An additive edge correction for the influence potential of trees

The influence potential on a quadrat (IPQ) is an index for measuring the ecological effect that trees have on understory vegetation observed in a quadrat of a plot. IPQ is defined as the sum of the effect of every trees in the plot, where the effect depends on the size of the tree and the distance between the tree and the quadrat. Since only the trees in the plot have been observed and not the trees outside the plot, the true IPQ may be underestimated. Existing edge corrections are not appropriate for this case. We propose a correction that consists of adding the expected IPQ due to effects of trees outside the plot to the observed IPQ. The expectation is obtained by applying the Campbell theorem for stationary marked point processes. Data from the 1985-86 National Forest Inventory of Finland was used to calculate IPQ for six quadrats systematically allocated to each of 1240 plots. The implementation of the correction for this data is described. The distributions of IPQ with and without the correction proved the existence of edge effects and the effectiveness of the correction to eliminate the bias. This method has the potential to be applied to other additive functions.