Emergent collective dynamics from motile photokinetic organisms

TL;DR

This paper develops a three-dimensional agent-based model to understand how individual photokinetic behaviors of aquatic organisms lead to diverse vertical migration patterns, revealing key regimes influenced by motility and light bias.

Contribution

It introduces a novel mechanistic framework linking individual swimming behaviors and environmental light cues to population-scale diel vertical migration patterns.

Findings

Four distinct migration regimes identified: Surface Accumulation, Shallow DVM, Deep DVM, Sinking.

Regimes governed by Peclet number and vertical swimming bias W.

Upward bias promotes surface aggregation; downward bias causes sinking.

Abstract

The day-night cycle drives the largest biomass migration on Earth: the diel vertical migration (DVM) of aquatic organisms. Here, we present a three-dimensional agent-based model that incorporates photokinesis, gyrotaxis, and stochastic reorientation to explore how individual-level swimming behaviors give rise to population-scale DVM patterns. By solving Langevin equations for swarms of swimmers, we identify four distinct regimes -- Surface Accumulation, Shallow DVM, Deep DVM, and Sinking -- governed by two key dimensionless parameters: the Peclet number (Pe), representing motility persistence, and the vertical swimming asymmetry ratio (W=wdown/wup), encoding photokinetic bias. These regimes emerge from nonlinear interactions between light-driven navigation and active noise, diagnosed through topological and statistical features of vertical distributions. A critical feedback is uncovered: upward-biased swimming (W<1) promotes surface aggregation, while excessive downward bias (W>1) leads to irreversible sinking. Analytical estimates link regime boundaries to gyrotactic alignment and velocity reversals. Together, our results provide a mechanistic framework to interpret DVM diversity and emphasize the central role of light gradients-beyond absolute intensity-in shaping ecological self-organization.