How Stand Productivity Results from Size- and Competition-Dependent Growth and Mortality

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Abstract
A better understanding of the relationship between stand structure and productivity is required for the development of: a) scalable models that can accurately predict growth and yield dynamics for the world's forests; and b) stand management regimes that maximize wood and/or timber yield, while maintaining structural and species diversity. We develop a cohort-based canopy competition model (“CAIN”), parameterized with inventory data from Ontario, Canada, to examine the relationship between stand structure and productivity. Tree growth, mortality and recruitment are quantified as functions of diameter and asymmetric competition, using a competition index (CAIh) defined as the total projected area of tree crowns at a given tree's mid-crown height. Stand growth, mortality, and yield are simulated for inventoried stands, and also for hypothetical stands differing in total volume and tree size distribution. For a given diameter, tree growth decreases as CAIh increases, whereas the probability of mortality increases. For a given CAIh, diameter growth exhibits a humped pattern with respect to diameter, whereas mortality exhibits a U-shaped pattern reflecting senescence of large trees. For a fixed size distribution, stand growth increases asymptotically with total density, whereas mortality increases monotonically. Thus, net productivity peaks at an intermediate volume of 100–150 m3/ha, and approaches zero at 250 m3/ha. However, for a fixed stand volume, mortality due to senescence decreases if the proportion of large trees decreases as overall density increases. This size-related reduction in mortality offsets the density-related increase in mortality, resulting in a 40% increase in yield. Size-related variation in growth and mortality exerts a profound influence on the relationship between stand structure and productivity. Dense stands dominated by small trees yield more wood than stands dominated by fewer large trees, because the relative growth rate of small trees is higher, and because they are less likely to die.