winbugs code - macquarie...
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WinBUGS code
WinBUGS code for the state-space model fitted to Argos/GPS and geolocation data. This model and code are modifications of the 'DCRW' model presented by Jonsen et al. (2005).
model;{
pi <- 3.141592653589pi2 <- 2 * pinpi <- pi * -1
Omega[1, 1] <- 1Omega[1, 2] <- 0Omega[2, 1] <- 0Omega[2, 2] <- 1
## priors on process uncertaintyiSigma[1:2, 1:2] ~ dwish(Omega[, ], 2)Sigma[1:2, 1:2] <- inverse(iSigma[, ])
## Priors for first locationfor(k in 1:2){
x[1, k] ~ dt(y[1, k], 100, 2)}
## Assume simple random walk to estimate 2nd regular positionx[2, 1:2] ~ dmnorm(x[1, ], iSigma[, ])
theta ~ dunif(npi, pi) ## prior for theta (mean turn angle)gamma ~ dbeta(1, 1) ## prior for gamma (persistence)logpsi ~ dunif(-10, 10) ## prior for scaling factor applied to Argos/GPS measurement errorpsi <- exp(logpsi)
## Priors for precisions in geolocation estimates of longitude and latitude.logvarg[1] ~ dunif(-1000, 1000)logvarg[2] ~ dunif(-1000, 1000)taug[1] <- 1 / exp(logvarg[1])taug[2] <- 1 / exp(logvarg[2])
## Transition equationfor(t in 2:(RegN - 1)){
## Build transition matrix for rotational componentT[t, 1, 1] <- cos(theta)T[t, 1, 2] <- -sin(theta)T[t, 2, 1] <- sin(theta)T[t, 2, 2] <- cos(theta)for(k in 1:2){
Tdx[t, k] <- T[t, k, 1] * (x[t, 1] - x[t - 1, 1]) + T[t, k, 2] * (x[t, 2] - x[t - 1, 2]) ## matrix multiplicationx.mn[t, k] <- x[t, k] + gamma * Tdx[t, k] ## predict next location (no process error)
}x[t + 1, 1:2] ~ dmnorm(x.mn[t, ], iSigma[, ]) ## predict next location (with process error)
}
## Measurement equation for Argos/GPS data.
1
for(t in 2:RegN){ ## loops over regular time intervals (t)for(i in idx[t - 1]:(idx[t] - 1)){ ## loops over observed locations within interval t
for(k in 1:2){itau2.psi[i, k] <- itau2[i, k] * psizhat[i, k] <- (1 - j[i]) * x[t - 1, k] + j[i] * x[t, k] ## interpolate irregularly observed locationsy[i, k] ~ dt(zhat[i, k], itau2.psi[i, k], nu[i, k]) ## robust measurement equation
}}
}
##Measurement equation for geolocation data.for(t in 2:RegN){ ## loops over regular time intervals (t)
for(i in idxg[t - 1]:(idxg[t] - 1)){ ## loops over observed locations within interval tfor(k in 1:2){
zhatg[i, k] <- (1 - jg[i]) * x[t - 1, k] + jg[i] * x[t, k] ## interpolate irregularly observed locationsyg[i, k] ~ dnorm(zhatg[i, k], taug[k]) ## measurement equation
}}
}
}
2
Tagging methods
The following sections describe details of the tagging methods for each species group.
Sharks
We analyzed data from four shark species that together provided a broad latitu-dinal coverage: blue (Prionace glauca Linnaeus, 1758), Galapagos (Carcharhinusgalapagensis Snodgrass and Heller, 1905), short-finned mako (Isurus oxyrinchusRafinesque, 1810), and salmon (Lamna ditropis Hubbs and Follett, 1947). Sharksranged in size from 125 to 230 cm in total length and were double-tagged withgeolocation PAT (pop-up archival transmitting) tags (Wildlife Computers PAT2,PAT3, PAT4 and Mk10) and Argos-positioning SPOT tags (Wildlife Computers,Redmond, WA, USA). Blue sharks (n = 14) were tagged off the coast of California,USA and Baja California, Mexico in 2004 and 2006-2008 during January, June, Julyand November. Mako sharks (n = 25) were tagged in the same geographic regionbetween 2003 and 2008 mainly during June and July but one mako shark was taggedin each of January, October and November. Salmon sharks (n = 34) were taggedin Prince William Sound, Alaska, USA during July and August between 2003 and2007. Galapagos sharks (n = 2) were tagged near the Galapagos Islands, Ecuadorduring July 2006. Release locations were known exactly for all shark deployments,but sharks were not recaptured so exact final positions were not available.
Birds
We analyzed data from two albatross species: black-footed (Phoebastria nigripesAudubon, 1839) and Laysan (P. immutabilis Rothschild, 1893). Both species weretagged during the breeding season at Tern Island (23◦N, 166◦W), French FrigateShoals, Northwest Hawaiian Islands, USA from mid-December to late January. Allbirds were of breeding age (> 6 years) and there were roughly equal numbers of bothsexes for each species. Individuals were captured off the nest and tagged prior totheir departure to sea to forage during the egg incubation period. After returningfrom sea (5-30 days later), birds were captured either before or shortly after resumingnest duties. Albatrosses were equipped with a satellite platform transmitter terminal
3
(PTT), which was either a Microwave Telemetry 35g Pico-100 (Microwave Telemetry,Columbia, MD, USA) or a Wildlife Computers 35g SPOT4. These tags were attachedto mantle feathers on the bird’s back using Tesa R© adhesive tape, wrapped aroundseveral layers of feathers. Each bird was also equipped with a Lotek LTD 2400 orLAT 2500 archival geolocation data logger (Lotek Wireless, St. John’s, NL, Canada)programmed to record ambient light, temperature, and pressure every 2-32 seconds,and to calculate daily light-based latitude and longitude. These loggers were fixedto a plastic band worn around a bird’s leg. In total, the combined mass of alltags added to each bird ranged from 1-1.5%. Black-footed albatross were taggedin the 2004/2005 and 2005/2006 seasons, and Laysan albatross were tagged in the2002/2003, 2004/2005 and 2005/2006 seasons. Further details about data processingare explained in Shaffer et al. (2005).
Pinnipeds
California sea lions (Zalophus californianus Lesson, 1828) were tagged at San Nico-las Island, California, USA in November 2007 and were recaptured in January andFebruary 2008. All sea lions were lactating adult females (n = 9). Sea lions weretagged with Wildlife Computers model Mk10-AF (Argos-linked Fastloc GPS) andLotek LTD 2300 or 2310 archival geolocation tags. All tags were attached to thedorsal pelage of the back. GPS tags were programmed to not store locations duringtimes when the sea lions were hauled out on land. Haul-out periods were inferredby visual identification of gaps in the GPS data preceded and followed by directedmovements to and from the deployment/recapture location, respectively. Geoloca-tion data that occurred between the two GPS data points defining these inferredhaul-out periods were removed from the analysis. Release and recovery locationswere known exactly for all sea lions.
Error estimates
The following describes how estimates of geolocation errors were calculated for eachindividual, species and species group from the posterior probability distributions.For each individual i, the samples of SDlon and SDlat from the joint posterior proba-bility distribution were log-transformed and the means and variances were calculated
4
( ˆlog SDlon,i and σ2ˆlog SDlon,i
, respectively, and similarly for latitude). We used means
on the log scale so that the mean estimated precision would equal the reciprocal ofthe mean estimated variance. Estimates were also calculated for each group j on thelog-scale ( ˆlog SDlon,j and ˆlog SDlat,j) as the average of the relevant individual meansweighted by the inverse of their variance. The weighted average on the log-scale wasmore appropriate as the individual means were weighted by their CVs rather thantheir variances and thus the weighting partially reflected the number of geolocationdata for each animal rather than the positive relationship between a variance esti-mate and the variance of that estimate. Group estimates were calculated as followsusing formulas for a fixed-effects meta-analysis (Normand, 1999):
ˆlog SDlon,j =
∑iWi
ˆlog SDlon,i∑iWi
(1)
where
Wi =1
σ2ˆlog SDlon,i
(2)
and individuals subscripted by i belong to group j. The variance of the group meanon the log-scale (σ2
ˆlog SDlon,j) was calculated as (Normand, 1999):
σ2ˆlog SDlon,j
= (∑i
Wi)−1 (3)
Individual and group estimates and their variances were then back-transformed sothat:
SDlon = eˆlog SDlon (4)
and assuming a normal distribution for ˆlog SDlon:
σ2SDlon
= e2ˆlog SDlone
σ2ˆlog SDlon (e
σ2ˆlog SDlon − 1) (5)
References
Jonsen, I. D., Flemming, J. M. & Myers, R. A. (2005). Robust state-space modelingof animal movement data. Ecology , 86, 2874–2880.
Normand, S.-L. T. (1999). Meta-analysis: formulating, evaluating, combining andreporting. Statistics in Medicine, 18, 321–359.
5
Shaffer, S. A., Tremblay, Y., Awkerman, J. A., Henry, R. W., Teo, S. L. H., Anderson,D. J., Croll, D. A., Block, B. A. & Costa, D. P. (2005). Comparison of light- andSST-based geolocation with satellite telemetry in free-ranging albatrosses. MarineBiology , 147, 833–843.
6
Supple
men
tary
Tab
le1.
Num
ber
ofA
rgos
/GP
Sdat
a(n
Argos/GPS),
num
ber
ofge
oloca
tion
dat
a(n
geo
loca
tion),
model
trac
kle
ngt
h(d
),es
tim
ated
SD
ofer
rors
inlo
ngi
tude
(SD
lon)
and
lati
tude
(SD
lat)
geol
oca
tion
s(d
egre
es),
SD
sof
thes
eer
ror
esti
mat
es(σ
SD
lon
andσSD
lat),
and
the
pro
por
tion
ofm
ean
esti
mat
edlo
ngi
tudes
and
lati
tudes
from
the
model
fitt
edto
Arg
os/G
PS
and
geol
oca
tion
dat
ath
atfe
llw
ithin
the
95%
pos
teri
orpro
bab
ilit
y
inte
rval
for
the
corr
esp
ondin
ges
tim
ates
from
the
model
fitt
edto
only
geol
oca
tion
dat
a(c
over
age;n
=num
ber
oflo
cati
ons
that
wer
eco
mpar
edb
etw
een
model
s)fo
rea
chin
div
idual
.
Indiv
idual
nArgos/GPS
ngeo
loca
tion
Tra
ckle
ngt
hS
Dlon
σSD
lon
SD
lat
σSD
lat
Cov
erag
e
Lon
.L
at.
n
blu
esh
ark
166
1145
0.4
0.1
0.9
0.2
1.00
1.00
22
287
1642
0.7
0.1
1.0
0.2
0.96
1.00
23
323
16
920.
20.
11.
50.
51.
001.
0012
428
559
0.5
0.2
1.0
0.4
1.00
1.00
10
533
1133
0.5
0.1
0.9
0.2
1.00
1.00
22
691
1348
0.4
0.1
0.6
0.1
1.00
1.00
16
766
1530
0.4
0.1
1.9
0.4
1.00
0.61
18
814
69
138
0.4
0.1
6.7
1.8
1.00
0.36
14
927
326
151
0.4
0.1
1.4
0.2
1.00
1.00
49
1020
215
107
0.6
0.1
3.3
0.6
0.97
0.57
30
1130
711
208
0.4
0.1
3.9
0.9
1.00
0.59
22
7
Supple
men
tary
Tab
le1.
Con
tinued
.
Sp
ecie
s/In
div
idual
nArgos/GPS
ngeo
loca
tion
Tra
ckle
ngt
hS
Dlon
σSD
lon
SD
lat
σSD
lat
Cov
erag
e
Lon
.L
at.
n
1211
28
217
0.4
0.1
6.4
1.8
1.00
0.63
16
1337
316
246
0.5
0.1
1.5
0.3
1.00
0.81
32
1450
49
303
0.5
0.1
0.5
0.1
1.00
1.00
16
Gal
apag
ossh
ark
162
645
0.5
0.2
0.4
0.1
1.00
1.00
7
254
1126
0.8
0.2
1.2
0.3
0.92
1.00
13
mak
osh
ark
150
453
670.
60.
10.
50.
11.
001.
0061
257
128
442
0.7
0.1
1.3
0.2
1.00
0.96
56
320
316
157
0.5
0.1
1.1
0.2
1.00
0.91
32
431
121
217
0.6
0.1
1.9
0.3
1.00
0.95
42
574
718
396
0.5
0.1
1.0
0.2
1.00
1.00
29
618
17
841.
10.
32.
00.
60.
861.
0014
790
780
125
0.7
0.1
1.5
0.1
0.95
0.87
103
897
170
240
0.6
0.05
1.7
0.1
0.99
0.85
105
912
1797
290
0.7
0.05
1.3
0.1
0.99
0.86
136
1031
225
640.
70.
11.
30.
21.
000.
9539
1110
916
470.
50.
10.
70.
11.
001.
0031
1266
714
346
0.6
0.1
1.2
0.2
1.00
1.00
28
8
Supple
men
tary
Tab
le1.
Con
tinued
.
Sp
ecie
s/In
div
idual
nArgos/GPS
ngeo
loca
tion
Tra
ckle
ngt
hS
Dlon
σSD
lon
SD
lat
σSD
lat
Cov
erag
e
Lon
.L
at.
n
1326
612
118
0.6
0.1
2.1
0.4
1.00
0.91
23
1416
923
810.
50.
12.
30.
31.
000.
8046
1558
918
347
0.5
0.1
3.2
0.6
1.00
0.74
35
1642
017
388
0.6
0.1
2.0
0.4
1.00
0.85
34
1713
315
126
0.8
0.1
1.0
0.2
1.00
1.00
30
1899
125
707
0.5
0.1
0.8
0.1
0.98
1.00
50
1929
319
364
0.5
0.1
0.9
0.1
1.00
1.00
38
2049
427
301
0.5
0.1
1.0
0.1
1.00
1.00
54
2169
121
581
0.6
0.1
0.7
0.1
1.00
1.00
41
2249
027
416
0.6
0.1
1.0
0.1
1.00
0.92
52
2352
825
283
0.6
0.1
1.5
0.2
0.98
1.00
47
2434
927
257
0.7
0.1
1.0
0.1
1.00
1.00
53
2522
516
249
0.5
0.1
2.8
0.5
1.00
0.84
31
salm
onsh
ark
116
87
274
0.6
0.2
4.5
1.4
1.00
0.62
13
254
1030
0.9
0.2
6.8
1.7
1.00
0.14
14
354
736
1.1
0.3
3.3
1.0
0.92
0.38
13
413
3646
619
1.0
0.1
3.2
0.4
0.94
0.51
71
513
2050
934
1.1
0.1
1.9
0.2
0.93
0.86
81
9
Supple
men
tary
Tab
le1.
Con
tinued
.
Sp
ecie
s/In
div
idual
nArgos/GPS
ngeo
loca
tion
Tra
ckle
ngt
hS
Dlon
σSD
lon
SD
lat
σSD
lat
Cov
erag
e
Lon
.L
at.
n
679
77
1326
0.7
0.2
1.5
0.5
1.00
1.00
12
711
6018
677
0.5
0.1
2.5
0.4
1.00
0.79
33
812
7513
714
0.9
0.2
5.2
1.1
1.00
0.60
25
970
116
973
0.7
0.1
3.4
0.6
1.00
0.72
32
1021
323
300
0.9
0.1
5.4
0.9
0.96
0.26
46
1159
19
370
0.8
0.2
3.5
0.9
0.94
0.78
18
1210
2213
1034
1.1
0.2
5.5
1.2
0.88
0.52
25
1312
5414
987
1.7
0.3
18.0
3.7
0.83
0.00
24
1410
0185
483
0.8
0.1
7.1
0.6
0.91
0.57
159
1581
424
590
2.2
0.3
7.3
1.1
0.67
0.46
48
1631
548
211
0.8
0.1
1.8
0.2
0.96
0.93
94
1727
39
763
0.6
0.2
7.0
1.8
1.00
0.78
18
1863
338
470
0.6
0.1
3.6
0.4
1.00
0.59
76
1924
88
581
0.8
0.2
7.7
2.2
1.00
0.56
16
2010
8868
549
1.4
0.1
5.0
0.4
0.82
0.64
136
2146
530
0.9
0.3
1.4
0.5
1.00
1.00
10
2213
214
441.
00.
21.
20.
20.
931.
0028
2312
4759
756
1.1
0.1
5.5
0.5
0.91
0.59
103
2467
277
551
0.7
0.1
2.7
0.2
0.93
0.71
123
10
Supple
men
tary
Tab
le1.
Con
tinued
.
Sp
ecie
s/In
div
idual
nArgos/GPS
ngeo
loca
tion
Tra
ckle
ngt
hS
Dlon
σSD
lon
SD
lat
σSD
lat
Cov
erag
e
Lon
.L
at.
n
2545
537
277
0.9
0.1
2.8
0.3
0.93
0.77
60
2654
1559
0.6
0.1
5.3
1.1
1.00
0.29
24
2740
254
300
0.7
0.1
2.8
0.3
0.93
0.87
87
2869
924
447
0.6
0.1
2.1
0.3
1.00
0.94
48
2912
9014
620
0.8
0.2
4.4
0.9
0.96
0.50
28
3040
320
224
0.7
0.1
2.6
0.4
1.00
0.71
38
3156
519
337
0.8
0.1
4.1
0.7
1.00
0.62
37
3223
819
510.
60.
12.
60.
41.
000.
7629
3311
1235
674
1.1
0.1
1.0
0.1
0.92
1.00
48
3476
544
673
0.5
0.1
5.8
0.6
1.00
0.33
61
blac
k-fo
oted
alba
tros
s
129
115
17.2
52.
50.
52.
30.
50.
940.
8816
236
210
21.7
53.
50.
91.
50.
40.
620.
9213
340
511
214.
00.
91.
50.
30.
751.
0016
417
36
104.
51.
51.
30.
50.
830.
836
516
59
10.5
2.7
0.7
0.8
0.2
1.00
1.00
9
621
310
114.
41.
12.
60.
60.
670.
789
725
810
12.2
55.
71.
41.
40.
30.
730.
9111
835
313
235.
31.
15.
11.
10.
800.
7315
11
Supple
men
tary
Tab
le1.
Con
tinued
.
Sp
ecie
s/In
div
idual
nArgos/GPS
ngeo
loca
tion
Tra
ckle
ngt
hS
Dlon
σSD
lon
SD
lat
σSD
lat
Cov
erag
e
Lon
.L
at.
n
927
26
105.
01.
70.
90.
30.
571.
007
1023
17
114.
71.
41.
20.
41.
001.
008
1128
85
11.2
56.
12.
42.
30.
80.
710.
717
1224
38
9.25
2.1
0.6
2.7
0.7
1.00
1.00
8
Lay
san
alba
tros
s
169
318
302.
00.
31.
50.
30.
951.
0021
257
916
281.
50.
31.
40.
31.
000.
9020
354
119
27.5
2.6
0.4
0.8
0.1
0.92
0.92
24
460
523
32.2
52.
50.
41.
30.
20.
960.
8824
533
616
17.2
51.
70.
31.
60.
31.
000.
8816
650
824
272.
40.
41.
40.
20.
920.
9624
736
918
222.
10.
41.
20.
21.
000.
8919
843
722
231.
10.
21.
00.
20.
951.
0021
920
511
122.
10.
50.
70.
20.
801.
0010
1019
26
8.75
2.0
0.7
0.9
0.3
0.71
1.00
7
1130
015
16.7
51.
50.
30.
80.
21.
001.
0015
1239
86
151.
10.
40.
80.
31.
001.
007
1349
213
20.2
54.
61.
01.
60.
31.
000.
9111
1431
211
122.
10.
51.
10.
31.
001.
0010
12
Supple
men
tary
Tab
le1.
Con
tinued
.
Sp
ecie
s/In
div
idual
nArgos/GPS
ngeo
loca
tion
Tra
ckle
ngt
hS
Dlon
σSD
lon
SD
lat
σSD
lat
Cov
erag
e
Lon
.L
at.
n
1544
016
16.7
50.
80.
21.
30.
30.
870.
9315
Cal
ifor
nia
sea
lion
172
756
76.2
50.
80.
12.
70.
30.
960.
3974
291
864
85.2
50.
80.
12.
90.
30.
920.
4174
311
7451
80.2
50.
90.
12.
90.
30.
990.
5169
493
857
78.2
50.
70.
11.
30.
10.
990.
9970
595
356
75.2
51.
20.
12.
70.
30.
960.
4372
612
9230
81.2
50.
70.
13.
00.
40.
920.
3839
774
936
77.2
51.
10.
11.
30.
21.
000.
7642
813
0655
83.2
51.
20.
12.
00.
20.
930.
6773
917
4939
87.2
50.
90.
12.
40.
30.
960.
7557
13
Supplementary Figures
Supplementary Figures 1-7. State-space model fitted to Argos/GPS and geolocationdata for example individual black-footed albatrosses (Supplementary Fig. 1, individ-uals #5 (a-c), #1 (d-f), #6 (g-i) and #11 (j-l)), Laysan albatrosses (SupplementaryFig. 2, individuals #8 (a-c), #3 (d-f), #13 (g-i) and #10 (j-l)), mako sharks (Sup-plementary Fig. 3, individuals #1 (a-c), #9 (d-f), #6 (g-i) and #13 (j-l)), bluesharks (Supplementary Fig. 4, individuals #1 (a-c), #2 (d-f), #8 (g-i) and #3 (j-l)),salmon sharks (Supplementary Fig. 5, individuals #28 (a-c), #14 (d-f), #20 (g-i)and #3 (j-l)), Galapagos sharks (Supplementary Fig. 6, individuals #1 (a-c) and#2 (d-f)), and California sea lions (Supplementary Fig. 7, individuals #4 (a-c), #2(d-f), #5 (g-i) and #6 (j-l)). Blue and red points represent Argos/GPS location andgeolocation estimates, respectively. Blue and red lines represent the mean estimatedpaths from the state-space model fitted to Argos/GPS and geolocation data simulta-neously and only geolocation data, respectively. Dashed lines represent intervals of95% posterior probability. Light grey lines in panels a, d, g and j represent a sampleof estimated paths (n = 100) from the posterior probability distribution of the modelfitted to only geolocation data. Triangles indicate known deployment and invertedtriangles indicate known recapture locations. Dark grey represents land. Note thatsome outlying Argos data are outside of the plot boundaries and are not shown.
Supplementary Figures 8-11. Prior and posterior probability distributions for SDof errors in longitude (SDlon) for all individuals. Red lines indicate means on log-scale back-transformed. Much of the prior density was near zero, however, there wasnon-zero prior density across the full range of the x-axis and beyond its upper limitalthough it is not visible on the plot.
Supplementary Figures 12-15. Prior and posterior probability distributions for SDof errors in latitude (SDlat) for all individuals. Red lines indicate means on log-scale back-transformed. Much of the prior density was near zero, however, there wasnon-zero prior density across the full range of the x-axis and beyond its upper limitalthough it is not visible on the plot.
14
Supplementary Figure 1
15
Supplementary Figure 2
16
Supplementary Figure 3
17
Supplementary Figure 4
18
Supplementary Figure 5
19
Supplementary Figure 6
20
Supplementary Figure 7
21
prior
0.0 0.2 0.4 0.6 0.8 1.0
0
0.1
0.2
0.3
0.4
m. shark 1
0.0 0.2 0.4 0.6
0
0.01
0.02
0.03
0.04
Estimated longitude error SD (degrees)
Pro
babi
lity
m. shark 2
0.0 0.2 0.4 0.6 0.8 1.0 1.2
0
0.01
0.02
0.03
m. shark 3
0.0 0.2 0.4 0.6 0.8 1.0
0
0.01
0.02
0.03
m. shark 4
0.0 0.2 0.4 0.6 0.8 1.0 1.2
0
0.01
0.02
0.03
0.04
m. shark 5
0.0 0.2 0.4 0.6 0.8 1.0
0
0.01
0.02
0.03
m. shark 6
0 1 2 3 4
0
0.01
0.02
0.03
0.04
0.05
m. shark 7
0.0 0.2 0.4 0.6 0.8
0
0.01
0.02
0.03
0.04
0.05
m. shark 8
0.0 0.2 0.4 0.6 0.8
0
0.01
0.02
0.03
0.04
m. shark 9
0.0 0.2 0.4 0.6 0.8
0
0.01
0.02
0.03
0.04
0.05
m. shark 10
0.0 0.2 0.4 0.6 0.8 1.0 1.2
0
0.01
0.02
0.03
0.04
m. shark 11
0.0 0.2 0.4 0.6 0.8 1.0 1.2
0
0.01
0.02
0.03
0.04
m. shark 12
0.0 0.2 0.4 0.6 0.8 1.0 1.2
0
0.01
0.02
0.03
0.04
m. shark 13
0.0 0.5 1.0 1.5
0
0.01
0.02
0.03
0.04
m. shark 14
0.0 0.2 0.4 0.6 0.8 1.0
0
0.01
0.02
0.03
0.04
m. shark 15
0.0 0.2 0.4 0.6 0.8 1.0
0
0.01
0.02
0.03
m. shark 16
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
0
0.01
0.02
0.03
0.04
m. shark 17
0.0 0.5 1.0 1.5
0
0.01
0.02
0.03
0.04
m. shark 18
0.0 0.2 0.4 0.6 0.8 1.0
0
0.01
0.02
0.03
m. shark 19
0.0 0.2 0.4 0.6 0.8
0
0.01
0.02
0.03
0.04
m. shark 20
0.0 0.2 0.4 0.6 0.8
0
0.01
0.02
0.03
m. shark 21
0.0 0.2 0.4 0.6 0.8 1.0 1.2
0
0.01
0.02
0.03
m. shark 22
0.0 0.2 0.4 0.6 0.8 1.0
0
0.01
0.02
0.03
m. shark 23
0.0 0.2 0.4 0.6 0.8 1.0
0
0.01
0.02
0.03
m. shark 24
0.0 0.2 0.4 0.6 0.8 1.0
0
0.01
0.02
0.03
m. shark 25
0.0 0.2 0.4 0.6 0.8 1.0
0
0.01
0.02
0.03
b. shark 1
0.0 0.2 0.4 0.6 0.8 1.0
0
0.01
0.02
0.03
0.04
b. shark 2
0.0 0.4 0.8 1.2
0
0.01
0.02
0.03
b. shark 3
0.0 0.1 0.2 0.3 0.4 0.5 0.6
0
0.01
0.02
0.03
b. shark 4
0.0 0.5 1.0 1.5 2.0
0
0.01
0.02
0.03
0.04
b. shark 5
0.0 0.4 0.8 1.2
0
0.01
0.02
0.03
0.04
b. shark 6
0.0 0.2 0.4 0.6 0.8
0
0.01
0.02
0.03
Supplementary Figure 8
22
b. shark 7
0.0 0.2 0.4 0.6 0.8
0
0.01
0.02
0.03
b. shark 8
0.0 0.2 0.4 0.6 0.8 1.0 1.2
0
0.01
0.02
0.03
0.04
Estimated longitude error SD (degrees)
Pro
babi
lity
b. shark 9
0.0 0.1 0.2 0.3 0.4 0.5 0.6
0
0.01
0.02
0.03
0.04b. shark 10
0.0 0.2 0.4 0.6 0.8 1.0 1.2
0
0.01
0.02
0.03
b. shark 11
0.0 0.5 1.0 1.5
0
0.01
0.02
0.03
0.04
0.05
b. shark 12
0.0 0.5 1.0 1.5
0
0.01
0.02
0.03
0.04
0.05
b. shark 13
0.0 0.2 0.4 0.6 0.8 1.0 1.2
0
0.01
0.02
0.03
b. shark 14
0.0 0.2 0.4 0.6 0.8 1.0 1.2
0
0.01
0.02
0.03
s. shark 1
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0
0.01
0.02
0.03
0.04
0.05
s. shark 2
0.0 0.5 1.0 1.5 2.0 2.5
0
0.01
0.02
0.03
0.04
s. shark 3
0.0 1.0 2.0 3.0
0
0.01
0.02
0.03
s. shark 4
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
0
0.01
0.02
0.03
0.04
s. shark 5
0.0 0.5 1.0 1.5
0
0.01
0.02
0.03
0.04
s. shark 6
0.0 0.5 1.0 1.5 2.0 2.5
0
0.01
0.02
0.03
0.04
s. shark 7
0.0 0.2 0.4 0.6 0.8 1.0
0
0.01
0.02
0.03
s. shark 8
0.0 0.5 1.0 1.5 2.0
0
0.01
0.02
0.03
s. shark 9
0.0 0.4 0.8 1.2
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035s. shark 10
0.0 0.5 1.0 1.5
0
0.01
0.02
0.03
s. shark 11
0.0 0.5 1.0 1.5 2.0 2.5
0
0.01
0.02
0.03
0.04
s. shark 12
0.0 0.5 1.0 1.5 2.0 2.5
0
0.01
0.02
0.03
s. shark 13
0.0 1.0 2.0 3.0
0
0.01
0.02
0.03
s. shark 14
0.0 0.2 0.4 0.6 0.8 1.0
0
0.01
0.02
0.03
0.04
s. shark 15
0 1 2 3 4
0
0.01
0.02
0.03
0.04
s. shark 16
0.0 0.2 0.4 0.6 0.8 1.0 1.2
0
0.01
0.02
0.03
0.04
s. shark 17
0.0 0.5 1.0 1.5 2.0
0
0.01
0.02
0.03
0.04
0.05s. shark 18
0.0 0.2 0.4 0.6 0.8
0
0.01
0.02
0.03
0.04
s. shark 19
0.0 0.5 1.0 1.5 2.0 2.5
0
0.01
0.02
0.03
0.04
s. shark 20
0.0 0.5 1.0 1.5
0
0.01
0.02
0.03
0.04
s. shark 21
0 1 2 3 4
0
0.01
0.02
0.03
0.04
0.05
s. shark 22
0.0 0.5 1.0 1.5 2.0
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035s. shark 23
0.0 0.5 1.0 1.5
0
0.01
0.02
0.03
0.04
s. shark 24
0.0 0.2 0.4 0.6 0.8 1.0
0
0.01
0.02
0.03
0.04
0.05
Supplementary Figure 9
23
s. shark 25
0.0 0.2 0.4 0.6 0.8 1.0 1.2
0
0.01
0.02
0.03
0.04
s. shark 26
0.0 0.5 1.0 1.5
0
0.01
0.02
0.03
0.04
Estimated longitude error SD (degrees)
Pro
babi
lity
s. shark 27
0.0 0.2 0.4 0.6 0.8
0
0.01
0.02
0.03
0.04
s. shark 28
0.0 0.2 0.4 0.6 0.8 1.0
0
0.01
0.02
0.03
0.04
s. shark 29
0.0 0.5 1.0 1.5
0
0.01
0.02
0.03
s. shark 30
0.0 0.2 0.4 0.6 0.8 1.0 1.2
0
0.01
0.02
0.03
s. shark 31
0.0 0.5 1.0 1.5
0
0.01
0.02
0.03
0.04s. shark 32
0.0 0.5 1.0 1.5
0
0.01
0.02
0.03
0.04
s. shark 33
0.0 0.5 1.0 1.5
0
0.01
0.02
0.03
0.04
s. shark 34
0.0 0.2 0.4 0.6 0.8
0
0.01
0.02
0.03
0.04
G. shark 1
0.0 0.5 1.0 1.5
0
0.01
0.02
0.03
0.04
G. shark 2
0.0 0.5 1.0 1.5
0
0.01
0.02
0.03
b. albatross 1
0 1 2 3 4 5
0
0.01
0.02
0.03
b. albatross 2
0 2 4 6 8 10
0
0.01
0.02
0.03
b. albatross 3
0 2 4 6 8
0
0.01
0.02
0.03
b. albatross 4
0 5 10 15
0
0.01
0.02
0.03
0.04
b. albatross 5
0 1 2 3 4 5 6 7
0
0.01
0.02
0.03
b. albatross 6
0 5 10 15
0
0.01
0.02
0.03
0.04
0.05
b. albatross 7
0 5 10 15
0
0.01
0.02
0.03
0.04
b. albatross 8
0 2 4 6 8 10 12 14
0
0.01
0.02
0.03
0.04
b. albatross 9
0 5 10 15
0
0.01
0.02
0.03
0.04
b. albatross 10
0 5 10 15
0
0.01
0.02
0.03
0.04
0.05b. albatross 11
0 5 10 15 20 25 30
0
0.01
0.02
0.03
0.04
0.05
b. albatross 12
0 1 2 3 4 5 6 7
0
0.01
0.02
0.03
0.04
L. albatross 1
0 1 2 3
0
0.01
0.02
0.03
L. albatross 2
0.0 0.5 1.0 1.5 2.0 2.5
0
0.01
0.02
0.03
L. albatross 3
0 1 2 3 4 5
0
0.01
0.02
0.03
L. albatross 4
0 1 2 3 4 5
0
0.01
0.02
0.03
0.04
L. albatross 5
0.0 1.0 2.0 3.0
0
0.01
0.02
0.03
0.04L. albatross 6
0 1 2 3 4
0
0.01
0.02
0.03
0.04
L. albatross 7
0 1 2 3 4
0
0.01
0.02
0.03
0.04
L. albatross 8
0.0 0.5 1.0 1.5 2.0
0
0.01
0.02
0.03
Supplementary Figure 10
24
L. albatross 9
0 1 2 3 4 5 6
0
0.01
0.02
0.03
0.04
L. albatross 10
0 2 4 6 8 10
0
0.01
0.02
0.03
0.04
0.05
0.06
Estimated longitude error SD (degrees)
Pro
babi
lity
L. albatross 11
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
0
0.01
0.02
0.03
0.04
L. albatross 12
0 1 2 3 4 5
0
0.01
0.02
0.03
0.04
L. albatross 13
0 2 4 6 8
0
0.01
0.02
0.03
L. albatross 14
0 1 2 3 4
0
0.005
0.01
0.015
0.02
0.025
0.03
L. albatross 15
0.0 0.5 1.0 1.5
0
0.01
0.02
0.03
0.04
C. sea lion 1
0.0 0.2 0.4 0.6 0.8 1.0
0
0.01
0.02
0.03
0.04
0.05
C. sea lion 2
0.0 0.2 0.4 0.6 0.8 1.0 1.2
0
0.01
0.02
0.03
0.04
0.05
C. sea lion 3
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
0
0.01
0.02
0.03
0.04
C. sea lion 4
0.0 0.2 0.4 0.6 0.8 1.0
0
0.01
0.02
0.03
0.04
0.05C. sea lion 5
0.0 0.5 1.0 1.5
0
0.01
0.02
0.03
0.04
0.05
C. sea lion 6
0.0 0.2 0.4 0.6 0.8 1.0 1.2
0
0.01
0.02
0.03
C. sea lion 7
0.0 0.5 1.0 1.5
0
0.01
0.02
0.03
0.04
C. sea lion 8
0.0 0.5 1.0 1.5
0
0.01
0.02
0.03
0.04
C. sea lion 9
0.0 0.4 0.8 1.2
0
0.01
0.02
0.03
0.04
Supplementary Figure 11
25
prior
0.0 0.2 0.4 0.6 0.8 1.0
0
0.1
0.2
0.3
0.4
m. shark 1
0.0 0.2 0.4 0.6
0
0.01
0.02
0.03
0.04
Estimated latitude error SD (degrees)
Pro
babi
lity
m. shark 2
0.0 0.5 1.0 1.5 2.0 2.5
0
0.01
0.02
0.03
0.04
m. shark 3
0.0 0.5 1.0 1.5 2.0
0
0.01
0.02
0.03
m. shark 4
0 1 2 3 4
0
0.01
0.02
0.03
0.04
m. shark 5
0.0 0.5 1.0 1.5
0
0.01
0.02
0.03
m. shark 6
0 1 2 3 4 5 6 7
0
0.01
0.02
0.03
0.04
m. shark 7
0.0 0.5 1.0 1.5 2.0
0
0.01
0.02
0.03
0.04
0.05
m. shark 8
0.0 0.5 1.0 1.5 2.0
0
0.01
0.02
0.03
0.04
m. shark 9
0.0 0.5 1.0 1.5
0
0.01
0.02
0.03
0.04
0.05
m. shark 10
0.0 0.5 1.0 1.5 2.0 2.5
0
0.01
0.02
0.03
0.04
m. shark 11
0.0 0.5 1.0 1.5
0
0.01
0.02
0.03
0.04
m. shark 12
0.0 0.5 1.0 1.5 2.0 2.5
0
0.01
0.02
0.03
m. shark 13
0 1 2 3 4
0
0.01
0.02
0.03
m. shark 14
0 1 2 3
0
0.01
0.02
0.03
m. shark 15
0 1 2 3 4 5 6
0
0.01
0.02
0.03
m. shark 16
0 1 2 3
0
0.01
0.02
0.03
m. shark 17
0.0 0.5 1.0 1.5 2.0
0
0.01
0.02
0.03
m. shark 18
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
0
0.01
0.02
0.03
0.04m. shark 19
0.0 0.5 1.0 1.5
0
0.01
0.02
0.03
m. shark 20
0.0 0.5 1.0 1.5
0
0.01
0.02
0.03
0.04
m. shark 21
0.0 0.2 0.4 0.6 0.8 1.0 1.2
0
0.005
0.01
0.015
0.02
0.025
0.03
m. shark 22
0.0 0.5 1.0 1.5
0
0.01
0.02
0.03
m. shark 23
0.0 0.5 1.0 1.5 2.0 2.5
0
0.01
0.02
0.03
m. shark 24
0.0 0.5 1.0 1.5
0
0.01
0.02
0.03
m. shark 25
0 1 2 3 4 5 6
0
0.01
0.02
0.03
b. shark 1
0.0 0.5 1.0 1.5 2.0 2.5
0
0.01
0.02
0.03
0.04
b. shark 2
0.0 0.5 1.0 1.5 2.0 2.5
0
0.01
0.02
0.03
0.04
b. shark 3
0 1 2 3 4 5 6
0
0.01
0.02
0.03
0.04
b. shark 4
0 1 2 3 4
0
0.01
0.02
0.03
0.04
b. shark 5
0.0 0.5 1.0 1.5 2.0 2.5
0
0.01
0.02
0.03
0.04
b. shark 6
0.0 0.2 0.4 0.6 0.8 1.0 1.2
0
0.01
0.02
0.03
Supplementary Figure 12
26
b. shark 7
0 1 2 3 4
0
0.01
0.02
0.03
0.04
b. shark 8
0 5 10 15 20
0
0.01
0.02
0.03
0.04
Estimated latitude error SD (degrees)
Pro
babi
lity
b. shark 9
0.0 0.5 1.0 1.5 2.0 2.5
0
0.01
0.02
0.03
0.04
b. shark 10
0 1 2 3 4 5 6 7
0
0.01
0.02
0.03
b. shark 11
0 2 4 6 8
0
0.01
0.02
0.03
b. shark 12
0 5 10 15 20
0
0.01
0.02
0.03
0.04
b. shark 13
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0
0.01
0.02
0.03
b. shark 14
0.0 0.5 1.0 1.5 2.0
0
0.01
0.02
0.03
0.04
0.05
0.06
s. shark 1
0 5 10 15
0
0.01
0.02
0.03
0.04
s. shark 2
0 5 10 15
0
0.005
0.01
0.015
0.02
0.025
0.03
s. shark 3
0 2 4 6 8 10 12 14
0
0.01
0.02
0.03
0.04
0.05
s. shark 4
0 1 2 3 4 5
0
0.01
0.02
0.03
0.04
0.05
s. shark 5
0.0 0.5 1.0 1.5 2.0 2.5
0
0.01
0.02
0.03
0.04
s. shark 6
0 2 4 6 8
0
0.01
0.02
0.03
0.04
0.05
0.06
s. shark 7
0 1 2 3 4 5
0
0.01
0.02
0.03
s. shark 8
0 2 4 6 8 10 12
0
0.01
0.02
0.03
0.04
s. shark 9
0 1 2 3 4 5 6 7
0
0.01
0.02
0.03
s. shark 10
0 2 4 6 8
0
0.01
0.02
0.03
0.04
s. shark 11
0 2 4 6 8 10
0
0.01
0.02
0.03
0.04
s. shark 12
0 2 4 6 8 10 12 14
0
0.01
0.02
0.03
0.04
s. shark 13
0 10 20 30 40
0
0.01
0.02
0.03
s. shark 14
0 2 4 6 8
0
0.01
0.02
0.03
0.04
0.05
s. shark 15
0 2 4 6 8 10 12 14
0
0.01
0.02
0.03
0.04
s. shark 16
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0
0.01
0.02
0.03
0.04
s. shark 17
0 5 10 15 20
0
0.01
0.02
0.03
0.04
s. shark 18
0 1 2 3 4 5 6
0
0.01
0.02
0.03
0.04
s. shark 19
0 5 10 15 20
0
0.01
0.02
0.03
0.04
s. shark 20
0 1 2 3 4 5 6 7
0
0.01
0.02
0.03
0.04
0.05
s. shark 21
0 1 2 3 4 5 6
0
0.01
0.02
0.03
0.04
s. shark 22
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0
0.01
0.02
0.03
0.04
s. shark 23
0 2 4 6 8
0
0.01
0.02
0.03
0.04
0.05
s. shark 24
0.0 1.0 2.0 3.0
0
0.01
0.02
0.03
0.04
0.05
Supplementary Figure 13
27
s. shark 25
0 1 2 3 4
0
0.01
0.02
0.03
0.04
s. shark 26
0 2 4 6 8 10 12
0
0.01
0.02
0.03
0.04
Estimated latitude error SD (degrees)
Pro
babi
lity
s. shark 27
0 1 2 3 4
0
0.01
0.02
0.03
0.04
s. shark 28
0 1 2 3 4
0
0.01
0.02
0.03
s. shark 29
0 2 4 6 8 10
0
0.01
0.02
0.03
0.04
s. shark 30
0 1 2 3 4
0
0.01
0.02
0.03
s. shark 31
0 2 4 6 8
0
0.01
0.02
0.03
s. shark 32
0 1 2 3 4 5
0
0.01
0.02
0.03
s. shark 33
0.0 0.5 1.0 1.5
0
0.01
0.02
0.03
s. shark 34
0 2 4 6 8
0
0.01
0.02
0.03
0.04
G. shark 1
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
0
0.01
0.02
0.03
0.04
G. shark 2
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0
0.01
0.02
0.03
0.04
b. albatross 1
0 1 2 3 4 5
0
0.01
0.02
0.03
0.04
b. albatross 2
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0
0.005
0.01
0.015
0.02
0.025
0.03
b. albatross 3
0 1 2 3 4
0
0.01
0.02
0.03
0.04
b. albatross 4
0 1 2 3 4 5
0
0.01
0.02
0.03
0.04
b. albatross 5
0.0 1.0 2.0 3.0
0
0.01
0.02
0.03
0.04
0.05
b. albatross 6
0 1 2 3 4 5 6 7
0
0.01
0.02
0.03
b. albatross 7
0 1 2 3 4
0
0.01
0.02
0.03
0.04b. albatross 8
0 2 4 6 8 10 12
0
0.01
0.02
0.03
0.04
b. albatross 9
0 1 2 3 4
0
0.01
0.02
0.03
0.04
0.05
b. albatross 10
0 1 2 3 4 5
0
0.01
0.02
0.03
0.04
0.05
b. albatross 11
0 2 4 6 8 10
0
0.01
0.02
0.03
0.04
b. albatross 12
0 2 4 6 8
0
0.01
0.02
0.03
0.04
L. albatross 1
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0
0.01
0.02
0.03
0.04L. albatross 2
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0
0.01
0.02
0.03
0.04
L. albatross 3
0.0 0.5 1.0 1.5 2.0
0
0.01
0.02
0.03
0.04
L. albatross 4
0.0 0.5 1.0 1.5 2.0
0
0.01
0.02
0.03
0.04
L. albatross 5
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
0
0.01
0.02
0.03
L. albatross 6
0.0 0.5 1.0 1.5 2.0
0
0.01
0.02
0.03
0.04L. albatross 7
0.0 0.5 1.0 1.5 2.0
0
0.005
0.01
0.015
0.02
0.025
0.03
L. albatross 8
0.0 0.5 1.0 1.5 2.0
0
0.01
0.02
0.03
0.04
Supplementary Figure 14
28
L. albatross 9
0.0 0.5 1.0 1.5
0
0.01
0.02
0.03
L. albatross 10
0 1 2 3 4 5
0
0.02
0.04
0.06
Estimated latitude error SD (degrees)
Pro
babi
lity
L. albatross 11
0.0 0.5 1.0 1.5
0
0.01
0.02
0.03
0.04
L. albatross 12
0.0 1.0 2.0 3.0
0
0.01
0.02
0.03
0.04
0.05
L. albatross 13
0 1 2 3 4
0
0.01
0.02
0.03
0.04
L. albatross 14
0.0 0.5 1.0 1.5 2.0 2.5
0
0.01
0.02
0.03
L. albatross 15
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0
0.01
0.02
0.03
0.04
C. sea lion 1
0 1 2 3
0
0.01
0.02
0.03
0.04
C. sea lion 2
0 1 2 3 4
0
0.01
0.02
0.03
0.04
C. sea lion 3
0 1 2 3 4
0
0.01
0.02
0.03
0.04
C. sea lion 4
0.0 0.5 1.0 1.5 2.0
0
0.01
0.02
0.03
0.04
0.05
C. sea lion 5
0 1 2 3 4
0
0.01
0.02
0.03
0.04
0.05
C. sea lion 6
0 1 2 3 4 5
0
0.01
0.02
0.03
0.04
C. sea lion 7
0.0 0.5 1.0 1.5
0
0.01
0.02
0.03
0.04
C. sea lion 8
0.0 0.5 1.0 1.5 2.0 2.5
0
0.01
0.02
0.03
0.04
C. sea lion 9
0 1 2 3
0
0.01
0.02
0.03
0.04
Supplementary Figure 15
29