Spatial pattern analysis of line-segment data in ecology

The spatial analysis of linear features (lines and curves) is a challenging and rarely attempted problem in ecology. Existing methods are typically expressed in abstract mathematical formalism, making it difficult to assess their relevance and transfer ability into an ecological setting. We introduce a set of concrete and accessible methods to analyse the spatial patterning of line-segment data. The methods include Monte Carlo techniques based on a new generalisation of Ripley's K-function and a class of line-segment processes which can be used to specify parametric models - parameters are estimated using maximum likelihood and models compared using information-theoretic principles. We apply the new methods to fallen tree (dead log) data collected from two one-hectare Australian tall eucalypt forest plots. Our results show that spatial pattern of the fallen logs is best explained by plot-level spatial heterogeneity in combination with a slope-dependent non-uniform distribution of fallen-log orientations. These methods are of a general nature and are applicable to any line-segment data. In the context of forest ecology, the integration of fallen logs as linear structural features in a landscape with the point locations of living trees, and a quantification of their interactions, can yield new insights into the functional and structural role of tree fall in forest communities and their enduring post-mortem ecological legacy as spatially distributed decomposing logs.