Spatial pattern analysis of line-segment data in ecology

Abstract

O_LIThe 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 transferability into an ecological setting. A set of concrete and accessible tools is needed. C_LIO_LIWe develop a new method to analyse the spatial patterning of line-segment data. It is based on a generalisation of Ripleys K-function and includes an analogue of the transformed L-function, together with estimators and theoretical expectation values. We introduce a class of line-segment processes, related to the Boolean model, which we use in conjunction with Monte-Carlo methods and information criteria to generate and compare candidate models. We demonstrate the utility of our method using fallen tree (dead log) data collected from two one-hectare Australian tall eucalypt forest plots. C_LIO_LIComparing six line-segment models, we find for both plots that the distribution of fallen logs is best explained by plot-level spatial heterogeneity. The use of non-uniform distributions to model dead-log orientation on the forest floor improves model performance in one of the two sites. Our case study highlights the challenges of model comparison in spatial-pattern analysis, where Monte-Carlo approaches based on the discrepancy of simulated summary functions can generate a different ranking of models than that of information criteria. C_LIO_LIThese 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, will 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. C_LI