Range confidence intervals

Estimation of confidence intervals for first or last appearances or total stratigraphic range, for one taxon.

Assuming a random (Poisson) distribution of fossiliferous horizons, and given the first occurrence datum (level), last occurrence datum, and total number of horizons where the taxon is found, we can calculate confidence intervals for the stratigraphic range of one taxon (Strauss & Sadler 1989, Marshall 1990).

No data are needed in the spreadsheet. The program will ask for the number of horizons where the taxon is found, and levels or dates for the first and last appearances. If necessary, use negative values to ensure that the last appearance datum has a higher numerical value than the first appearance datum. 80%, 95% and 99% confidence intervals are calculated for the FAD considered in isolation, the LAD considered in isolation, and the total range.

The value α is the length of the confidence interval divided by the length of the observed range.

For the single endpoint case:

α = (1-C₁)^-1⁄(H-1) -1

where C₁ is the confidence level and H the number of fossiliferous horizons.

For the joint endpoint (total range) case, α is found by iterative solution of the equation

C₂ = 1 - 2(1+α)^-(H-1) + (1+2α)^-(H-1)

The assumption of random distribution will of course not hold in many real situations.

Solow’s method

Past also includes a method due to Solow (2003) that does not assume a uniform (stationary) distribution of finds. It only uses the occurrence datums of the lowest, second lowest, highest and second highest finds.

References

Marshall, C.R. 1990. Confidence intervals on stratigraphic ranges. Paleobiology 16:1-10.

Solow, A.R. 2003. Estimation of stratigraphic ranges when fossil finds are not randomly distributed. Paleobiology 29:181-185.

Strauss, D. & P.M. Sadler. 1989. Classical confidence intervals and Bayesian probability estimates for ends of local taxon ranges. Mathematical Geology 21:411-427.