Scale effects on the prediction of rare events in mature second-growth oak forests: a simulation study of cavity trees.

The abundance of cavity trees varies greatly due to the stochastic nature of cavity formation processes and involved disturbance agents. At small spatial scales such as a stand or plot, cavity tree abundance is extraordinarily difficult to predict precisely using tree and stand factors. In this study we used resampling methods to simulate the effect of spatial scale on cavity tree density (CTD) estimation using cavity tree data collected from a long-term forest experimental project. More than 53,000 measured trees were randomly divided into two approximately equal parts: the construction and test datasets, to construct classification and regression tree (CART) and logistic regression (LR) models to predict cavity probability and to test the accuracy of CTD estimation across varying spatial scales, respectively. Simulation results showed that when the spatial scale was < 10 ha, the predicted CTD varied dramatically, and with this specific dataset, CART tended to overestimate, whereas LR and the sample mean method underestimated the true CTD estimated by the construction dataset. Compared with the sample mean method, the use of tree characteristics in both CART and LR resulted in slight or moderate reduction of the relative error (RE) (< 20%) when the spatial scale was < 10 ha. However, CART and LR, particularly CART, could improve CTD prediction efficiency significantly at larger spatial scales. For instance, the RE of CART was only 17% of the sample mean method at a spatial scale of 50 ha. Resource managers could use this information for cavity tree sampling and monitoring.