MEPS 273:239-249 (2004)  -  doi:10.3354/meps273239

ABSTRACT: Polarity, group velocity, and inter-individual spacing are characteristics of fish schools that strongly affect individual school members. However, these characteristics are group-level Œemergent properties¹: collective outcomes of behavioral interactions among members, not under direct control of any single member. The relationships between members¹ behaviors and the emergent group properties they produce are complex and poorly understood. In this study, we quantified 3D trajectories of all individual fish within 4- and 8-fish populations of Danio aequipinnatus, using stereo videography and a computerized tracking algorithm. We compared group polarity, group speed, and mean nearest-neighbor distances of schools within these populations to a simulation model that explored how fish responded to attraction/repulsion, alignment and random forces. Real fish exhibited a high degree of temporal variability in both polarity and group speed. Polarity and speed of simulated schools depended very strongly on the strength of the alignment force. Time-averaged polarity of real fish schools was most similar to simulated schools when alignment force was 1 to 5% of the attraction/repulsion force. For both real and simulated fish, a clear relationship existed between group speed and polarity: polarized groups were faster than non-polarized groups. We propose a multi-dimensional state space where several emergent property statistics are represented along the axes, and suggest certain Œpreferred¹ ranges of state space within which animal groups tend to localize, and in which they can sustain distinct types of regular architecture.

KEY WORDS: Social aggregation · Schooling behavior · Emergent properties · Polarity · Group speed · Nearest-neighbor distance · Danio aequipinnatus