(Sample) Size Matters: Best Practices for Defining Error in Planktic Foraminiferal Proxy Records

Paleoceanographic research is a vital tool to extend modern observational datasets and to study the impact of climate events for which there is no modern analog. Foraminifera are one of the most widely used tools for this type of work, both as paleoecological indicators and as carriers for geochemical proxies. However, the use of microfossils as proxies for paleoceanographic conditions brings about a unique set of problems. This is primarily due to the fact that groups of individual foraminifera, which usually live about a month, are used to infer average conditions for time periods ranging from hundreds to tens of thousands of years. Because of this, adequate sample size is very important for generating statistically robust datasets, particularly for stable isotopes. In the early days of stable isotope geochemistry, instrumental limitations required hundreds of individual foraminiferal tests to return a value. This had the fortunate side-effect of smoothing any seasonal to decadal changes within the planktic foram population. With the advent of more sensitive mass spectrometers, smaller sample sizes have now become standard. While this has many advantages, the use of smaller numbers of individuals to generate a data point has lessened the amount of time averaging in the isotopic analysis and decreased precision in paleoceanographic datasets. With fewer individuals per sample, the differences between individual specimens will result in larger variation, and therefore error, and less precise values for each sample. Unfortunately, most (the authors included) do not make a habit of reporting the error associated with their sample size. We have created an open-source model in R to quantify the effect of sample sizes under various realistic and highly modifiable parameters (calcification depth, diagenesis in a subset of the population, improper identification, vital effects, mass, etc.). For example, a sample in which only 1 in 10 specimens is diagenetically altered can be off by >0.3‰ δ¹⁸O VPDB, or ~1°C. Here, we demonstrate the use of this tool to quantify error in micropaleontological datasets, and suggest best practices for minimizing error when generating stable isotope data with foraminifera.