A Comparative Analysis of
Time Averaging for Bivalves
and Brachiopods from a Modern
Tropical Shelf
R.A. Krause Jr.1, S.L. Barbour Wood1, J.F.
Wehmiller2, M. Kowalewski1, M.G. Simões3
1
3
Virginia Tech, Dept. of Geosciences, Blacksburg, VA
2 Univ. of Delaware, Earth Sciences, Newark, DE
Universidade Estadual Paulista, Instituto de Biociências, Sao
Paulo, Brazil
Geobiology Group
www.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?
Locality & Methods
10 m
30 m
10 m
30
36
66
28
36
64
58
72
130
30 m
• 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
Physical Characteristics
Bouchardia rosea
Semele casali
10 cm
Semele casali
Bouchardia rosea
- thin shell
- low organic content
- aragonitic
*infaunal life habit
- robust shell
- high organic content
- calcitic
*epifaunal life habit
Amino Acid Racemization Dating
• 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
0.3
0.12
Brachiopods
(D/L Aspartic)2
(D/L Aspartic)2
0.4
r2= 0.96
0.2
0.1
0
2000
4000
Age (Years BP)
6000
r2=0.73
0.08
0.06
0.04
0.02
0
0
Bivalves
0.1
0
1000
2000
Age (Years BP)
• D/L aspartic acid ratio determined with gas
chromatography
• Calibrated with 19 AMS radiocarbon dates
3000
Age-Frequency Distributions
35
30
25
Pooled Distribution For Bivalves and Brachiopods
n=130
median=985.5
g1=1.12
range=8438
SD=2246
g2=0.17
15
10
5
Age (years BP)
8000
7000
6000
5000
4000
3000
2000
0
1000
Frequency
20
Age-Frequency Distributions
10
8
6
4
Brachiopods: 10 m
n=30
median=661 yrs
range=4660 yrs
SD=1400 yrs
0
8
6
4
2
Bivalves: 30 m
n=36
median=775 yrs
range=6192 yrs
SD=1542 yrs
0
4
2
Brachiopods: 30 m
n=28
median=4003 yrs
range=7725 yrs
SD=2548 yrs
n=36
median=738 yrs
range=8438 yrs
SD=2417 yrs
0
16
14
Bivalves: 10 m
12
10
8
6
4
2
Age (years BP)
8000
7000
6000
5000
4000
3000
2000
0
1000
Frequency
2
Distribution Comparisons
Wilcoxon Two-Sample Test
Between-taxa comparisons
of central tendency
α=0.05
10 m
30 m
Z=-0.26 Z=4.0
p=0.79
p<0.001
Wilcoxon Two-Sample Test
Between-site comparisons
of central tendency
α=0.05
Brachiopods
Bivalves
Z=4.12
Z=0.08
p<0.001
p=0.94
Kolmogorov-Smirnov Test
Between-taxa comparisons
of distribution shape
α=0.05
10 m
30 m
D=0.22
D=0.5
p=0.43
p<0.001
Kolmogorov-Smirnov Test
Between-site comparisons
of distribution shape
α=0.05
Brachiopods
Bivalves
D=0.48
D=0.25
p<0.001
p=0.21
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
Confidence Intervals for SD
10
8
6
4
2
0
4
2
0
8
6
4
2
0
2000
1000
30 m
30 m
0
10 m
Brachiopods
Bivalves
10 m
Years
3000
16
14
12
10
8
6
4
2
0
Brachiopods: 10 m
Brachiopods: 30 m
Bivalves: 30 m
Bivalves: 10 m
Comparison With Other Studies
shelf
Brachiopods
Bivalves
inactive
beach
ridges
nearshore
fossil
assemblages
Ubatuba Bay, Brazil:
mixed carbonatesiliciclastic shelf
Flessa & Kowalewski, 1994
3000
Bahía la Choya
Gulf of California:
intertidal, low sed.
10 m 30 m
Tidal
channel
core
10 m
16 m
1000
Colorado River Delta:
beach ridges
core
Inner
tidal
flat
2000
Bahía Concepcíon
Gulf of California:
shallow, high sed.
fan
deltas pocket
6m
23 m
Standard Deviation of Shell Age
10000
9000
8000
7000
6000
5000
4000
bays
0
This Study
Carroll et al., 2003
Kowalewski et al., 1998
*95% & 99% confidence intervals calculated by bootstrapping
Flessa et al., 1993
Meldahl et al., 1997
Temporal Completeness
# of time intervals
with paleontological
record
Completeness (%) =
# of time intervals
X 100
• 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?
Frequency
Completeness Simulations
Uniform Distribution
Monte Carlo Simulations:
Randomly sample 100% complete
distributions
Frequency
Years
Exponential Distribution
– Uniform Distribution: Provides
conservative incompleteness
estimates
– Exponential Distribution: More
realistic distribution
Years
Frequency
Completeness Simulations
Uniform Distribution
Frequency
Years
Exponential Distribution
Years
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
Frequency
Completeness Simulations
Uniform Distribution
Years
0
Exponential Distribution
Years
40
% completeness
Frequency
Brachiopods: 30 m
4
2
30
uniform
20
exponential
10
0
Actual Completeness: 26.9%
Expected Completeness:
– Uniform Distribution: 30.7%
– Exponential Distribution: 19%
actual
completeness
95% probability that sample was
drawn from uniform age-frequency
distribution
Summary of Simulations
60
Brachiopods:
Samples are statistically
indistinguishable from those drawn
from a 100% complete, uniform
distribution
40
30
20
Bivalves 10m
Bivalves 30m
0
uniform distribution
exponential distribution
Brachiopods 10m
10
Brachiopods 30m
% completeness
50
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
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
8
6
4
2
0
10
8
6
4
2
0
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