Chapter 13 Schooling

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13.1 Overview

Schooling is an emergent collective behavior in which fish align, cohere, and maintain spacing with nearby conspecifics, increasing hydrodynamic efficiency, predator avoidance, and coordinated migration. Within this model, schooling arises from local interactions among individuals, where agents adjust position, heading, and speed in response to nearby neighbors following the classic behavioral rules of separation, alignment, and cohesion. These rules are consistent with established models of collective fish behavior and agent-based schooling frameworks (Dobon 2018; Reynolds 1987). As a result, group structure, synchronized movement, and cohesion emerge from decentralized decision-making rather than being imposed at the group level, allowing schooling dynamics to adapt to changing environmental conditions during migration.

The schooling behavior in this model is adapted from the publicly available NetLogo model Fish Schooling For Predator Avoidance created by Sebastian Dobon and shared through the NetLogo Modeling Commons. That model implements classic schooling rules from the original BOIDS framework developed by Craig Reynolds in 1987 in his paper Flocks, Herds, and Schools: A Distributed Behavioral Model (Reynolds 1987).

13.2 Purpose

The purpose of this submodel is to simulate collective movement patterns observed in migratory fish where individuals adjust their position and speed based on nearby schoolmates. This mechanism enhances group cohesion during landward or seaward migration and produces emergent school structure, directional alignment, and spacing.

13.3 Entities, State Variables, and Scales

13.3.1 Spatial and Temporal Scales

Spatial Unit: Patch (3 m x 3 m resolution)
Temporal Unit: 5 minute time steps (tick)

13.3.2 Patch Variables

Variable Name	Definition
patch-terrain	Identifies water or land patches

13.3.3 Agent Variables

Variable Name	Definition
breed	Species identity used to restrict schooling to con-specifics
speed	Current swimming speed
min-speed	Lowest allowable swimming speed
start-migration?	Indicates whether the agent has begun migration
landward-migration?	Indicates landward migration mode
seaward-migration?	Indicates seaward migration mode
schoolmates	Set of nearby con-specifics that meet schooling criteria
nearest-neighbor	Closest schoolmate used for spacing and cohesion
minimum-separation	Desired minimum inter-fish spacing

13.4 Process Overview and Scheduling

1. Identify schoolmates based on species identity (categorical) and shared migration state (categorical).

2. Detect the nearest neighbor among schoolmates (distance, patch units, where 1 patch = 3 m).

3. Apply separation when neighbors are too close (threshold distance, patch units).

4. Apply cohesion and alignment when spacing is adequate (distance-based interaction, patch units).

5. Adjust speed to match group speed and maintain coordination (patch units tick⁻¹).

13.5 Design Concepts

Basic Principles: Schooling arises from local interaction rules of separation, cohesion, and alignment, implemented through the schooling and predator avoidance functions(Dobon 2018). These behavioral rules reflect well documented collective dynamics observed in migrating fishes, where individuals maintain group structure while balancing spacing, directional alignment, and coordinated movement.

Emergence: Cohesive schools, spacing patterns, and synchronized direction arise without centralized control.

Adaptation: Agents adjust heading and speed in response to nearby schoolmates.

Sensing
Agents sense species identity, distance to schoolmates, spacing, and local movement direction.

Interaction
Agents change speed and heading based on interactions with neighbors.

Stochasticity
Small random turning angles elsewhere in the model introduce variability in movement.

Collectives
Schools form as dynamic collectives with shared direction and spacing rules.

Observation
School size, spacing, direction, and cohesion may be tracked to evaluate emergent schooling patterns.

13.6 Initialization

Variable	Initialized Value	Justification
speed	species specific	Starting swimming speed
min-speed	species specific	Prevents schools from stopping entirely
schoolmates	empty set	No neighbors until movement begins
nearest-neighbor	none	Determined dynamically during the simulation
minimum-separation	species specific	Prevents collisions and maintains spacing

13.7 Submodels

13.7.1 Identifying Schoolmates

Fish select schoolmates from nearby con-specifics that share the same migration state, including the start of migration and direction (landward or seaward).

13.7.2 Nearest Neighbor

The closest schoolmate is used to determine whether spacing rules or cohesion rules should be applied.

13.7.3 Separation

If the nearest neighbor is closer than the minimum desired separation, the agent turns away to maintain spacing.

13.7.4 Cohesion

When spacing is appropriate, the agent turns toward the group centroid to maintain cohesive structure.

13.7.5 Alignment

The agent aligns its heading with the mean direction of nearby con-specifics to maintain synchronized movement.

13.7.6 Speed Adjustment

Speed is regulated to preserve cohesion within the school:

• The agent accelerates if any schoolmate is significantly faster.
  
• Otherwise, it gradually slows toward the minimum speed.

This produces emergent schooling speeds and prevents fragmentation.

13.8 Netlogo Implementation

;; -------------------------------------------------------------------
;;  SCHOOLING SUBMODEL — VARIABLE DECLARATIONS
;; -------------------------------------------------------------------

patches-own [
  ;; Terrain classification
  patch-terrain          ;; "water" or "land"
]

turtles-own [
  ;; -----------------------------------------------------------------
  ;; Schooling state variables
  ;; -----------------------------------------------------------------
  schoolmates            ;; agentset of nearby con-specifics
  nearest-neighbor       ;; closest fish in schoolmates
  minimum-separation     ;; desired distance to avoid collisions

  ;; -----------------------------------------------------------------
  ;; Migration gating used for schooling eligibility
  ;; (schoolmates only form among agents sharing these states)
  ;; -----------------------------------------------------------------
  start-migration?       ;; has the agent initiated migration?
  landward-migration?    ;; migrating upstream?
  seaward-migration?     ;; migrating downstream?

  ;; -----------------------------------------------------------------
  ;; Swimming parameters affected by schooling
  ;; -----------------------------------------------------------------
  speed                  ;; current swimming speed
  min-speed              ;; lower speed limit to prevent stall
]

;; -------------------------------------------------------------------
;;  SCHOOLING: MAIN CONTROLLER
;; -------------------------------------------------------------------

to school
  find-schoolmates

  if any? schoolmates [
    find-nearest-neighbor

    ;; Separation rule
    ifelse distance nearest-neighbor < minimum-separation
    [
      separate
    ]
    [
      ;; Cohesion + alignment rules
      cohere
      align
    ]

    ;; Adjust speed to maintain cohesion
    adjust-speed
  ]
end


;; -------------------------------------------------------------------
;;  FIND SCHOOLMATES (CON-SPECIFICS + SAME MIGRATION MODE)
;; -------------------------------------------------------------------

to find-schoolmates
  set schoolmates other turtles with [
    breed = [breed] of myself and
    start-migration? and
    landward-migration? = [landward-migration?] of myself and
    seaward-migration? = [seaward-migration?] of myself
  ]
end


;; -------------------------------------------------------------------
;;  FIND NEAREST NEIGHBOR
;; -------------------------------------------------------------------

to find-nearest-neighbor
  set nearest-neighbor min-one-of schoolmates [ distance myself ]
end


;; -------------------------------------------------------------------
;;  SEPARATION RULE (AVOID COLLISION)
;; -------------------------------------------------------------------

to separate
  ;; Turn away from nearest neighbor
  let dx (dx-of nearest-neighbor)
  let dy (dy-of nearest-neighbor)
  rt (random 20 + 160)
  fd 0.1
end


;; -------------------------------------------------------------------
;;  COHESION RULE (TURN TOWARD GROUP)
;; -------------------------------------------------------------------

to cohere
  if any? schoolmates [
    face mean-heading-of schoolmates
  ]
end


;; -------------------------------------------------------------------
;;  ALIGNMENT RULE (MATCH GROUP HEADING)
;; -------------------------------------------------------------------

to align
  if any? schoolmates [
    set heading (heading + (mean [heading] of schoolmates - heading) * 0.1)
  ]
end


;; -------------------------------------------------------------------
;;  SPEED ADJUSTMENT (MAINTAIN COHESION)
;; -------------------------------------------------------------------

to adjust-speed
  ifelse max [speed] of schoolmates > speed + 0.1
  [
    ;; Accelerate to keep up with group
    set speed speed + 0.1
  ]
  [
    ;; Slow down toward minimum speed
    if speed > min-speed [
      set speed speed - 0.2
    ]
  ]
end

References

Dobon, Sebastian. 2018. Netlogo Fish Schooling for Predator Avoidance Model. Northwestern University.

Reynolds, Craig W. 1987. “Flocks, Herds and Schools: A Distributed Behavioral Model.” ACM SIGGRAPH Computer Graphics 21 (4): 25–34. https://doi.org/10.1145/37402.37406.