Individual behavior and emergent properties of fish schools: a comparison of observation and theory

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 'emergent properties': collective outcomes of behavioral interactions among members, not under direct control of any single member. The relationships between members' 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 'preferred' ranges of state space within which animal groups tend to localize, and in which they can sustain distinct types of regular architecture.

From behavioural analyses to models of collective motion in fish schools

“…In particular, a series of simulation studies have shown that the mean speed of an individual could be considered as an emergent property as well [51,69,74]. In self-propelled particles models, fixed speed implies a direct proportionality between polarization and mean speed of the school.…”

“…An intensification of the modelling and simulation effort over the last decades yield an important collection of models and studies, shedding some light on the complex interplay between the individual and school levels, and subsequent methodological and conceptual issues [51].…”

Automated image-based tracking and its application in ecology

“…Recent break throughs in remote quantification of physical landscapes [58 60] and 3D imaging [29] should be especially helpful for these questions. Second, collective behavior in animal groups [1,26,33,38,40,43,45,62,82,83], including understanding how information about the physical and biological environment transfers between individuals. Generally, this research centers on intraspecific groups comprising large numbers of similar sized individuals.…”

“…Tracking systems designed for 2D can provide some resolution for behavior in a third spatial dimension [34), but ultimately developers must produce tracking systems that can successfully track large numbers of animals in 3D space (Movie S8 in the supplementary material online). Tracking unconstrained flying or swimming animals can be achieved in several ways, but most often multiple cameras are employed [18,29,[35][36][37][38][39][40][41][42][43][44][45] (Movie S6, Movie 88, and Movie S22 in the supplementary material online). Although only two calibrated cameras taking images of the same point in space are required for triangulation, information from additional cameras can incrementally improve localization, especially if some cameras are limited by occlusion or low contrast [18) .…”

Comparing the EthoVision 2.3 system and a new computerized multitracking prototype system to measure the swimming behavior in fry fish

“…The second approach, consisting of the development of mathematical models by computer scientists (Reynolds, 1987), by biologists (Parrish, Viscido, & Grünbaum, 2002;Suzuki, Tsumonu, & Hiraishi, 2003;Viscido, Parrish, & Grünbaum, 2004), or by physicists (Grégoire & Chaté, 2004;Vicsek, Czirók, Ben-Jacob, Cohen, & Shochet, 1995;Vicsek, Czirók, Farkas, & Helbing, 1999) is artificial. It requires a comparison with empirical results to validate and determine the degree of validity for each model.…”