Post on 04-Jul-2015
description
Corey J. A. Bradshaw1,2, Barry W. Brook1, Chris S. M. Turney3, Alan Cooper1,4
1THE ENVIRONMENT INSTITUTE, University of Adelaide; 2South Australian Research & Development Institute; 3School of Geography, University of Exeter; 4Australian Centre for Ancient DNA
• extinction must be inferred from record of sightings/collections
• when a species becomes increasingly rare before extinction, might persist unseen for many years
• so the time of last sighting often poor estimate of extinction date
Roberts & Solow 2003 Nature 426:245
present pastx x x xx x x?? xx x x
• optimal linear estimation• joint distribution of k same Weibull form regardless of parent
distribution• estimated extinction time q
• L: symmetric k×k matrix
• n: Estimated shape parameter of joint Weibull distribution of k
Roberts & Solow 2003 Nature 426:245
present pastx x x xx x x
qxx x x
kTTTT ...321
k
i
iiTa1
q̂
eeea t 111 LL
ijji
ji
i
iiij
,
ˆ
ˆ2ˆ2
n
nn
2
1 11
1log1
1ˆ
k
i i
k
TT
TT
kn
CI
11000 12000 13000 14000
YBP
11000 12000 13000 14000
YBP
• maximum likelihood to account for radio carbon dating error
• assume true ages U independent/uniformly distributed over (b1,g1) where b1 = extinction date
• PDF of Xj:
Solow et al. 2006 PNAS 103:7351
present pastx x x xx x x
b1 xx x x
jjj UX
11
11
)(bg
g
b
jj
j
xx
xf
11000 12000 13000 14000
YBP
• but... previous sighting rate important• length of period since last sighting informative• given previous sighting rate(n/tn), probability of next sighting
• where p drops below threshold with increasing T-tn, TE inferred
McInerny et al. 2006 Conserv Biol 20:562
present pastx x x xx x x
TE xx x x
ntT
nt
np
1
5 10 15 20 25 30
10
90
01
10
00
11
10
01
12
00
11
30
01
14
00
11
50
0
samples
Te
• but... TE depends on number of samples in ‘final’ period• declining influence of dates within time since last sighting• sequentially recalculated TE, weighting by cumulative distance
from T1
present pastx x x xx x x
TE xx x xT1
5 10 15 20
12
00
01
21
00
12
20
01
23
00
12
40
01
25
00
samples
Te
2 4 6 8 10 12 14
16
00
01
70
00
18
00
01
90
00
20
00
0
samples
Te
2 4 6 8 10 12 14 16
27
40
02
76
00
27
80
02
80
00
28
20
0
samples
Te
2 4 6 8 10 12
25
50
02
60
00
26
50
02
70
00
27
50
0
samples
Te
2 4 6 8 10
23
00
02
40
00
25
00
02
60
00
27
00
02
80
00
29
00
0
samples
Te
2 4 6 8 10 12 14
29
50
03
00
00
30
50
03
10
00
samples
Te
5 10 15 20 25 30
10
90
01
10
00
11
10
01
12
00
11
30
01
14
00
11
50
0
samples
Te
• but... TE depends on number of samples in ‘final’ period• declining influence of dates within time since last sighting• sequentially recalculated TE, weighting by cumulative distance
from T1
present pastx x x xx x x
TE xx x xT1x x x xx x x xx x x
• now simply combine methods with Gaussian resampler within carbon date errors for each record
10000 11000 12000 13000 14000 15000
YBP
Solow
10588
11112
9907
10000 11000 12000 13000 14000 15000
YBP
weighted McInerney
11097
11514
10662
11097
11514
10662
11097
11514
10662
11097
11514
10662
• now simply combine methods with Gaussian resampler within carbon date errors for each record
15000 16000 17000 18000 19000 20000
0e
+0
01
e-0
42
e-0
43
e-0
44
e-0
45
e-0
46
e-0
4
YBP
Pr
uniform
linearsigmoidal
exponential
logarithmic
‘true’extinction
15000 15200 15400 15600 15800 16000
15000 15200 15400 15600 15800 16000
15000 15200 15400 15600 15800 16000
15000 15200 15400 15600 15800 16000
15000 15200 15400 15600 15800 16000
YBP
uniform
linear
sigmoidal
exponential
logarithmic
uniform linear sigmoidal exponential logarithmic0.0001
0.001
0.01
0.1
1
10
100
S&RSolowMMwMw-rs
Method
2
uniform linear sigmoidal exponential logarithmic0
5
10
15
S&RSolowwM-rs
Method
CV
uniform linear sigmoidal exponential logarithmic0.0
0.2
0.4
0.6
0.8
1.0
S&RSolowwM-rs
Method
Pr(
overl
ap
)
incre
asin
g a
ccu
racy
incre
asin
g p
recis
ion
incre
asin
g o
verl
ap
uniform linear sigmoidal exponential logarithmic0.0001
0.001
0.01
0.1
1
10
100
SolowMw-rs
Method
2
uniform linear sigmoidal exponential logarithmic0.0
0.2
0.4
0.6
0.8
1.0
SolowwM-rs
Method
Pr(
ove
rla
p)
Glacials, Interglacials, Stadials and Interstadials
stadial
interstadial
Interglacial
Glacial
Interglacial
Extracting An Ice Core
Annual Layers In Ice Core
Cariaco Basin Bathymetry
• water exchange with the open Caribbean Sea is restricted
• intense seasonal productivity and high sedimentation rate
• anoxic below 300 m
• limited bioturbation (post-depositional mixing of sediments by marine life)
10000 20000 30000 40000 50000
YBP
BisonX.Eur
SaigaAnt.Eur
Mammoth.Eur BisonPris.Eur
CaveBear.Eur
Neand.Eur Muskox.Eur
Mammoth.NA
Equus.NA CaveLion.NA
StiltHorse.NA
ArctSim.NA
Cervalces.NA
SaigaAnt.NA
Dasypus.NA
Camelops.NA
Bootherium.NA
0 10000 20000 30000 40000 50000
01
00
00
20
00
03
00
00
40
00
05
00
00
calibrated AMS
ca
lib
rate
d M
w-r
sMw-rs ~ -83+ 0.98 × AMS
10000 20000 30000 40000 50000
YBP
HOL IS1 IS2 IS3 IS4 IS5 IS6 IS7 IS8 IS9IS10 IS11 IS12
BisonX.Eur
SaigaAnt.Eur
Mammoth.Eur BisonPris.Eur
CaveBear.Eur
Neand.Eur Muskox.Eur
Mammoth.NA
Equus.NA CaveLion.NA
StiltHorse.NA
ArctSim.NA
Cervalces.NA
SaigaAnt.NA
Dasypus.NA
Camelops.NA
Bootherium.NA
UrsArc.NA.Occ
CavBear.NA.Occ
BisonCau.Eur.Occ
10000 15000 20000 25000 30000 35000 40000
YBP
IS1 IS2 IS3 IS4 IS5 IS6 IS7 IS8 IS9 IS10
Mammoth Equus S.Horse
Bison
C.BearSF.Bear
Neand
10000 15000 20000 25000 30000 35000 40000
YBP
IS1 IS2 IS3 IS4 IS5 IS6 IS7 IS8 IS9 IS10
Mammoth Equus S.Horse
Bison
C.BearSF.Bear
Neand
Interstadials – OXCAL wPDFs
extinctions - unconstrained
P(rand overlap = 0.12)
extinctions - constrained
P(rand overlap) = 0.09
combined ext/app P(rand overlap) = 0.13
10000 15000 20000 25000 30000 35000 40000
YBP
IS1 IS2 IS3 IS4 IS5 IS6 IS7 IS8 IS9 IS10
U.arctosWapiti
10000 15000 20000 25000 30000 35000 40000
YBP
IS1 IS2 IS3 IS4 IS5 IS6 IS7 IS8 IS9 IS10
Mammoth Equus S.Horse
Bison
C.BearSF.Bear
Neand
Interstadials – OXCAL raw dates
extinctions - raw dates
P(rand overlap = 0.06)
appearances – raw dates
combined ext/app P(rand overlap) = 0.11
10000 15000 20000 25000 30000 35000 40000
YBP
S1.GS1YD S2.H1 S3.C1 S4.C2 S5.C3 S6.H2 S7.C4 S8.GS4C5S9.H3 S10.GS6C6S11.GS7C7S12.GS8C8 S13.H4 S14.GS10C9S15.GS11C10
Mammoth Equus S.Horse
Bison
C.BearSF.Bear
Neand
Stadials – OXCAL raw dates
extinctions - raw dates
P(rand overlap = 0.46)
combined ext/app P(rand overlap) = 0.27