Correcting estimations of copepod volume from two-dimensional images

Accurate plankton biomass estimations are essential to study marine ecological processes and biogeochemical cycles. This is particularly true for copepods, which dominate mesozooplankton. Such estimations can efficiently be computed from organism volume estimated from images. However, imaging devices only provide two-dimensional (2D) projections of three-dimensional objects. The classical procedures to retrieve volumes, based on the equivalent spherical diameter (ESD) or the best-fitting ellipse, are biased. Here, we present a method to correct these biases. First, a new method aims to measure body area and fit an ellipse. Then, the body of copepods is modeled as an ellipsoid whose 2D silhouette is mathematically derived. Samples of copepod bodies are simulated with realistic shapes/sizes and random orientations. Their total volume is estimated from their silhouettes using the two classical methods and a correction factor is computed, relative to the known, total, volume. On real data, individual orientations and volumes are unknown but the correction factor still holds for the total volume of a large number of organisms. The correction is around -20% for the ESD method and + 10% for the ellipse method. When applied to a database of similar to$$ \sim $$ 150,000 images of copepods captured by the Underwater Vision Profiler, the corrections decreased the gap between the two methods by a factor of 54. In addition, the same procedure is used to evaluate the consequence of the bias in the estimation of individual volumes on the slopes of normalized biovolume size spectra and show that they are, fortunately, not sensitive to the bias.