Sedimentary pyrite framboid size-frequency distributions: A meta-analysis
Abstract Framboids, microscopic sub-spheroidal aggregates of pyrite microcrystals, are found in sediments of all ages and framboid size-frequency distributions are widely used to determine the oxygenation states of paleo-waters. Sedimentary framboid populations display unimodal log-normal size distributions as a consequence of the multiplicative central limit theorem in probability theory. The application of additive statistics to framboid populations and their consequent characterization in terms of arithmetic means and standard deviations is wrong because it predicts a subset of framboids with negative diameters. A meta–analysis of 377 sets of measurements of the diameters of 48,063 pyrite framboids from 104 sediment and sedimentary rock locations shows that the geometric mean diameter of sedimentary framboids is 6.2 μm and the geometric standard deviation is 1.5. Ninety-five percent of all sedimentary framboids have geometric mean diameters between 2.9 and 13.9 μm. The geometric mean diameter of modern syngenetic framboids formed within euxinic water columns is 4.7 μm and that of diagenetic framboids formed within sediments is 6.7 μm. The estimated measurement error is ±10%. Framboid mean diameters can be used to help discriminate the oxygenation state of paleo-waters. A minimum number of 30 measurements is required and ideally ≥100 measurements are recommended. The conflicting evidence reported in the literature for the application of framboid size-frequency measurements results mainly from the intrinsic nature of statistical analyses: there is always a finite chance that a particular framboid size-frequency distribution is a result of either syngenetic or diagenetic processes. Including the systematic stereological error in framboid size measurements, the geometric mean size range for syngenetic framboids is 2.9–10.9 μm and that for diagenetic framboids 3.1–20.9 μm. This suggests a significant overlap in geometric mean diameters of framboids from euxinic and non-euxinic environments between ~3 and ~11 μm. Geometric mean framboid diameters within this size range are not robust proxies for paleo-water oxygenation conditions. The origin of the smaller sizes of syngenetic compared with diagenetic framboids appears to be related to the limited time available for framboid crystal growth within the water column. The statistical uncertainty in assigning particular framboid size-frequency distributions to defined oxygenation conditions results mainly from (a) some diagenetic framboids forming over a limited time, thereby also producing smaller framboids and (b) mixtures of syngenetic and diagenetic framboid populations through unavoidable time-averaging of samples. The absence of any significant differences in the sizes of modern and ancient framboids indicates that framboids do not continue to grow over extended time periods: once formed they remain the same over geologic time periods and only change through infilling, overgrowth and recrystallization. The result is that ancient framboids may sample the contemporary paleoenvironment in the sedimentary system in which they are found.