A summary of experimental studies that directly estimate the energetic saving of group movement in aerial and aquatic vertebrates that move through a fluid environment.

No energetic measurements have made for freely-moving bird flocks. Three studies measured the energetics of fish schools over a range of narrow speeds; two other studies measured the energetics of fish schooling at one speed. But no studies have quantified both the aerobic and anaerobic energetic cost of swimming as a group compared to solitary locomotion.

A summary of biomechanical principles underlying proposed hydrodynamic advantages of schooling behaviour in fish.

When fish swim into free-stream flow (Ufs), experimental data show that fish schools are dynamic with fish changing position frequently. Regardless of fish position within a school and changes in relative position, theoretical and robotic analyses have demonstrated at least four mechanisms (indicated by numbers) provide an advantage in the form of reduced power consumption. 1. Reduced oncoming velocity (U2) requires less thrust for a fish swimming in the wake between two leading fish (6); 2. The Knoller-Betz effect of leading edge suction reduces costs for a trailing fish due to accelerated oscillating flow at the head (U1) (22) (67); 3. Added mass “push” from follower to leader can reduce costs for the leader in front of another fish (68) (21) (67); 4. Wall effects benefit neighbouring fish where swimming next to another fish reduces swimming costs (69) (18). These principles suggest that regardless of the relative positions of the individuals within the fish school, the fish school as a collective unit should be able to save metabolic energy.

Measurements of aerobic and anaerobic locomotor cost of fish schools and solitary fish.

(A) Average traces of metabolic rate (ṀO2) of fish schools over a 40-hour experiment. Following the first 18-h quiescent state, a critical swimming speed (Ucrit) test quantifies the aerobic cost of active swimming. The ensuing 18-h measurement of excess post-exercise oxygen consumption (EPOC) quantifies the anaerobic cost. (B) Comparison of ṀO2 for conditions of aggregating behaviour, minimum demand speed, and resting condition with the minimal flow (ṀO2aggregate, ṀO2min, ṀO2rest) (C) Comparisons of J-shaped ṀO2-speed curve over the entire range (0.3–8 body length s-1, BL s-1) and (D) U-shaped ṀO2-speed curve at the lower speeds (0.3–3 BL s-1). (E, F) Percentage (%) aerobic scope used by fish schools and solitary fish during the Ucrit test. (G, H) Comparisons of EPOC and EPOC durations between fish schools and solitary fish. Statistical significance is denoted by asterisk(s). Green colour = school data (n=5); blue colour = solitary fish data (n=5); shading indicates the 95% confidence interval. Statistical details are available in the statistical analyses section.

Modeling of simultaneous aerobic and non-aerobic costs of fish schools and solitary fish for a critical swimming speed (Ucrit) test.

(A) Modeling the O2 cost of the metabolic rate (ṀO2)-speed curve and the ensuing recovery cost (excess post-exercise oxygen consumption, EPOC) as a function of speed. After Ucrit, fish returned to the same resting ṀO2 (ṀO2rest) as a pre-test. (B, C) In addition to ṀO2 (solid line & filled symbols), we modeled the total O2 cost (dash line & half-filled symbols) for fish schools and solitary fish and when performing the Ucrit swimming test. The estimated partitioning of aerobic and non-aerobic contributions to swimming are denoted (red-&-bold) with respect to speed for 4–8 BL s-1 is shown below each graph. (D, E) Using total O2 cost, we computed total energy expenditure (10-min period per point) and the total cost of transport (including both aerobic metabolism, high-energy phosphate, and anaerobic glycolysis) for both fish schools and solitary fish. Statistical significance is denoted by asterisk(s). Green colour = school data (n=5); blue colour = solitary fish data (n=5); shading indicates the 95% confidence interval. See methods for modeling and statistical details.

Three-dimensional characterization of swimming kinematics and fish schooling dynamics as a function of speed.

(A) Total energy expenditure per tail beat, (B) Tail beat frequency, (C) The angle of fish to free-stream water flow, measured as the mean and the S.D. of the angles of the individuals within the school. (D) Three-dimensional angle of fish to the frontal plane. (E) Turning frequency, (F) Three-dimensional school length. (G) Three-dimensional distances among all individuals in the school and the S.D. of the distance. The visual illustrations of the upper and lower boundaries of the metrics are indicated. Statistical significance is denoted by asterisk(s). Green colour = school data (n=3-4); blue colour = solitary fish data (n=3-4); shading indicates the 95% confidence interval. See methods for details of three-dimensional reconstruction and statistics.