Spatial modeling of habitat trees based on line transect sampling and point pattern reconstruction

An approach is presented for the spatial modeling of rare habitat trees surveyed by line transect sampling (LTS) in a protected area of the European Natura 2000 network. The observed tree pattern is defined as a realization of a thinned point process where the thinning can be modeled by a parametric detection function. A complete pattern is reconstructed using an optimization algorithm. The start configuration contains detected tree locations and randomly generated tree positions. Empirical cumulative distribution functions (ECDFs) for intertree and location-to-tree distances estimated from the original LTS are set as target characteristics. The same ECDFs are estimated by means of virtual LTS in the reconstruction. Tree positions are relocated during the optimization. The sum of squared deviations between the ECDFs from the original LTS and the virtual LTS in the reconstruction is considered as a contrast measure. A new configuration is accepted if the contrast is lowered compared with the previous state. The nonparametrically reconstructed habitat tree patterns are described by a log Gaussian Cox process model. Evaluations by means of line transect resamplings in a complete habitat pattern show small deviations between the second-order functional characteristics obtained from the true pattern and their analogs derived from the reconstructions.