Larval Volume Quantification in Stylophora pistillata

LAB PROTOCOL — Larval Volume Quantification in Stylophora pistillata, reasonable logic.

Version: May 7, 2026

1. Rationale and Geometric Model Selection

Direct measurement of three-dimensional volume in microscopic, motile marine larvae is technically challenging. While many studies traditionally use a prolate spheroid (ellipsoid) model, this research utilizes the Capsule Model (also known as a Spherocylinder) for the following reasons:

  1. Vermiform Morphology: S. pistillata planulae exhibit a worm-like (vermiform) shape characterized by a cylindrical midsection and hemispherical ends. The capsule model captures the “shoulders” of the larva more accurately than an ellipsoid, which tapers too sharply and underestimates volume.
  2. Flexion Robustness: Live planulae constantly flex and contract. By deriving dimensions analytically from Area ($A$) and Perimeter ($P$) rather than simple linear length/width, the calculated volume remains robust even if the specimen is curved during imaging.
  3. Physiological Normalization: Precise volume is a prerequisite for calculating mass-specific metabolic rates (e.g., $nmol\ O_2 \cdot mm^{-3} \cdot h^{-1}$), ensuring that metabolic differences are due to physiology and not just size variation.

2. Morphometric Data Acquisition

2.1 Image Acquisition

  • Larvae are imaged using a calibrated stereoscope (e.g., ZEISS Stemi 305 with Axiocam 208).
  • Ensure larvae are swimming freely in a shallow dish to allow for natural horizontal orientation.

2.2 Measurement via ImageJ/Fiji

  1. Calibration: Set the global scale using a stage micrometer image (e.g., 272 pixels = 200 $\mu m$).
  2. Manual Tracing: Use the Freehand Selection tool to trace the precise 2D boundary of the planula.
  3. Data Export: Execute the Measure command to obtain the projected Area ($A$ in $\mu m^2$) and Perimeter ($P$ in $\mu m$).

3. Mathematical Derivation

The planula is modeled as a cylinder of length $l$ and radius $r$, capped by two hemispheres.

Step 1: Solving for Radius ($r$)

The relationship between the 2D projection and the 3D shape is defined by the following system: \(P = 2\pi r + 2l\) \(A = \pi r^2 + 2rl\)

Solving the quadratic system for $r$: \(r = \frac{P - \sqrt{P^2 - 4\pi A}}{2\pi}\)

Step 2: Calculating cylindrical length ($l$)

Once $r$ is determined, the length of the cylindrical section is: \(l = \frac{P - 2\pi r}{2}\)

Step 3: 3D Volume Calculation ($V$)

The total volume is the sum of the cylinder and the two hemispheres (one sphere): \(V = \pi r^2 l + \frac{4}{3} \pi r^3\)

Note: Final values are converted from $\mu m^3$ to $mm^3$ ($V_{mm^3} = V_{\mu m^3} / 10^9$) for standard reporting.

4. Quality Control (QC) & Outlier Filtering

4.1 Orientation Filter (Aspect Ratio)

Projected 2D images suffer from “foreshortening” if the larva is tilted in the Z-axis (pointing toward the camera).

  • Metric: Aspect Ratio ($AR$) = Total Length ($l+2r$) / Width ($2r$).
  • Threshold: Only planulae with an $AR \ge 2.5$ are retained.
  • Justification: Low aspect ratios indicate a “rounded” appearance caused by vertical tilting, which leads to significant underestimation of the actual volume.

4.2 Statistical Outlier Removal

To ensure the data follows a normal distribution for parametric testing:

  1. Apply the 1.5 $\times$ Interquartile Range (IQR) rule to remove extreme biological outliers within each morph and year.
  2. Verify normality for each group using the Shapiro-Wilk test ($p > 0.05$).

5. Statistical Analysis

Because biological variance often differs between morphs (heteroscedasticity), a Weighted Two-Way ANOVA is employed using spawning year and larval morph as fixed factors. Weights are defined as the inverse of the group variance ($1/\sigma^2$). This model evaluates the consistency of morph-specific size differences across independent spawning seasons.

Written on May 7, 2026