Concepts of aggregation and their quantification: A critical review with some new results and applications

Summary Various indices of spatial patterns based on plot counts are reviewed for theoretical population models appropriate to ecological studies. It is seen that many of the indices proposed in the literature are essentially equivalent to either the index ω= σ²/μ or to the index γ= (σ²-μ)/μ², thus providing a variety of motiviations and interpretations of these two indices as measures of spatial patterns. A vector approach to measuring spatial patterns which suggests both a unifying relationship between these indices and an extension of them is proposed. This leads to an interpretation of the measures of spatial patterns in terms of the transition probabilities of a pure birth process. Part of a Doctoral Dissertation of the junior author at the Pennsylvania State University.