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Geobiology Group. www.geol.vt.edu/paleo. 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. Sim ões 3. 1 Virginia Tech, Dept. of Geosciences, Blacksburg, VA - PowerPoint PPT Presentation
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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