands: simulations and management implications. FPL-RP-569. USDA ForServ., For. Products Lab., Madison, pp. 13.) predicts that in about 3 centuries, pines are replaced by more shade-tolerant hardwood species. Pines are also absent in the deterministic steady state. We modified this model to recognize the effects of small-scale, high-frequency disturbances on stand growth. Stochastic simulations with the same initial condition as the deterministic simulation gave very different results. With stochastic disturbances pines and hardwoods always co-existed and in the steady state there was about the same basal area in pines as in hardwoods. As a result, the stochastic nonlinear model predicted much higher species diversity than the deterministic one. In contrast, a linear stochastic matrix growth model would predict the same expected steady state as the linear deterministic model. Thus, nonlinearities in stochastic forest growth models may change considerably the predictions of the expected future stand state, relative to those of the nonlinear deterministic counterpart. In this study, significant differences remained between the expected stochastic and the deterministic predictions even after scaling down the stochastic term by a factor of 2–10.