Climate and nitrogen deposition constrain the maximum size-density boundary for mature and old-growth stands

Christopher E Looney ^1* John D Shaw ²

• ¹ Pacific Southwest Research Station, Forest Service (USDA), Albany, United States
• ² Rocky Mountain Research Station, Forest Service (USDA), Fort Collins, Colorado, United States

Forest stocking guidelines traditionally reference self-thinning lines representing the tradeoff between maximum trees per unit area vs. maximum mean tree size for even-aged stands. While selfthinning lines are roughly linear on logarithmic scales, certain forest types display a curvilinear "mature stand boundary" (MSB). The existence of the MSB suggests that beyond self-thinning, processes such as recruitment limitation, density-independent mortality, and their interactions with site quality may also contribute to a more universal maximum size-density boundary (MSDB). To advance forest modeling and the management of mature stands under global change, we investigated: 1) how the MSDB may differ as stands biologically mature in response to climate and N deposition, 2) whether mortality and recruitment contribute to the curvilinearity of the MSDB. To accomplish this, we compiled forest inventory, climate, and total N deposition data for four western U.S. forest types (California mixed-conifer, ponderosa pine, Douglas-fir, and pinyon-juniper). We examined three aspects of climate: thermal loading, aridity, and seasonality of precipitation. We used 0.95 quantile regression to model the MSDB and generalized linear modeling for mortality and recruitment. Unlike studies of even-aged stands that found abrupt MSBs, we found evidence for curvilinear MSDBs in all four forest types, with climate and/or N deposition modulating the degree of curvilinearity. Aridity constrained maximum stocking in medium-large diameter stands of California mixed-conifer and Douglas-fir, while higher growing-season precipitation constrained maximum stocking in large-diameter ponderosa pine. Heavier N deposition lowered maximum stocking in large-diameter stands of California mixed-conifer and pinyon-juniper. In California mixed-conifer and Douglas-fir, N deposition steepened the slope of the MSDB in small-diameter stands. Mortality was consistent along the MSDB for ponderosa pine, concentrated in large-diameter California mixed-conifer and Douglas-fir stands, and small-diameter pinyon-juniper stands. Recruitment was elevated in small-diameter stands of all four forest types. Our results support roles for both mortality and recruitment in driving curvilinear MSDBs. Our findings caution against assuming that self-thinning consistently defines the MSDB throughout stand development, while having important implications for the management of mature and old-growth stands under global change, especially at extremes of resource availability where the limitations of traditional tools may be most acute.