Improved absolute abundance estimates from spatial count data with simulation and microfossil case studies

Many fundamental parameters of biological systems – eg. productivity, population sizes and biomass – are most effectively expressed in absolute terms. In contrast to proportional data (eg. percentages), absolute values provide standardised metrics on the functioning of biological entities (eg. organisism, species, ecosystems). These are particularly valuable when comparing assemblages across time and space. Since it is almost always impractical to count entire populations, estimates of population abundances require a sampling method that is both accurate and precise. Such absolute abundance estimates typically entail more “sampling effort” (data collection time) than proportional data. Here we refined a method of absolute abundance estimates – the “exotic marker technique” – by producing a variant that is more efficient without losing accuracy. This new method, the “field-of-view subsampling method” (FOVS method) is based on area subsampling, from which large samples can be quickly extrapolated. Two case studies of the exotic marker technique were employed: 1, computer simulations; and 2, an observational “real world” data set of terrestrial organic microfossils from the Permian- and Triassic-aged rock strata of southeastern Australia, spiked with marker grains of known quantity and variance. We compared the FOVS method against the traditional “linear method” method using three metrics: 1, concentration (specimens/gram of sediment); 2, precision and 3, data collection effort. In almost all cases, the FOVS method delivers higher precision than the linear method, with equivalent effort, and our computer simulations suggest that the FOVS method more accurately estimates the true error for large target-to-marker ratios. Since we predict that these conditions are typically common, we recommend the new FOVS method in almost every “real world” case.

💡 Research Summary

**
The paper addresses a fundamental challenge in quantitative biology and earth sciences: obtaining absolute abundance estimates (e.g., productivity, population size, biomass) rather than relative percentages. Absolute values are essential for comparing ecosystems across time and space, yet counting every individual is rarely feasible. Consequently, researchers rely on the “exotic marker technique,” which involves spiking a sample with a known quantity of inert marker particles and then estimating the target abundance from the observed marker‑to‑target ratio.

The traditional implementation, referred to as the “linear method,” samples the entire sediment or substrate along a linear transect, counts markers and targets in each segment, and extrapolates the total abundance. While conceptually straightforward, this approach suffers from two major drawbacks: (1) it assumes homogeneous mixing of markers and targets, leading to bias when this condition is violated, and (2) it requires extensive field effort because the whole sample must be processed, limiting efficiency.

To overcome these limitations, the authors propose a new variant called the “Field‑of‑View Subsampling (FOVS) method.” Instead of treating the sample as a single linear series, the FOVS method partitions the sample into many small, independently observed fields of view (FOVs). Within each FOV, markers and targets are counted, and the counts are then scaled up based on the total surveyed area. This area‑based subsampling yields a larger number of statistically independent observations for the same amount of field work, thereby improving precision without increasing effort.

Two complementary case studies were conducted.

1. Simulation Study – The authors generated synthetic datasets that varied key parameters: target‑to‑marker ratios ranging from 1:1 to 100:1, marker count variability (standard deviations of 5 % to 30 %), and spatial heterogeneity of the sample matrix. For each scenario, 1,000 Monte‑Carlo replicates were performed, comparing the linear method and FOVS in terms of bias, root‑mean‑square error, and 95 % confidence‑interval width. Results showed that when the target‑to‑marker ratio exceeds roughly 10:1, FOVS provides unbiased estimates with a 20‑35 % reduction in standard error relative to the linear method. The advantage is most pronounced when marker variability is low (σ < 10 %).

2. Real‑World Microfossil Data – Sedimentary rocks from the Permian‑Triassic succession of southeastern Australia were collected, and known quantities of silica marker grains (0.5 %–5 % of the sample mass) were added. In the laboratory, 200 random FOVs (each 0.5 mm²) were examined under a microscope. The linear method used the same number of observations but arranged them along a continuous line. Both methods yielded statistically indistinguishable mean concentration estimates, but the FOVS method produced 95 % confidence intervals that were on average 28 % narrower, indicating substantially higher precision. Moreover, for high target‑to‑marker ratios (> 20:1) the linear method tended to underestimate abundance, a bias that was absent in the FOVS results.

Effort Comparison – Field time (≈2 hours) and the number of microscope observations (≈200) were identical for both approaches. The only additional step for FOVS was a simple area‑based scaling calculation, which can be performed in a spreadsheet or with a short R script. Thus, the method achieves “higher precision at equal effort.”

Applicability and Limitations – The authors delineate the conditions under which FOVS is most beneficial: (i) markers and targets need not be perfectly mixed, because each FOV provides an independent ratio; (ii) the method excels when the target‑to‑marker ratio is large and marker count variability is modest; (iii) it works well for heterogeneous samples where spatial variation can be captured by multiple small FOVs. Limitations include very small total sample areas (fewer than a handful of FOVs) where statistical gains diminish, and scenarios where markers segregate physically from the target matrix, requiring careful pre‑mixing.

Conclusions and Future Directions – The study concludes that the FOVS method offers a robust, efficient alternative to the linear method for absolute abundance estimation in a wide range of ecological and paleo‑environmental contexts. Because it delivers higher precision without additional field labor, the authors recommend its adoption as a standard protocol, either replacing or complementing existing practices. Future work will focus on automating FOV detection and marker‑target counting through image‑analysis pipelines, enabling fully automated data acquisition and processing. Such integration promises to scale the approach to large‑scale monitoring programs, high‑throughput paleo‑ecological studies, and any discipline where absolute quantification of organisms or particles is essential.