# How Big Is That Manta Ray? A Novel and Non-Invasive Method for Measuring Reef Manta Rays Using Small Drones

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Data Collection

#### 2.3. Image Processing and Measurements

#### 2.4. Demographic Parameters

#### 2.5. Statistical Analysis

## 3. Results

#### 3.1. Measurement Summary, Accuracy, and Precision

#### 3.2. Relationships between Measured Dimensions

#### 3.3. Using the Model to Predict Unmeasured DW from Other Measured Dimensions

#### 3.4. Size at Maturity and Evidence of Sexual Dimorphism

## 4. Discussion

#### 4.1. Accuracy and Measurement Methods

#### 4.2. Allometric Growth, Size at Maturity and Sexual Dimorphism

#### 4.3. Limitations of the Methodology

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

#### Appendix A.1. True Measurements

#### Appendix A.2. Measurement Error

#### Appendix A.3. Model Parameters

- $\mathit{\mu}=\left({\mathit{\mu}}_{1},\cdots ,{\mathit{\mu}}_{G}\right)$, where ${\mathit{\mu}}_{g}$ contains the underlying population means of the morphometric dimensions for the $g$th group;
- $\mathit{\sigma}=\left({\mathit{\sigma}}_{1},\cdots ,{\mathit{\sigma}}_{G}\right)$, where ${\mathit{\sigma}}_{g}$ contains the underlying population standard deviations of the morphometric dimensions for the $g$th group;
- $\mathit{\rho}=\left({\mathit{\rho}}_{1},\cdots ,{\mathit{\rho}}_{G}\right)$, where ${\mathit{\rho}}_{g}$ contains underlying population correlations between all pairs of morphometric dimensions;
- $\mathit{\psi}$ containing underlying standard deviations of the measurement errors for each of the $m$ dimensions; and
- $\mathit{\varphi}$ containing underlying correlations between measurement errors of all morphometric dimensions.

#### Appendix A.4. Relationships between Dimensions

#### Appendix A.5. Parameter Estimation

## References

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**Figure 1.**Three dimensions (disc width—DW, disc length—DL, and cranial width—CW) of M. alfredi measured during image processing, as defined by Notarbartolo Di Sciara [15].

**Figure 3.**Surface-feeding (

**A**) mature chevron female and (

**B**) melanistic unsexed individual M. alfredi and the 2-m floating black-and-white PVC reference pipe as observed from a drone (research boat also visible in frame).

**Figure 4.**A mature chevron male M. alfredi (

**left**) with claspers (white coloration) extended beyond pelvic fins and a mature chevron female (

**right**) with mating scars (black-and-white marks) on her left wing.

**Figure 6.**Correlation between each pairing of disc width (DW), disc length (DL), and cranial width (CW) for all individual M. alfredi measured using drones and estimated using our model. Black circles represent estimated measurements of each manta ray; horizontal and vertical lines crossing the circles represent the confidence intervals of estimated true measurements of each individual.

**Figure 7.**Correlations between DW and DW:DL, DW:CW, and CW:DL ratios of M. alfredi measured using drones.

**Figure 8.**The estimated true measurements of DW predicted using a single drone measurement of CW (red) and drone measurements of both CW and DL (blue) with 95% confidence intervals shown from 13 individuals measured from drones.

**Figure 9.**Estimated mean DW (in cm) with 95% confidence intervals of sexually mature female (n = 8; solid red circle with CI) and male (n = 30; solid blue circle with CI) M. alfredi measured using drones and estimated by our model. The transparent circles represent the estimated true measurements of the DW of each individual, color-coded by sex.

**Table 1.**Estimates of model parameters, including standard errors (SE), and 95% confidence intervals (CIs) for all individual manta rays combined and for sexually mature males and females separately. The model parameters consisted of population mean ($\mathit{\mu}$) for the dimensions for each demographic group, population standard deviations ($\mathit{\sigma}$) for the dimensions for each demographic group, population correlation between two dimensions ($\mathit{\rho}$) for each demographic group, and standard deviation of measurement error ($\mathit{\psi}$) for each dimension. DW = disc width, DL = disc length, and CW = cranial width.

Demographic Group | Model Parameters | Estimates | Standard Error (SE) | 95% CIs | |
---|---|---|---|---|---|

Lower | Upper | ||||

All manta rays combined (n = 86) | ${\mathit{\mu}}_{\mathrm{DW}}$ | 286.5 | 4.87 | 277.0 | 296.1 |

${\mathit{\mu}}_{\mathrm{DL}}$ | 129.8 | 2.54 | 124.8 | 134.7 | |

${\mathit{\mu}}_{\mathrm{CW}}$ | 74.3 | 1.37 | 71.6 | 77.0 | |

${\mathit{\sigma}}_{\mathrm{DW}}$ | 45.1 | 3.44 | 38.4 | 51.9 | |

${\mathit{\sigma}}_{\mathrm{DL}}$ | 23.5 | 1.79 | 20.0 | 27.0 | |

${\mathit{\sigma}}_{\mathrm{CW}}$ | 12.7 | 0.97 | 10.8 | 14.6 | |

${\mathit{\rho}}_{\mathrm{DW},\mathrm{DL}}$ | 0.99 | 0.003 | 0.982 | 0.993 | |

${\mathit{\rho}}_{\mathrm{DW},\mathrm{CW}}$ | 0.99 | 0.003 | 0.980 | 0.991 | |

${\mathit{\rho}}_{\mathrm{DL},\mathrm{CW}}$ | 0.98 | 0.004 | 0.977 | 0.991 | |

${\mathit{\psi}}_{\mathrm{DW}}$ | 2.16 | 0.07 | 2.01 | 2.30 | |

${\mathit{\psi}}_{\mathrm{DL}}$ | 1.69 | 0.06 | 1.58 | 1.80 | |

${\mathit{\psi}}_{\mathrm{CW}}$ | 1.13 | 0.04 | 1.06 | 1.21 | |

Sexually mature males (n = 30) | ${\mathit{\mu}}_{\mathrm{DW}}$ | 290.1 | 1.7 | 286.9 | 293.4 |

${\mathit{\mu}}_{\mathrm{DL}}$ | 131.1 | 0.9 | 129.3 | 132.8 | |

${\mathit{\mu}}_{\mathrm{CW}}$ | 75.2 | 0.4 | 74.4 | 76.1 | |

${\mathit{\sigma}}_{\mathrm{DW}}$ | 9.0 | 1.2 | 6.7 | 11.3 | |

${\mathit{\sigma}}_{\mathrm{DL}}$ | 4.8 | 0.6 | 3.5 | 6.0 | |

${\mathit{\sigma}}_{\mathrm{CW}}$ | 2.4 | 0.3 | 1.8 | 3.0 | |

Sexually mature females (n = 8) | ${\mathit{\mu}}_{\mathrm{DW}}$ | 353.4 | 4.9 | 343.7 | 363.1 |

${\mathit{\mu}}_{\mathrm{DL}}$ | 167.3 | 3.1 | 161.2 | 173.3 | |

${\mathit{\mu}}_{\mathrm{CW}}$ | 93.5 | 1.7 | 90.1 | 96.9 | |

${\mathit{\sigma}}_{\mathrm{DW}}$ | 13.9 | 3.5 | 7.1 | 20.8 | |

${\mathit{\sigma}}_{\mathrm{DL}}$ | 8.7 | 2.2 | 4.4 | 13.0 | |

${\mathit{\sigma}}_{\mathrm{CW}}$ | 4.8 | 1.2 | 2.4 | 7.2 |

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## Share and Cite

**MDPI and ACS Style**

Setyawan, E.; Stevenson, B.C.; Izuan, M.; Constantine, R.; Erdmann, M.V.
How Big Is That Manta Ray? A Novel and Non-Invasive Method for Measuring Reef Manta Rays Using Small Drones. *Drones* **2022**, *6*, 63.
https://doi.org/10.3390/drones6030063

**AMA Style**

Setyawan E, Stevenson BC, Izuan M, Constantine R, Erdmann MV.
How Big Is That Manta Ray? A Novel and Non-Invasive Method for Measuring Reef Manta Rays Using Small Drones. *Drones*. 2022; 6(3):63.
https://doi.org/10.3390/drones6030063

**Chicago/Turabian Style**

Setyawan, Edy, Ben C. Stevenson, Muhamad Izuan, Rochelle Constantine, and Mark V. Erdmann.
2022. "How Big Is That Manta Ray? A Novel and Non-Invasive Method for Measuring Reef Manta Rays Using Small Drones" *Drones* 6, no. 3: 63.
https://doi.org/10.3390/drones6030063