Space-irrelevant scaling law for fish school sizes

Area of Science:

• Ecology
• Statistical Physics
• Marine Biology

Background:

• Understanding the collective behavior of organisms, such as fish schooling, is crucial in ecology.
• Previous studies have observed various patterns in fish school dynamics, but universal scaling laws were not fully established.

Purpose of the Study:

• To establish universal scaling laws in the power-law size distribution of pelagic fish schools.
• To determine the key factors influencing fish school size and their distribution.

Main Methods:

• Utilized data collapse to extract the power-law exponent of fish school size distributions.
• Employed extensive numerical simulations to verify the universality of the observed scaling laws across different spatial dimensions.

Main Results:

• Established a universal power-law scaling for pelagic fish school size distributions.
• Demonstrated that school size distribution depends on the ratio of school size to expected individual engagement size.
• Showed that this expected size is linearly related to the ratio of fish population density to school breakup rate.

Conclusions:

• The established power-law scaling is independent of the spatial dimensions, highlighting a fundamental principle in fish school dynamics.
• The findings provide a robust framework for understanding fish school integrity and collective behavior over time.