A Comparative Analysis of A Comparative Analysis of Time Averaging for Bivalves Time Averaging for Bivalves and Brachiopods from a Modern and Brachiopods from a Modern

Tropical ShelfTropical Shelf

R.A. Krause Jr.1, S.L. Barbour Wood1, J.F. Wehmiller2, M. Kowalewski1, M.G. Simões3

1 Virginia Tech, Dept. of Geosciences, Blacksburg, VA2 Univ. of Delaware, Earth Sciences, Newark, DE

3 Universidade Estadual Paulista, Instituto de Biociências, Sao Paulo, Brazil

Geobiology GroupGeobiology Groupwww.geol.vt.edu/paleo

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)

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

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?

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 5830 m 36 36 72 66 64 130

Brach

iopods

Bival

ves

Totals

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

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

0 2000 4000 6000Age (Years BP)

(D/L

As

pa

rtic

)2

r2= 0.96

Brachiopods

0

0.02

0.04

0.06

0.08

0.1

0.12

0 1000 2000 3000

Bivalvesr2=0.73

(D/L

As

pa

rtic

)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

Age-Frequency Distributions

Age (years BP)

10

00

20

00

30

00

40

00

50

00

60

00

70

00

80

00

Fre

qu

enc

y

0

5

10

15

20

25

30

35

n=130 range=8438median=985.5 SD=2246g1=1.12 g2=0.17

Pooled Distribution For Bivalves and Brachiopods

Brachiopods: 30 m

Brachiopods: 10 m

0

2

4

6

8

Bivalves: 30 m

0

2

4

Bivalves: 10 m

0

2

4

6

8

10

12

14

16

10

00

20

00

30

00

40

00

50

00

60

00

70

00

80

00

Fre

qu

enc

yAge-Frequency Distributions

4

8

0

2

6

10

Age (years BP)

n=30 range=4660 yrsmedian=661 yrs SD=1400 yrs

n=36 range=6192 yrsmedian=775 yrs SD=1542 yrs

n=28 range=7725 yrsmedian=4003 yrs SD=2548 yrs

n=36 range=8438 yrsmedian=738 yrs SD=2417 yrs

Distribution ComparisonsDistribution Comparisons

Wilcoxon Two-Sample TestBetween-taxa comparisons of central tendencyα=0.05 10 m 30 m

Z=4.0p<0.001

Z=-0.26p=0.79

Wilcoxon Two-Sample TestBetween-site comparisons of central tendencyα=0.05 Brachiopods Bivalves

Z=0.08p=0.94

Z=4.12p<0.001

Kolmogorov-Smirnov TestBetween-taxa comparisons of distribution shapeα=0.05 10 m 30 m

D=0.5p<0.001

D=0.22p=0.43

Kolmogorov-Smirnov TestBetween-site comparisons of distribution shapeα=0.05 Brachiopods Bivalves

D=0.25p=0.21

D=0.48p<0.001

Scale of Time AveragingScale 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

0

1000

2000

3000

BrachiopodsBivalves

Yea

rs

10

m

30

m

10

m

30

m

4

8

02

6

10

024

02468

10121416

02468

Brachiopods: 30 m

Brachiopods: 10 m

Bivalves: 30 m

Bivalves: 10 m

Confidence Intervals for SDConfidence Intervals for SD

Comparison With Other StudiesComparison With Other Studies

0

1000

2000

3000

This Study Carroll et al., 2003

Ubatuba Bay, Brazil:mixed carbonate-siliciclastic shelf

Sta

nd

ard

De

via

tio

n o

f S

he

ll A

ge

Kowalewski et al., 1998

Colorado River Delta:beach ridges

10 m 30 m

10

m1

6 m

23

m6

m

Flessa et al., 1993

Bahía la ChoyaGulf of California:intertidal, low sed.

Inner tidal flat

Tidalchannel

core co

re

fan deltas pocket

bays

Bahía ConcepcíonGulf of California:shallow, high sed.

Meldahl et al., 1997

40005000600070008000

900010000

Flessa & Kowalewski, 1994

nearshore

shelf

fossilassemblages

inactive beach ridges

*95% & 99% confidence intervals calculated by bootstrapping

BrachiopodsBivalves

Temporal CompletenessTemporal 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

# of time intervalswith paleontologicalrecord

Completeness (%) = X 100

Completeness Simulations

Monte Carlo Simulations: Randomly sample 100% complete distributions

– Uniform Distribution: Provides conservative incompleteness estimates

– Exponential Distribution: More realistic distribution

Uniform Distribution

Years

Fre

qu

en

cy

Exponential Distribution

Years

Fre

qu

en

cy

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

Fre

qu

en

cy

Exponential Distribution

Years

Fre

qu

en

cy

Completeness Simulations

Actual Completeness: 26.9%

Expected Completeness:– Uniform Distribution: 30.7%– Exponential Distribution: 19%

Uniform Distribution

Years

Fre

qu

en

cy

Exponential Distribution

Years

Fre

qu

en

cy

0

10

20

30

40

% c

om

ple

ten

ess

uniform

exponential

actualcompleteness

95% probability that sample was drawn from uniform age-frequency distribution

0

2

4 Brachiopods: 30 m

Summary of Simulations

0

10

20

30

40

50

60

% c

om

ple

ten

ess

Bra

chio

po

ds

30m

Bra

chio

po

ds

10m

Biv

alv

es 3

0m

Biv

alv

es 1

0m

uniform distributionexponential 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

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

ConclusionsConclusionsScale 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

02

6

10

02468