An extreme-value approach to detect clumping and an application to tropical forest gap-mosaic dynamics

Abstract

Although forest tree pattern-dynamics has long been a focus for ecological theory, many aspects of basic analysis remain problematic. This paper describes, examines and illustrates an ‘extreme-value’ approach to clump detection. Simulations demonstrate that the approach, though simple, is sensitive and well suited to identifying aggregation, even in small data sets. The test is complementary to the χ² approach and significantly outperforms it when high-density clusters form a relatively small fraction of the total area. This difference holds true as density declines, though the power of both tests decreases and the χ² test eventually fails. Though powerful, the extreme-value tests are slightly conservative. The approach is adaptable to other null distributions and applications. An illustration uses tree data from a Ugandan forest plot with records from 1939 to 1992. One plausible explanation for observed stem increases in this plot is an unusually high incidence of large tree-fall events. Evidence for this is sought through spatial localization of various stem populations. Chi-square tests detect non-random density patterns in the populations that comprise ‘all stems > 10 cm diameter recorded in the 1992 survey’, and ‘all recruits in 1976’. In the extreme-value test three populations are found to be clumped, these are ‘pioneers > 10 cm diameter recorded in the 1992 survey’, ‘all recruits in 1992’ and again ‘all recruits in 1976’. These patterns, particularly the pioneer trees and stem recruitment, signal a ‘gap-dynamic process’ of tree regeneration. Despite this, the trends observed in the Ugandan plot appear unlikely to be caused by tree-falls alone. Various technical and ecological aspects of the extreme-value approach and tree spatial analyses are discussed.