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iForest -Biogeosciences and Forestry
IntroductionCanopy trees may influence understorey species composition in an individual or collective manner (Økland & Eilertsen 1993, Kuuluvainen 1994, Berger & Puettmann 2000, Michalet et al. 2002, Barbier et al. 2008, Chávez & Macdonald 2010, Strong 2011. In boreal forests, the properties of tree layer have proven important as determinants of understorey properties such as micro-climate, soil moisture, litter depth, litter distribution and light conditions (Økland 1996). The distance from a given point on the forest floor to the nearest trees and the properties of these trees were important predictors of understorey species composition in boreal spruce forests (Økland et al. 1999). In tropical forests, properties of individual trees have proven to affect the distribution of lianas (Nesheim & Økland 2007), but it remains unknown whether understorey species composition is more effectively predicted by local tree neighborhood or by average stand properties (Berger & Puettmann 2000, Thomsen et al. 2005, Barbier et al. 2008.Ecological Field Theory (EFT) is a methodology for studying the interaction between plants of different size (Wu et al. 1985, Kuuluvainen & Pukkala 1989. One of the main features of EFT is that it addresses interactions within a spatial context by determining a domain or size of the influence field. EFT models of tree influence express the effect of tree(s) on a given point x in the space as an exponential function of individual tree properties and the point's distance to neighboring trees. EFT models have been applied to studies of single-tree influence on soil chemical properties, radiation at forestfloor level, seedling growth and understorey vegetation composition (Pukkala et al. , Økland et al. 1999) in boreal forests with one dominant tree species (e.g., Norway spruce, Scots pine). To our knowledge, however, EFT models have not yet been applied to assess the influence of single-tree properties on the composition of the understorey in (sub-) tropical forest (Walker et al. 1989).Constrained Ordination (CO) is a family of multivariate statistical methods that optimize the fit of abundance data for species in sample plots to one or a set of explanatory (constraining) variable(s), under the assumption that variation in species abundance along the constraining variable(s) gradients is in accordance with a given species response model (ter Braak & Prentice 1988). The fit of data to an explanatory variable (provided the response model is appropriate) is measured by the eigenvalue of the CO axis (ter Braak 1986, 1987, Borcard et al. 1992. Eigenvalues corresponding to different constraining variables, measured in the same set of sample plots, may thus be compared (Rydgren 1994, Økland & Eilertsen 1994, Aude & Lawesson 1998, Økland 1999. Furthermore, constrained ordination is likely to be suited for finding the combination of singletree influence index parameters that optimizes the fit to species abundance data (Øk-land et al. 1999).Every CO method is derive...