# Experiments and Agent Based Models of Zooplankton Movement within Complex Flow Environments

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## Abstract

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## 1. Introduction

## 2. Methods

#### 2.1. Relevant Dimensionless Numbers

#### 2.2. Macrophyte Models

#### 2.3. Flow Tank Set Up

#### 2.4. Measurements of Flow

#### 2.4.1. Particle Image Velocimetry

#### 2.4.2. Computational Fluid Dynamics

#### 2.5. Dispersal Experiments

#### 2.5.1. Preparation of Artemia Larvae

#### 2.5.2. Injection of Brine Shrimp into the Flow Tank

#### 2.5.3. Recording Dispersal of Plankton

#### 2.5.4. Processing Recordings

#### 2.6. Agent-Based Modeling (ABM) Framework: Planktos

- VTK-based import of 2D or 3D time-dependent fluid flow data and flow interpolation between grid points
- Fluid flow tiling with periodic boundary conditions to expand the domain
- Selection of boundary conditions for agents
- 2D and 3D plotting of agent movement, including summary statistics and density histograms

#### 2.7. Agent-Based Simulation and Experimental Results

## 3. Results

#### 3.1. Flow Fields

#### 3.1.1. Validation of COMSOL Results

#### 3.1.2. Flow Dependence on Cylinder Density and Height

#### 3.2. Artemia Concentration over Time

#### 3.3. Shelter Effect of Macrophyte Models

#### 3.4. Agent Based Model Results

## 4. Discussion

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Experimental set up of submerged macrophyte models in the flow tank: (

**a**) the view of flow tank setup from side; and (

**b**) the view of flow tank from above. Flow tank is 100 cm (L) × 8 cm (W) × 8 cm (H).

**Figure 2.**Position of laser sheet for the empty tank (

**a**) and the cylinder models (

**b**). Light and dark green lines denote the position of the laser at different times. The vertical dashed-dotted line is the y-axis. Dashed-dotted horizontal lines represent the x-axis for each setup. Red dashed-lines denote the beginning and the end the region that the camera can capture for PIV. The dark blue arrow shows the direction of flow during PIV measurements.

**Figure 3.**Computational domain for COMSOL fluid physics simulations. The domain represents the experimental setup in the flow tank and is an 80 mm × 640 mm × 80 mm box. Parabolic inflow conditions and zero pressure outflow conditions are used. No slip conditions were used elsewhere.

**Figure 4.**Larvae injector with a modified tip design: (

**a**) the injector was constructed using a 1-mL insulin injector, 65-mm and 10-mm sections of aquarium tubing with 5 mm diameter, a straight 45-mm plastic straw piece, a 19-mm bendy section of the straw, and the tip of a 3-mL pipette that has an opening that is 2 mm in diameter and 35 mm in length; (

**b**) the complete injector as assembled; and (

**c**) flow tank setup for the dispersal experiments. The injector was positioned immediately upstream of the macrophyte model. Green and blue rectangles denote the green and blue zones, respectively, where the concentrations of brine shrimp were recorded. A circular diffuser and LED panel wrapped in plain paper to serve as a diffuser were placed above and below the tank immediately after the model.

**Figure 5.**The x-component of the velocity as a function of height taken along a vertical line positioned in the middle of the model for the COMSOL simulation (solid line) and experiment (dashed line): (

**a**) the flow profiles with no model; and (

**b**) the profiles with the 10 × 20 2-cm model.

**Figure 6.**Velocity magnitude of the flow through models of varying cylinder density: (

**A**) the velocity magnitude in mm/s taken in a vertical plane tangential to the direction of flow and through the center of the tank; and (

**B**) the velocity magnitude in a horizontal plane 1 cm above the bottom of the tank. The models considered include: (i) no model; (ii) 8 × 15 cylinders; (iii) 10 × 20 cylinders; and (iv) 15 × 30 cylinders.

**Figure 7.**Velocity magnitude of the flow through models of varying cylinder height: (

**A**) the velocity magnitude in mm/s taken in a vertical plane through the center of the tank; and (

**B**) the velocity magnitude in a horizontal plane 1 cm above the bottom of the tank. The models considered include the 10 × 20 model with cylinder height equal to: (i) 1 cm; (ii) 2 cm; and (iii) 3 cm.

**Figure 8.**Streamlines showing the flow trajectories through the 10 × 20 model that is 2 cm in height. The color of the streamline corresponds to the velocity magnitude: (

**A**) side view showing the magnitude and direction of flow through the cylinders using streamlines seeded in the vertical plane parallel to flow; (

**B**) top view of streamlines that start at the midpoint of the cylinders in the z-direction along a horizontal line; and (

**C**) the same streamlines as (

**B**) in side view.

**Figure 9.**Normalized brine shrimp count over time in the green (left) and blue (right zones). Each panel shows models of the same height, namely: 1-cm cylinders (

**a**,

**b**); 2-cm cylinders (

**c**,

**d**); and 3-cm cylinders (

**e**,

**f**). The solid black lines show results for the no model case. Blue dotted-dashed lines, red dashed lines, and green dotted lines are for the 8 × 15, 10 × 20, and 15 × 30 models, respectively.

**Figure 10.**Box plots showing the mean (red dot), median (red line), upper and lower quartiles, and minimum and maximum of the distributions shown in Figure 9. Note that these statistics describe the typical times from the start of the experiment when the brine shrimp appear in the green (left) and blue (right) zones. The panels show cylinder heights set equal to: 1 cm (

**a**,

**b**); 2 cm (

**c**,

**d**); and 3 cm (

**e**,

**f**).

**Figure 11.**Sheltered region formed downstream of the macrophyte models. The red rectangle is a symbolic depiction of the sheltered region. This sheltered region begins at the downstream end of the macrophyte model and continuous downstream of the model. “L” is the length of the sheltered region, and it varies with the density and height of the macrophyte model.

**Figure 12.**The average arrival time vs. cylinder height for agents in the simulations into: the green zone (

**left**); and blue zone (

**right**).

**Table 1.**Statistics for the timing of brine shrimp agents entering the green zone by model. All values are given in units of seconds, and both skewness and kurtosis are calculated as Pearson standardized moments.

Mean | Median | Mode | Std | Skewness | Kurtosis | |
---|---|---|---|---|---|---|

plate | 10.26556 | 7.60 | 4.8 | 6.644776 | 1.577448 | 5.648092 |

8 × 15_1 cm | 16.60715 | 11.80 | 7.1 | 12.855364 | 1.867912 | 7.226498 |

8 × 15_2 cm | 16.34799 | 12.80 | 7.1 | 10.679333 | 1.703749 | 6.641543 |

8 × 15_3 cm | 14.50401 | 11.40 | 5.4 | 9.753728 | 1.685753 | 6.397291 |

10 × 20_1 cm | 16.60729 | 11.80 | 7.1 | 12.855351 | 1.867895 | 7.226457 |

10 × 20_2 cm | 24.37854 | 20.55 | 15.9 | 12.792898 | 1.755368 | 7.025288 |

10 × 20_3 cm | 20.02696 | 16.80 | 11.0 | 10.779727 | 1.657012 | 6.375421 |

15 × 30_1 cm | 25.48717 | 15.20 | 7.5 | 29.562239 | 3.637440 | 21.971364 |

15 × 30_2 cm | 53.94625 | 35.00 | 20.3 | 51.528729 | 2.332308 | 9.424739 |

15 × 30_3 cm | 53.52796 | 51.20 | 48.6 | 23.670932 | 0.971755 | 4.696066 |

**Table 2.**Statistics for the timing of brine shrimp agents entering the blue zone by model. All values are given in units of seconds, and both skewness and kurtosis are calculated as Pearson standardized moments.

Mean | Median | Mode | Std | Skewness | Kurtosis | |
---|---|---|---|---|---|---|

plate | 16.73456 | 14.1 | 8.5 | 8.821590 | 1.266366 | 4.496077 |

8 × 15_1 cm | 24.60723 | 19.4 | 12.3 | 15.809911 | 1.596273 | 6.157659 |

8 × 15_2 cm | 28.81300 | 25.1 | 21.7 | 13.554596 | 1.344732 | 5.116872 |

8 × 15_3 cm | 24.74002 | 21.7 | 16.3 | 11.189394 | 1.478259 | 5.706537 |

10 × 20_1 cm | 24.60797 | 19.4 | 12.3 | 15.810498 | 1.596170 | 6.157190 |

10 × 20_2 cm | 46.45774 | 38.0 | 29.0 | 27.945304 | 1.706768 | 6.729241 |

10 × 20_3 cm | 36.81893 | 32.8 | 25.4 | 14.341388 | 1.438209 | 5.511163 |

15 × 30_1 cm | 31.69173 | 20.6 | 12.3 | 31.655163 | 3.339417 | 19.205411 |

15 × 30_2 cm | 65.00588 | 42.2 | 23.5 | 62.218139 | 2.383948 | 9.495929 |

15 × 30_3 cm | 77.31394 | 67.3 | 39.9 | 48.245441 | 2.082177 | 10.752551 |

**Table 3.**Statistics for the timing of brine shrimp agents entering the green zone by diffusivity. All values are given in units of seconds, and both skewness and kurtosis are calculated as Pearson standardized moments.

$2\xb7\mathit{D}$ (mm${}^{2}$/s) | Mean | Median | Mode | Std | Skewness | Kurtosis |
---|---|---|---|---|---|---|

0 | 13.50000 | 13.50 | 13.5 | 0.000000 | 0.000000 | 0.000000 |

0.25 | 34.90953 | 21.40 | 11.5 | 36.072997 | 2.916802 | 13.992966 |

0.5 | 33.21686 | 23.90 | 11.7 | 27.674093 | 2.490382 | 11.650339 |

0.75 | 31.17568 | 23.60 | 12.2 | 23.050775 | 2.357897 | 10.953085 |

1 | 29.57997 | 23.20 | 13.9 | 19.933192 | 2.237405 | 10.726133 |

2.5 | 24.37854 | 20.55 | 15.9 | 12.792898 | 1.755368 | 7.025288 |

5 | 20.75572 | 18.30 | 15.8 | 9.750290 | 1.376773 | 5.397198 |

7.5 | 18.78547 | 17.00 | 13.9 | 8.774293 | 1.223732 | 5.023428 |

10 | 17.39927 | 15.90 | 16.0 | 8.201403 | 1.088226 | 4.535014 |

25 | 13.30244 | 11.90 | 7.3 | 6.887721 | 0.957236 | 3.731665 |

**Table 4.**Statistics for the timing of brine shrimp agents entering the blue zone by diffusivity. All values are given in units of seconds, and both skewness and kurtosis are calculated as Pearson standardized moments.

$2\xb7\mathit{D}$ (mm${}^{2}$/s) | Mean | Median | Mode | Std | Skewness | Kurtosis |
---|---|---|---|---|---|---|

0 | 69.30000 | 69.3 | 69.3 | 0.000000 | 0.000000 | 0.000000 |

0.25 | 85.77890 | 59.9 | 42.1 | 65.286745 | 2.185369 | 8.832309 |

0.5 | 74.05316 | 54.6 | 35.8 | 52.298372 | 2.005044 | 7.897292 |

0.75 | 66.46952 | 50.3 | 33.8 | 45.059692 | 2.005264 | 8.396994 |

1 | 61.38943 | 47.3 | 34.7 | 40.119159 | 1.877701 | 7.387855 |

2.5 | 46.45774 | 38.0 | 29.0 | 27.945304 | 1.706768 | 6.729241 |

5 | 37.13526 | 31.4 | 17.5 | 21.720836 | 1.463269 | 5.702837 |

7.5 | 32.43831 | 27.5 | 21.2 | 19.078510 | 1.347951 | 5.084803 |

10 | 29.31992 | 24.8 | 15.1 | 17.390467 | 1.294047 | 4.795384 |

25 | 21.03663 | 17.3 | 8.8 | 12.828173 | 1.295601 | 4.659608 |

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## Share and Cite

**MDPI and ACS Style**

Ozalp, M.K.; Miller, L.A.; Dombrowski, T.; Braye, M.; Dix, T.; Pongracz, L.; Howell, R.; Klotsa, D.; Pasour, V.; Strickland, C. Experiments and Agent Based Models of Zooplankton Movement within Complex Flow Environments. *Biomimetics* **2020**, *5*, 2.
https://doi.org/10.3390/biomimetics5010002

**AMA Style**

Ozalp MK, Miller LA, Dombrowski T, Braye M, Dix T, Pongracz L, Howell R, Klotsa D, Pasour V, Strickland C. Experiments and Agent Based Models of Zooplankton Movement within Complex Flow Environments. *Biomimetics*. 2020; 5(1):2.
https://doi.org/10.3390/biomimetics5010002

**Chicago/Turabian Style**

Ozalp, Mustafa Kemal, Laura A. Miller, Thomas Dombrowski, Madeleine Braye, Thomas Dix, Liam Pongracz, Reagan Howell, Daphne Klotsa, Virginia Pasour, and Christopher Strickland. 2020. "Experiments and Agent Based Models of Zooplankton Movement within Complex Flow Environments" *Biomimetics* 5, no. 1: 2.
https://doi.org/10.3390/biomimetics5010002