The use of radial distribution and pair-correlation functions to analyze and describe biological aggregations

Abstract

Patterns are pervasive in nature with many examples being found in both living and inanimate systems. While researchers recognize the importance of the behavior of individuals to the structure and shape of an aggregation, a major hurdle in describing aggregated organisms has been the difficulty of tracking the movement of individuals over time. Here we present an innovative application of an analytical technique derived from statistical mechanics (a subfield of physics) to describe the spatial distribution of grouped organisms. Radial distribution and pair-correlation functions are traditionally used by physicists to describe inert particle dynamics. This novel biological application allows one to infer the behavioral characteristics of individuals within a group based solely on the spatial distribution of the aggregate population. Additionally, the method allows one to determine the correlation length, the average maximum distance over which one individual may exert an influence on another member of the aggregation. The analytical technique presented here is also important in that it minimizes two problems that typically plague studies of grouped organisms: it eliminates the need to track the movements of individuals, and it partially takes into account the presence of occluded individuals. This technique also permits quantitative comparison between aggregations formed under various environmental and/or experimental conditions. Thus, this technique may be of value to resource managers, ecologists, and others working with grouped organisms (e.g., plankton swarms, schooling fish, flocking birds, or migratory mammals) who seek to gain information about factors influencing the structure and behavior of such groups.