Geostatistics provides tools to model, estimate, map, and eventually predict spatial patterns of tree size and growth. Variogram models and kriged maps were used to study spatial dependence of stem diameter (DBH), basal area (BA), and 10-year periodic basal area increment (BAI) in an old-growth forest stand. Temporal variation of spatial patterns was evaluated by fitting spatial stochastic models at 10-year intervals, from 1920 to 1990. The study area was a naturally seeded stand of southwestern ponderosa pine (Pinusponderosa Dougl. ex Laws. var. scopulorum) where total BA and tree density have steadily increased over the last decades. Our objective was to determine if increased stand density simply reduced individual growth rates or if it also altered spatial interactions among trees. Despite increased crowding, stem size maintained the same type of spatial dependence from 1920 to 1990. An isotropic Gaussian variogram was the model of choice to represent spatial dependence at all times. Stem size was spatially autocorrelated over distances no greater than 30 m, a measure of average patch diameter in this forest ecosystem. Because patch diameter remained constant through time, tree density increased by increasing the number of pine groups, not their horizontal dimension. Spatial dependence of stem size (DBH and BA) was always much greater and decreased less through time than that of stem increment (BAI). Spatial dependence of BAI was close to zero in the most recent decade, indicating that growth rates in 1980–1990 varied regardless of mutual tree position. Increased tree crowding corresponded not only to lower average and variance of individual growth rates, but also to reduced spatial dependence of BAI. Because growth variation was less affected by intertree distance with greater local crowding, prediction of individual growth rates benefits from information on horizontal stand structure only if tree density does not exceed threshold values. Simulation models and area estimates of tree performance in old-growth forests may be improved by including geostatistical components to summarize ecological spatial dependence.

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Multiply By To obtain foot (ft) 0.3048 meter inch (in.) 25.4 millimeter million gallons per day (Mgal/d) 3,785 cubic meter per day gallon per day (gal/d) 0.003785 cubic meter per day gigawatt-hour (GWh) 3,413 x 109 British thermal unit IV Contents

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