Spatial analysis for continuously changing point patterns along a gradient and its application to an Abies sachalinensis population

The spatial pattern and the patch structure of trees reflect small-scale disturbance regimes such as gap formation by single tree-falls; therefore, when gap parameters such as frequency and intensity are changing along an environmental gradient, spatial patterns should also be changing. This paper develops a point process model that can illustrate continuous changes in patch structure along a gradient and quantitatively estimate the gap parameters. The new model is a combination of the Neyman–Scott process and the inhomogeneous Poisson process. Its second-order moment can be approximately reduced to a function of two variables—i.e. the gradient and the spatial scale—and therefore can be visualized graphically for descriptive purposes as well as for constructing models, optimising parameters and checking model fit. The methodology is applied to an Abies sachalinensis population in a coniferous broad-leaved mixed forest on a slope in the boreal region of northern Japan. The results quantified the patch structure as being more frequent, denser and smaller with elevation, reflecting strong ocean winds that resulted in frequent disturbance in the more elevated areas.