Hidden Sampling Gaps Skew Plankton Models, Study Warns

Zooplankton may be small, but they carry the weight of the ocean’s food web on their translucent shoulders. These drifting animals form the critical trophic bridge between the microscopic phytoplankton that fuel marine primary production and the fish, seabirds, and whales that depend on them, while also playing a central role in the biological pump that exports carbon from the surface ocean to the deep sea. Getting their abundance estimates right is therefore not a niche statistical concern but a foundational requirement for understanding how marine ecosystems respond to a changing climate. A new study published in Discover Oceans argues that one of the most common tools in the plankton ecologist’s statistical toolbox may be quietly distorting the very patterns scientists are trying to detect.

The research, led by Yulia Egorova of the University of Miami’s Rosenstiel School of Marine, Atmospheric, and Earth Science together with statisticians and oceanographers at the University of British Columbia, focuses on a deceptively simple question: how should scientists model the abundance of calanoid copepods, one of the most widespread groups of zooplankton in the world’s oceans? The team’s answer carries a warning for the field. When datasets combine samples collected over different vertical depth intervals, the resulting differences in measurement precision can quietly reshape which environmental relationships appear statistically significant, and which fade into uncertainty.

The problem begins with how zooplankton are actually collected. Research vessels tow nets through the water column, and the vertical extent covered by each tow, known as the sampling bin width, varies widely between surveys and even between stations on the same cruise. A net hauled through a 400 to 600 meter layer integrates a much smaller volume of water than one dragged from 300 to 700 meters. Although abundance is routinely standardized to volumetric units of individuals per cubic meter, this standardization does not eliminate the underlying difference in precision. A wide bin blends several distinct vertical habitats, each with its own temperature, oxygen regime, and copepod concentration, into a single averaged number, making that number inherently less consistent than an estimate from a narrow, focused interval.

Compounding this design issue is a long-standing habit in biological oceanography: log-transforming abundance data before fitting standard Gaussian linear models. Because volumetric abundance is strictly positive and strongly right-skewed, with most values clustering below one individual per cubic meter and a few extreme values reaching four, researchers have long reached for the logarithm to make the data look more normally distributed. Statisticians have cautioned for years that this transformation can bias inference and obscure how results depend on distributional assumptions, yet the practice remains entrenched in the zooplankton literature.

To test whether these conventions hold up under scrutiny, the team assembled 867 sampling records from 1987 in the waters surrounding the Kerguelen Islands in the Southern Ocean, drawn from the Mesopelagic Mesozooplankton and Micronekton Database. The records covered five dominant calanoid species, including Rhincalanus gigas, Metridia lucens, Calanus simillimus, Pleuromamma robusta, and Ctenocalanus vanus, matched to environmental conditions from the World Ocean Atlas 2018. After screening for multicollinearity among candidate predictors, temperature and average sampling depth, along with their interaction, were retained as the key covariates, with salinity and dissolved oxygen excluded due to strong correlations with depth and with each other.

The researchers then compared four statistical frameworks: a Gaussian model fitted to log-transformed abundance, reflecting conventional practice, and three generalized linear models fitted directly to the original abundance scale assuming log-normal, Gamma, and inverse Gaussian error distributions. Model selection using the generalized Akaike information criterion, with a Jacobian correction to place all models on a common response scale, identified the inverse Gaussian model as the clear winner. Its variance structure, in which variability grows with the cube of the mean, proved best suited to data where dense copepod aggregations are far less predictable than sparse observations. The inverse Gaussian model outperformed the alternatives by a substantial margin, and the log-normal and Gamma models failed to improve on the transformed Gaussian baseline.

But choosing the right error distribution was only half the story. The team extended the best-performing model using generalized additive modeling for location, scale and shape functionality, allowing the dispersion parameter to vary as a function of normalized sampling bin width. This single change improved model fit further and, crucially, altered the ecological conclusions. The temperature-by-depth interaction, which was statistically significant in the constant-dispersion model with a p-value of 0.0023, became non-significant once bin-width-dependent precision was included, with the p-value rising to 0.0657. In contrast, the negative relationship between copepod abundance and depth remained robust throughout, with coefficient estimates changing only marginally and standard errors staying small.

The quantification of the bin-width effect is striking: for every additional 100 meters of sampling depth interval, the residual spread around predicted abundance increased by approximately 15.4 percent. In the study dataset, bin widths ranged across 31 unique intervals from 195 to 537 meters, a level of heterogeneity that is far from unusual in compiled zooplankton databases. The authors suggest that wider bins integrate multiple vertical habitats containing different environmental conditions and copepod concentrations, reducing vertical resolution and producing less consistent abundance estimates. Ignoring this heterogeneity, they argue, can overstate confidence in weaker covariate effects, potentially leading researchers to report environmental relationships that are artifacts of unequal sampling resolution rather than robust biological patterns.

A leave-one-out sensitivity analysis, refitting the final model 867 times after deleting each observation in turn, strengthened confidence in the core findings. The negative depth effect and the positive bin-width effect in the dispersion model were never rendered non-significant by the removal of any single observation, and the temperature main effect remained non-significant throughout. The temperature-by-depth interaction proved more fragile: deleting seven of the 867 observations pushed its p-value below 0.05, although the interaction coefficient stayed positive in every refit. The most influential cases were observations with large positive residuals, primarily from Rhincalanus gigas and Calanus simillimus. The authors recommend treating the interaction as a tentative ecological hypothesis rather than a firm conclusion.

The implications extend well beyond Southern Ocean copepods. The authors suggest that the approach is likely applicable to any ecological dataset with a positive, right-skewed response collected under unequal sampling effort or integration scales, including benthic abundance indexed by sampled area and environmental DNA concentrations indexed by processed volume. They emphasize that allowing dispersion to depend on covariates is established statistical functionality rather than a new model class; the novelty lies in using sampling bin width, a feature of survey design, as a predictor of precision. The team cautions that their conclusions are limited to the four candidate frameworks and the single-year dataset evaluated, and that validation across other regions, years, taxa, and comparisons with weighting schemes, measurement-error models, and hierarchical formulations remain important future directions. For now, the message to marine ecologists is clear: the depth intervals printed in the methods section of a survey report may matter as much as the environmental variables in the analysis itself.

The setting of the study itself adds ecological weight to its methodological message. The Kerguelen Islands sit within the circumpolar Southern Ocean, where the surrounding waters are among the most productive in the region, supporting food webs that include krill, seabirds, and marine mammals. Copepods such as Calanus simillimus and Rhincalanus gigas dominate the mesozooplankton there, and their vertical distributions shift seasonally and with life stage, which is precisely why the depth interval covered by a net tow shapes both what is captured and how precise the resulting estimate can be. In waters where abundance declines steeply with depth, averaging across a broad vertical slab blurs real ecological structure into a single number.

The inverse Gaussian distribution, the best-supported error structure in the comparison, has a long history in statistics. It describes positive, right-skewed data in which the variance grows steeply with the mean, a pattern familiar from physics and reliability engineering before its adoption in ecology. Its arrival as the top candidate for copepod abundance is biologically intuitive: sparse plankton samples are relatively predictable, while dense aggregations, which arise from swarming behavior and patchy advection, are far more variable. Distributions such as the Gamma allow variance to scale linearly with the mean, which evidently understates this heterogeneity in the Kerguelen data.

The environmental covariates came from the World Ocean Atlas 2018, a gridded climatological product built from decades of ship-based measurements. Matching atlas values to individual plankton records by location and mean sampling depth is standard practice, but it introduces its own smoothing, since the atlas represents long-term average conditions rather than the water properties a net actually encountered on a given day. The authors noted that temperature and depth were retained after screening out salinity and dissolved oxygen, which were strongly correlated with depth and with each other, a common multicollinearity problem in oceanographic datasets.

The reliance on a single year, 1987, deserves emphasis. That year supplied the largest eligible sample in the source database by a wide margin, which made it attractive for a methodological comparison but leaves open whether the same error structure and dispersion behavior hold in other years or across seasonal cycles. Interannual variability in Southern Ocean zooplankton is substantial, and the authors themselves frame validation across regions, years, and taxa as the necessary next step before their recommendations become general guidance.

Subject of Research: Statistical modelling of zooplankton abundance accounting for error distribution choice and sampling depth bin width

Article Title: How error distribution and sampling depth strata affect plankton abundance modelling

Article References: Egorova, Y., Tamvada, N., Forrest, D., Pakhomov, E. A., & Auger-Méthé, M. (2026). How error distribution and sampling depth strata affect plankton abundance modelling. Discover Oceans, 3(1), Article 53. https://doi.org/10.1007/s44289-026-00166-w

Image Credits: AI Generated

DOI: 10.1007/s44289-026-00166-w

Keywords: zooplankton, copepods, generalized linear models, inverse Gaussian distribution, heteroscedasticity, sampling bin width, Kerguelen Islands, Southern Ocean, log-transformation, dispersion modelling, marine ecology, statistical inference