1. A Comparative Analysis of Time Averaging for Bivalves and Brachiopods from a Modern Tropical Shelf R.A. Krause Jr. 1, S.L. Barbour Wood 1, J.F. Wehmiller 2, M. Kowalewski 1, M.G. Simões 3 1 Virginia Tech, Dept. of Geosciences, Blacksburg, VA 2 Univ. of Delaware, Earth Sciences, Newark, DE 3 Universidade Estadual Paulista, Instituto de Biociências, Sao Paulo, Brazil Geobiology Group www.geol.vt.edu/paleo

2. Funding NSF Geology & Paleontology (MK & JFW) ACS-Petroleum Research Fund (MK) David R. Wones Geoscience Scholarship, Dept. of Geosciences, Virginia Tech (RAK) Graduate Research Development Grant, Virginia Tech (RAK)

3. Introduction Time averaging = Temporal mixing Duration of temporal mixing determines resolution Quantitative estimates of time averaging are increasingly available, although studies are biased toward mollusks Importance First study to investigate duration of time averaging on two very different shelled invertebrates from the same environment Allows more accurate interpretation of polytypic shell beds

4. Outline Age-Frequency Distributions (AFD): –Comparison of scale of time averaging –Are there differences between brachiopods and bivalves? Analysis of Completeness: –How complete is the record for each taxon? –With 100% completeness, what would AFD look like?

5. 10 m 30 m Locality & Methods Shells dredged from two offshore sites (10m, 30m) Dated using amino acid racemization –D/L ratios calibrated with AMS radiocarbon dates Comparison of Age-frequency distributions Analysis of completeness of each sample 10 m 30 28 58 30 m 36 36 72 66 64 130 Brachiopods Bivalves Totals

6. Physical Characteristics 10 cm Semele casali Bouchardia rosea Semele casali - thin shell - low organic content - aragonitic *infaunal life habit Bouchardia rosea - robust shell - high organic content - calcitic *epifaunal life habit

7. Amino Acid Racemization Dating D/L aspartic acid ratio determined with gas chromatography Calibrated with 19 AMS radiocarbon dates 0 0.1 0.2 0.3 0.4 0200040006000 Age (Years BP) (D/L Aspartic) 2 r 2 = 0.96 Brachiopods 0 0.02 0.04 0.06 0.08 0.1 0.12 0 100020003000 Bivalves r 2 =0.73 (D/L Aspartic) 2 Age (Years BP) Ratio of 'D' to 'L' form of aspartic acid predicts well age of shell Ratios of many shells can be calculated for the cost of one radiocarbon date

8. Age-Frequency Distributions Age (years BP) n=130range=8438 median=985.5SD=2246 g 1 =1.12g 2 =0.17 Pooled Distribution For Bivalves and Brachiopods

9. Brachiopods: 30 m Brachiopods: 10 m 0 2 4 6 8 Bivalves: 30 m Bivalves: 10 m 1000 2000 3000 4000 50006000 7000 8000 Frequency Age-Frequency Distributions 4 8 0 2 6 10 Age (years BP) n=30range=4660 yrs median=661 yrsSD=1400 yrs n=36range=6192 yrs median=775 yrsSD=1542 yrs n=28range=7725 yrs median=4003 yrsSD=2548 yrs n=36range=8438 yrs median=738 yrsSD=2417 yrs

10. Distribution Comparisons Wilcoxon Two-Sample Test Between-taxa comparisons of central tendency α=0.05 10 m 30 m Z=4.0 p<0.001 Z=-0.26 p=0.79 Wilcoxon Two-Sample Test Between-site comparisons of central tendency α=0.05 Brachiopods Bivalves Z=0.08 p=0.94 Z=4.12 p<0.001 Kolmogorov-Smirnov Test Between-taxa comparisons of distribution shape α=0.05 10 m 30 m D=0.5 p<0.001 D=0.22 p=0.43 Kolmogorov-Smirnov Test Between-site comparisons of distribution shape α=0.05 Brachiopods Bivalves D=0.25 p=0.21 D=0.48 p<0.001

11. Scale of Time Averaging Dispersion metrics –Range: sensitive to sample size –Shell half-life: assumes continuous input of shells –Standard deviation: less sensitive to sample size, no restrictive assumptions Confidence intervals around SD –estimated using independent 1000 iter. bootstrap simulations –95% and 99% confidence intervals calculated from 0.5, 2.5, 97.5, and 99.5 percentiles of sampling distribution

12. 0 1000 2000 3000 Brachiopods Bivalves Years 10 m 30 m 10 m30 m 4 8 0 2 6 10 0 2 4 6 8 Brachiopods: 30 m Brachiopods: 10 m Bivalves: 30 m Bivalves: 10 m Confidence Intervals for SD

13. Comparison With Other Studies 0 1000 2000 3000 This StudyCarroll et al., 2003 Ubatuba Bay, Brazil: mixed carbonate- siliciclastic shelf Standard Deviation of Shell Age Kowalewski et al., 1998 Colorado River Delta: beach ridges 10 m 30 m 10 m 16 m 23 m 6 m Flessa et al., 1993 Bahía la Choya Gulf of California: intertidal, low sed. Inner tidal flat Tidal channel core fan deltas pocket bays Bahía Concepcíon Gulf of California: shallow, high sed. Meldahl et al., 1997 4000 5000 6000 7000 8000 9000 10000 Flessa & Kowalewski, 1994 nearshore shelf fossil assemblages inactive beach ridges *95% & 99% confidence intervals calculated by bootstrapping Brachiopods Bivalves

14. Temporal Completeness Completeness is scale-dependant –decreases with increasing resolution and/or range –increases with increasing sample size, generally speaking High incompleteness suggests discontinuous time averaging However, most distributions have gaps due to sampling –With 100% complete fossil record, how likely is it to get samples as complete as ours? # of time intervals with paleontological record Completeness (%) = X 100

15. Completeness Simulations Monte Carlo Simulations: Randomly sample 100% complete distributions –Uniform Distribution: Provides conservative incompleteness estimates –Exponential Distribution: More realistic distribution Uniform Distribution Years Frequency Exponential Distribution Years Frequency

16. Completeness Simulations Monte Carlo Simulations: Randomly sample 100% complete distributions sample size k; observed age range r; resolution b - 1000 iterations - draw k observations from each distribution with range r - calculate expected completeness for each sample at a resolution of b Uniform Distribution Years Frequency Exponential Distribution Years Frequency

17. Completeness Simulations Actual Completeness: 26.9% Expected Completeness: –Uniform Distribution: 30.7% –Exponential Distribution: 19% Uniform Distribution Years Frequency Exponential Distribution Years Frequency 0 10 20 30 40 % completeness uniform exponential actual completeness 95% probability that sample was drawn from uniform age-frequency distribution Brachiopods: 30 m

18. Summary of Simulations 0 10 20 30 40 50 60 % completeness Brachiopods 30m Brachiopods 10m Bivalves 30m Bivalves 10m uniform distribution exponential distribution Brachiopods: Samples are statistically indistinguishable from those drawn from a 100% complete, uniform distribution Bivalves: 30 m sample is significantly different from uniform and exponential distribution. 10 m sample is statistically indistinguishable from those drawn from a 100% complete, exponential distribution

19. Interpretation Simulations suggest different underlying distribution for brachiopods and bivalves At least two possible explanations –Different rate of destruction: uniform distribution = low destruction rate caused by differing physical characteristics –Different input rate: bivalves input at constant rate brachiopods input in pulses –possibly due to fluctuations in upwelling location and intensity

20. Conclusions Scale of Time Averaging - Brachiopods and Bivalves similar within closely related sites - Environment and Burial History may be most important - Suggests that polytypic shell beds may have similar time averaging durations for each taxon Completeness - Brachiopod record may be 100% complete and uniform - Bivalve record may be 100% complete, but not uniform - Difference in underlying distribution could reflect ecology, taphonomy, or both 4 8 0 2 6 10 0 2 4 6 8