The Distribution of Epiphytes on Tropical Trees

A frequent problem in ecology is determining whether the observed spatial distribution of a plant species can be attributed to a completely random spatial process. Usually the analysis of these data is simplified by the fact that the locations of the plants are the two-dimensional coordinates in a rectangular region. This paper considers a more difficult problem of assessing the spatial pattern of points that lie on a tree structure. The application in this work involves the distribution of a type of epiphyte found in the crowns of a group of tropical trees. These methods, however, are not limited to biological trees and could be useful for the spatial analysis of other treelike structures or networks. A tree structure imposes complicated constraints on the three-dimensional relationships among different points on the network. For this reason it is not possi~le to obtain simple. analytical expressions for testing statistical hypotheses about the spatial distribution of the observed data. The basic idea behind our approach is to use Monte Carlo simulation of point patterns to test for spatial randomness in the observed data. One advantage of this approach is that it can handle spatial statistics that may be very relevant for a particular problem but may be too complicated to work with analytically. Our spatial analysis of the bromeliads' distributions in tree crowns yields surprising results. The distribution of plants on different trees appear to depart from a completely random (uniform) pattern both in the direction toward clustering and also toward hyperdispersion (regularity). These results suggest that there may be other factors besides the basic tree architecture that influence the distribution of epiphytes within tree crowns. The analysis of the spatial distribution of epiphytes in tree crowns requires detailed knowledge of the three-dimensional structure of the tree crown and we believe this is the first instance where the structure of standing trees has been mapped. Because of the novelty of these data some discussion is given on the statistical issues of converting pairs of transit sitings to an xyz coordinate system. Often botanical and ecological questions can be formulated in terms of the presence or absence of spatial patterns. These data typically involve the positions or quadrat counts over a two-dimensional rectangular region and many statistical methods have been developed for interpreting such data (Ripley 1981, Diggle 1983). This article considers the extension of these methods to analyze spatial point patterns that are …