Generating sediment age chronologies from incomplete 210Pb radioisotope profiles: An application of Gibbs sampling to the untamed sediments of a Hawaiian tropical rainforest

Background/Question/Methods

Ecosystems are difficult to comprehend not only because they respond to drivers-of-change on multiple interacting spatial scales but also because they exhibit substantial variation across time. Paleoecologists have increasing access to techniques to look at temporal variation in ecosystems beyond the scope of repeated measures of plot data. An additional part of the complexity of ecosystems is that the vagaries of field sampling and the sometimes uncooperative nature of sediment records prevent straight-forward analysis. We encountered such travails when developing age chronologies of sediment records using lead-210 isotopes in a set of unconventional forest hollow cores from the rainforest of windward Mauna kea in Hawai`i. The initial lead-210 curves did not approach a steady background level (the “supported” lead-210) and so could not be used accurately in conventional age chronology calculations. We used a technique from Bayesian statistics, the Gibbs Sampler, to reconstruct age chronologies from the inadequate radioisotope data. Each data point of the relevant “unsupported” lead-210 activity was constructed by taking a constrained guess of the “supported” fraction drawn from the Uniform distribution and subtracting it from the Gaussian distribution of the total lead activity measured in the lab.

Results/Conclusions

Each simulation calculated an age model and after 100,000 iterations provided a 95% confidence interval for the age of all intervals in the sediment records. On a subsequently collected core radium-226 isotopes were measured as an alternative proxy for unsupported lead-210 levels across the landscape. The simulation method provided estimates of unsupported lead that bracket the measured radium-226 levels adequately characterizing supported and unsupported lead-210 levels but with a greater level of uncertainty. Uncertainty in age estimates increased with depth. The 95% confidence intervals ranged from <0.5 years from near surface samples to over 50 years at the deepest parts of the core. Combined with high temporal resolution pollen data the age chronologies helped illuminate the successional status of three structurally distinctive sections of the Hawaiian rainforest. The effort may also suggest a way forward to other researchers with recalcitrant datasets. The key is not statistical sophistication so much as a robust process-based model of how the system works.