SUPPLEMENTAL ONLINE MATERIAL FOR VAN HOUTAN, HALLEY, AND MARKS; “TERRESTRIAL BASKING
SEA TURTLES ARE RESPONDING TO SPATIOTEMPORAL SST PATTERNS”
In this Supplement, we present more extensive information on the methods, additional figures and
tables that provide additional quantitative data and other information.
Fourier-series inversion formulas
The following inversion formulas were used to find the components Ak and Bk of the Fourier series given
in the equations from the manuscript text,
𝑇
𝐴𝑘 = ∫ 𝑦(𝑡) cos[𝑘𝜔0 𝑡] 𝑑𝑡
0
𝑇
𝐵𝑘 = ∫ 𝑦(𝑡) sin⁡[𝑘𝜔0 𝑡]𝑑𝑡
0
Here ω0 = 2π/T is the fundamental angular frequency, and T the associated cycle time (1 year), while y(t)
is the value of the data observed at time t.
Since the data are a weekly series we have y1, y2,… , y52 for t = 1, 2, … 52 weeks. The integrals are
approximated by a sum, with dt t=1 week. Thus:
52
𝐴𝑘 ≅ ∑ 𝑦𝑡 cos⁡[𝑘𝜔0 𝑡]
𝑡=1
52
𝐵𝑘 ≅ ∑ 𝑦𝑡 sin⁡[𝑘𝜔0 𝑡]
𝑡=1
A thorough summary of periodic models in general and Fourier series in particular is available in
reference [17].
Figure S1. Chronology estimates for bone stress marks (LAGs) given known dates of OTC marking and
death. By definition, accretion of bone tissue is not linear or constant (light grey line), and it has been
argued that it likely follows an annual cycle, such that lines of arrested growth (LAGs) appear in seasonal
times of stress, and consequently growth rates slow. Since green turtle basking in Hawaii is on
apparently similar seasonal cycle as SST stress (Figure 1b), it makes sense that such stressors might be
visible in the bones tissues an on a similar schedule. As estimated from the Fourier model fits, this peak
stress period would be from late March to mid-May each year. Given this, we applied the SST Fourier
model to modulate the accretion rate of bone tissues (blue lines, see Materials and Methods), providing
an estimate of the schedule of bone LAGs (orange shaded areas) between the validated times of
oxytetracycline (OTC) marking and death (orange points). The result plotted here shows a hypothetical
schedule for seasonal variability in bone growth, according to SST forcing. We display this for 3 Hawaiian
green turtles whose stained, humeri bone cross-sections were provided to us as images by the lead
author of a previous study on skeletochronology [13]. We analyze the 3 turtles that had the shortest
spans between initial capture and death, to minimize the potential error from interannual growth
variation. From these 3 turtles, we estimated the chronology of 6 LAGs, 5 of which were between the
bookended, validated dates and one immediately proximate. In addition, we chronicled one LAG
deemed “faint” by the authors of that study.
Figure S2. Annual SST averages for 1990-2014 for the 11 major global green turtle populations and the
global series average. Turtle site data are from NOAA Ocean Watch server (available at
http://oceanwatch.pifsc.noaa.gov/las) and are AVHRR satellite data from January 1990 to January 2014.
Global series is the NASA GISS series (available at http://data.giss.nasa.gov/gistemp/) discussed in
reference [16]. We excluded the El Niño year 1997 from the Galapagos series due to that anomaly.
Points are the annual surface temperature averages, with fitted model being a simple first-order GLM,
with both the form and goodness-of-fit displayed. The SST series from all turtle populations are warming
(white panels); some at alarming rates. These trends are especially a concern when compared to the
global series (blue panel). All x-axis scaling is constrained between plots. All data available as
supplemental data file.
Chart Nester
Nesting
Symbol Abundance Rookery
Green turtle
Population
M
NP
NI
SA
NA
WP
A
SP
IP
SI
EP
Medi terra nea n
Centra l North Pa ci fi c
North Indi a n
South Atla nti c
North Atla nti c
Centra l Wes t Pa ci fi c
Southwes t Pa ci fi c
Centra l South Pa ci fi c
Ea s t Indi a n Wes t Pa ci fi c
Southwes t Indi a n
Ea s t Pa ci fi c
248
3,697
17,743
29,133
131,790
1,441
30,640
1,029
14,915
25,258
3,603
Akya ta n, Turkey
Fr. Fri ga te Shoa l s , USA
Ra s Sha rma , Yemen
Pol i ã o, Gui nea Bi s s a u
Tortuguero, Cos ta Ri ca
Ul i thi Atol l , FSM
Ra i ne Is l a nd, Aus tra l i a
Sci l l y Atol l , Fr. Pol ynes i a
Wel l es l ey, Aus tra l i a
Europa Is l a nd, Fra nce
Ga l a pa gos , Ecua dor
Habitat
Lat Lon
36.6
23.8
14.8
11.3
10.4
9.9
-11.6
-16.5
-16.6
-22.4
0.0
35.2
-166.2
50.0
-16.1
-83.5
139.9
144.0
-154.6
139.8
40.4
-90.5
Winter SST
lo 95% ave hi 95% n
21.3
24.6
26.6
24.8
27.1
27.5
25.3
27.3
26.1
25.4
22.5
22.5
25.2
27.4
26.3
27.8
28.6
26.6
27.8
27.1
26.3
23.9
23.2
25.8
28.1
27.4
28.5
29.3
27.7
28.5
27.8
26.9
26.3
316
315
313
314
328
322
319
320
312
315
302
1990-2014 SST
min lo 95% hi 95% max
n
14.6
21.2
22.9
21.2
25.5
25.8
22.2
24.8
20.4
22.5
18.8
15.8
22.4
24.6
22.8
26.3
26.9
24.0
26.1
22.0
23.1
20.3
29.4
27.8
30.3
29.5
29.7
30.0
29.7
29.6
31.3
29.7
28.4
31.0
28.5
31.6
30.0
30.9
30.8
30.8
30.6
32.4
30.7
31.1
1221
1178
1182
1048
863
1007
1032
1085
1141
1213
1143
ΔSST ΔSST yr -1
1.2
0.8
0.7
2.2
1.0
1.4
1.4
0.6
0.3
0.7
0.8
0.048
0.034
0.029
0.090
0.044
0.059
0.059
0.023
0.011
0.029
0.035
Table S1. Full results from the global green turtle population SST analysis. The primary metrics of
interest are the 95% interval for winter SST and annual SST, and in addition, the extreme annual values.
ΔSST is the observed change in the linear SST changes during the entire period displayed in Figure S2,
and discussed in the Materials and Methods. Populations, locations, and nester abundance are from
reference [3]. Hawaii has the coolest peak SST of all populations as expressed in terms of the extreme
peak (28.5 °C) and upper 95% interval (27.8 °C) of annual SST. Over these 24 years of data, SST profiles
at these sites increased on average 1.0 °C (range 0.3-2.2 °C), which amounts to 4.1 °C century-1, but as
high as 9.0 °C century-1 (Polião, Guinea Bissau). This average increase is 3 times (range 0.8–6.3 times) the
average global surface temperature change (0.01 °C yr-1) during this period, based on the data from
reference [16].