Supplementary information
Tolerance landscapes in thermal ecology
E.L. Rezende, L. E. Castañeda and M. Santos.
Measuring thermal tolerance .................................................................. 2
Static versus ramping assays .................................................................. 2
Fig. S1 – Building a thermal tolerance landscape ..................................... 6
Fig. S2 – The tolerance landscape and subordinate traits .......................... 7
Body mass and thermal inertia ............................................................... 8
Appendix S1 ........................................................................................ 10
Appendix S2 ........................................................................................ 12
References ........................................................................................... 13
1
Measuring thermal tolerance
The thermal landscape can be readily estimated from knockdown time estimates
obtained across different temperatures (Fig. S1). Given an adequate sample size, TDT
curves can be estimated not only for the median lethal time in which 50% of
individuals succumb to heat, which roughly corresponds to the average knockdown
times (see Cooper et al. 2008), but also for other lethal time values. Briefly,
individuals are submitted to different constant stressful temperatures and their
knockdown times are recorded (i.e., static assay, e.g., Santos et al. 2011). The time
taken for a given fraction of the sample to collapse (say, 90% of all individuals) in
each temperature is then estimated. Subsequently, a TDT curve describing the isocline
for this survival probability (= 0.1 in this example) can be readily calculated with a
regression of log-transformed time estimates against T (eqn. 1). One can then build
thermal tolerance landscape by superimposing TDT curves describing different
survival probability isoclines (Fig. S1).
STATIC VERSUS RAMPING ASSAYS
The proposed framework suggests that, deviations due to varying cumulative thermal
effects and hardening aside, static and ramping protocols provide different estimates
of a single underlying relationship between thermal tolerance and time (see fig. 3b in
Santos et al. 2011). Nonetheless, a systematic analysis of thermal tolerance curves
must take into account these deviations and their potential effects on the
quantification of parameters CTmax and z. Whereas the effects of hardening are
relatively straightforward to control, methodology has such a great impact of
estimates of thermal tolerance (Lutterschmidt and Hutchison 1997; Chown et al.
2009; Santos et al. 2011; Ribeiro et al. 2012) that it may jeopardize comparative
2
efforts, the quest for general patterns and, more importantly, the validation of results
(Rezende and Santos 2012). Circumventing these issues requires an understanding of
the pros and cons of different methods and, ultimately, a concerted effort to employ a
standardized methodology.
We presently advocate for the use of static assays at different temperatures
because thermal tolerance varies both with the intensity and the duration of the heat
stress, and neither are independent nor controlled in ramping assays. Without
understanding how the total cumulative thermal stress resulting in impaired
physiological function changes with temperature and time, it is virtually impossible to
compare estimates from assays obtained with different ramping protocols (e.g., it is
unclear whether a starting temperature of 40 C and a ramping rate of 0.05 C min 1
results on a higher thermal challenge than a starting temperature of 38 C and a rate


of 0.1 C min 1). Because the intensity
and duration of the thermal stress is
 and heating rates, their
determined by the interaction between starting temperatures

effects cannot be readily partitioned or controlled by statistical means (see Rezende et
al. 2011).
Conversely, in static assays the intensity and duration of the thermal stress are
orthogonal to one another because temperature is kept constant. These assays are
more adequate for analyses at the population level because they permit the
quantification of the death rate constant k, which can be directly compared across
species measured at the same temperatures (additionally, lethal times and the intensity
of selection can be readily extrapolated from k for different scenarios). For the same
reason, regression models to estimate CTmax and z differ between protocols. Parameter
estimation with static assays involves ordinary least squares (OLS), including T as
and log10 t as the independent and dependent variable, without and with measurement

3
error, respectively (CTmax and z are then calculated from the slope and intercept, see
main text). In ramping assays, both T and log10 t involve measurement error, hence
OLS results may be jeopardized because it attempts to minimize a sum of squared
errors that is not orthogonal to neither
T or log10 t.

Measurement accuracy is also expected to be lower in ramping assays,
primarily because it is easier to maintain a constant temperature than temperatures
increasing at a constant rate (e.g., this probably explains some of the contradictory
results listed in Rezende and Santos 2012). Failing to detect when an animal collapses
will result in error in knockdown time in static assays, and in knockdown time and
temperature in ramping assays (see Castañeda et al. 2012). Thermal inertia may also
be more problematic for ramping assays, particularly those employing fast rates of
temperature increase, than static assays in which Ta and Tb eventually reach thermal
equilibrium (eqn S1 and S2). Taken together, these factors might explain, for
instance, why heat tolerance in Drosophila is seemingly unaffected by water status
when assayed with ramping protocols (Overgaard et al. 2012) and highly dependent
on humidity when comparisons involve static assays at a common temperature
(Maynard Smith 1957; Bubliy et al. 2012).
To summarize, estimates obtained with ramping assays are, in principle,
suitable for parameter estimation. However, in practice it is advisable to focus on
measurements of knockdown times at different temperatures, to ensure that
measurement noise is minimal and the statistical power to detect potentially relevant
associations is maximized (see also Santos et al. 2011). Differences in goodness of fit
between analyses employing estimates obtained with static versus ramping assay
support these concerns: whereas the semi-logarithmic relationship explains 98.8% of
the variation in knockdown times measured in D. subobscura at different
4
temperatures (r2 = 0.988; see Fig. 1), this value drops to roughly 50.7% when
analyses are repeated pooling mean knockdown temperatures and times of G.
pallidipes estimated with different ramping assays (r2 = 0.507; values from fig. 1a in
Terblanche et al. 2007, who reported r2 = 0.576 assuming a linear relation between
knockdown temperature and time). If this anecdotic observation happens to be
general, then ramping assays should be avoided during the estimation of parameters
CTmax and z of TDT curves.
5
Fig. S1 – Building a thermal tolerance landscape from experimental data. Top left. Simulated
datasets illustrating the outcome of static assays at different temperatures, with individuals measured
in each temperature slightly displaced to better visualize the data. Top right. Cumulative mortality
curves in time allow the estimation of multiple lethal times LT in which a defined fraction of the
population collapses, as demonstrated in this example for LT10, LT50 and LT90. Bottom left. The
association between these estimates of LT (log10-transformed) and temperature is described by two
parameters (intercept and slope) that can be easily calculated with ordinary least square regressions
and back-transformed to obtain CTmax and z (see eqns 1 and 2). Bottom right. The regressions plotted
as multiple TDT curves, which depict where the isoclines of survival probability lie in the thermal
tolerance landscape.
6
Fig. S2 – Subordinate traits and break points in a thermal tolerance landscape. Top. The proposed
model describes a linear relationship between tolerated temperatures and log-transformed time, as
shown here for Drosophila melanogaster (data from static assays compiled from Mitchell &
Hoffmann 2010; Parkash et al. 2010; Sgrò et al. 2010; Overgaard et al. 2011 and Kimura 2004).
Bottom. TDT curves at the organismal level likely reflect the interaction between multiple traits at
lower levels of organization, as shown schematically here. Based on the dose-response
relationship, cumulative effects of temperature on subordinate traits may result in curves of
decaying performance that resemble TDT curves. This conceptual model provides a temporal
component to the thermobiological scale proposed by Vannier (1994) and accounts for the
existence of different proxies of thermal tolerance (lethal and non-lethal) that can vary with the
nature of the assay. For instance, whereas enzyme denaturation and metabolic imbalance during a
thermal challenge can be lethal, other end points such as the onset of muscle spasms or loss of
motor coordination are non-lethal and may give rise to seemingly different results. This model can
also explain, from a physiological perspective, the presence of break-points along the TDT curve
(Santos et al. 2011).
7
BODY MASS AND THERMAL INERTIA
The proposed approach is highly general and applicable to other systems, being
limited primarily by the thermal tolerance and environmental data available for
hypothesis testing. This is particularly true for small organisms in which thermal
inertia is not a concern, and even some time lag between ambient temperature Ta and
body temperature Tb (within the range of minutes) may not alter dramatically the
predictions of the model. However, for larger organisms thermal inertia may have an
impact on estimates of thermal tolerance measured in the laboratory and on Tb in the
field.
The impact of thermal inertia on these variables can be estimated with
knowledge of the time constant  (Bell 1980; Stevenson 1985; Huey et al. 1992),
which can be measured empirically or estimated from allometry (Lactin and Johnson

1998). According to simplified
heat transfer models:
dTb (t) Ta (t)  Tb (t)
.

dt

eqn S1
The solution of this
differential equation will have the form f (Ta )  e(t /  ), and  (min)
can be defined as the time it takes Tb to reach 1 – 1/e = 63.2% of its final asymptotic
value. Thus, in a static assay in which animals are 
initially submittedto a step change
in Ta (from room temperature to T; eqn 1), the time t necessary for T to drop to
levels corresponding to a 1% of T(t0 ) corresponds to t   ln(1/0.01) . For example,

t < 5 min when  1.086 min , which can be contrasted against
the total duration of a



8
static assay to analyze to what extent thermal inertia might affect knockdown times
estimates.
To quantify the impact of thermal inertia during warming conditions, which
apply both to ramping assays and estimations of Tb in the field, Huey et al. (1992)
demonstrated that the maximum lag between Ta and Tb is:
Ta (t)  Tb (t)  b ,
eqn S2
where b ( C min 1 ) 
corresponds to the rate of temperature increase. Consequently, the
absolute maximum lag between Ta and Tb for an organism with  = 1 min will be

small for typical fast ramping experiments employing heating rates of 0.5Cmin 1,

and virtually negligible in the field (see fig. 1 in Terblanche et al. 2011). Because
 encounters
warming rates in the field are generally low (unless the organism
contrasting Ta during displacement from one microenvironment to another), larger
values of  seem to be more of a concern during estimations of thermal tolerance in
the laboratory than for extrapolations to field conditions.

9
Appendix S1. Thermal death time parameters calculated from heat tolerance measurements
Species
Cydia pomonella
Plodia interpunctella
Amyelois transitella
Ceratitis capitata
Anastrepha ludens
Tribolium castaneum
Bactrocera latifrons
Ceratitis capitata
Bactrocera cucurbitae
Bactrocera dorsalis
Bactrocera latifrons
Ceratitis capitata
Ceratitis capitata
Bactrocera cucurbitae
Bactrocera dorsalis
Stegobium paniceum
Cataglyphis rosenhaueri
Cataglyphis velox
Drosophila subobscura
Cimex lectularius
Anopheles gambiae
Drosophila melanogaster
Deleatidium sp
Sephlebia dentata
Aoteapsyche colonica
Pyconocentria evecta
Deleatidium autumnale
Class
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Stage
last instar
last instar
last instar
last instar
last instar
last instar
egg
egg
egg
egg
third instar
third instar
third instar
third instar
third instar
first instar
adult
adult
adult
adult
egg
third instar
larvae
larvae
larvae
larvae
nymph
Habitat
terrestrial
terrestrial
terrestrial
terrestrial
terrestrial
terrestrial
terrestrial
terrestrial
terrestrial
terrestrial
terrestrial
terrestrial
terrestrial
terrestrial
terrestrial
terrestrial
terrestrial
terrestrial
terrestrial
terrestrial
aquatic
terrestrial
aquatic
aquatic
aquatic
aquatic
aquatic
LT
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
50
100
100
50
100
100
50
50
50
50
50
50
CTmax
53.96
51.5
54.58
51.23
50.17
52.34
50.14
50.22
49.24
50.01
50.66
50.25
49.71
50.67
50.66
61.57
53.53
60.03
41.4
48.84
48.59
44.05
48.84
44.23
37.91
59.58
40.06
10
z
4.35
3.85
3.85
3.33
3.45
2.44
2.98
3.16
3.03
3.21
3.7
3.03
3.17
3.87
3.06
6.47
3.92
6.26
3.93
4
3.04
3.4
7
5.48
3.18
9.3
4.24
r2
0.996
0.998
0.987
0.999
0.997
0.993
0.947
0.986
0.994
0.997
0.997
0.979
0.977
0.998
0.971
0.936
0.935
0.959
0.988
0.995
0.991
0.998
0.997
0.999
0.992
0.964
0.991
Reference
Tang et al. 2007 Table 6.3
Tang et al. 2007 Table 6.3
Tang et al. 2007 Table 6.3
Tang et al. 2007 Table 6.3
Tang et al. 2007 Table 6.3
Tang et al. 2007 Table 6.3
Armstrong et al. 2009 Table 5
Armstrong et al. 2009 Table 5
Armstrong et al. 2009 Table 5
Armstrong et al. 2009 Table 5
Armstrong et al. 2009 Table 6
Armstrong et al. 2009 Table 6
Armstrong et al. 2009 Table 6
Armstrong et al. 2009 Table 6
Armstrong et al. 2009 Table 6
Abdelghany et al. 2010 Table3
Cerda and Retana 2000 Fig3
Cerda and Retana 2000 Fig3
Maynard-Smith 1957 Fig1
Pereira et al. 2009 Fig2
Huang et al. 2006 Table1
Feder et al. 1997 Fig7
Quinn et al. 1994 Table1
Quinn et al. 1994 Table1
Quinn et al. 1994 Table1
Quinn et al. 1994 Table1
Cox and Rutherford 2000 Fig2
Trogoderma granarium
Sphaerium novaezelandiae
Argopecten purpuratus
Semele corrugata
Semele solida
Gari solida
Donax vittatus
Donax semistriatus
Donax trunculus
Tellina fabula
Tellina tenuis
Tellina tenuis
Cardium glaucum
Cardium tuberculatum
Cardium edule
Ameiurus nebulosus
Semotilus atromaculatus
Rhinichthys atratulus
Salmo salar
Salvelinus frontinalis
Oncorhynchus tshawytscha
Cristivomer namaycush
Trematomus bernacchii
Trematomus hansoni
Trematomus borchgrevinki
Salvelinus confluentus
Fundulus parvipinnis
Girella nigricans
Atherinops affinis
Insecta
Bivalvia
Bivalvia
Bivalvia
Bivalvia
Bivalvia
Bivalvia
Bivalvia
Bivalvia
Bivalvia
Bivalvia
Bivalvia
Bivalvia
Bivalvia
Bivalvia
Actinopterygii
Actinopterygii
Actinopterygii
Actinopterygii
Actinopterygii
Actinopterygii
Actinopterygii
Actinopterygii
Actinopterygii
Actinopterygii
Actinopterygii
Actinopterygii
Actinopterygii
Actinopterygii
larvae
adult
adult
adult
adult
adult
adult
adult
adult
adult
adult
adult
adult
adult
adult
adult
adult
adult
adult
adult
adult
adult
adult
adult
adult
juvenile
adult
young
young
terrestrial
aquatic
aquatic
aquatic
aquatic
aquatic
aquatic
aquatic
aquatic
aquatic
aquatic
aquatic
aquatic
aquatic
aquatic
aquatic
aquatic
aquatic
aquatic
aquatic
aquatic
aquatic
aquatic
aquatic
aquatic
aquatic
aquatic
aquatic
aquatic
100
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
60.01
44.99
47.15
49.04
50.28
43.8
38.39
39.34
45.03
33.53
40.13
42.78
41.31
40.83
49.71
36.4
35.86
34.57
32.52
31.94
30.15
29.36
16.99
16.96
17.87
34.87
42.14
38.15
34.59
11
4.22
3.84
6.01
5.87
6.91
5.39
2.87
2.71
3.55
2.02
2.68
3.28
2.04
2.99
5.3
1.35
1.9
1.32
1.78
2
1.34
1.47
3.1
3.03
3.73
2.83
1.65
2.09
0.82
0.911
0.994
0.92
0.985
0.937
0.988
0.902
0.854
0.957
0.889
0.868
0.96
0.921
0.911
0.975
0.987
0.969
0.984
0.988
0.993
0.955
0.993
0.972
0.932
0.974
0.999
0.991
0.995
0.967
Cotton 1950 in Strang1992
Quinn et al. 1994 Table1
Urban 1994 Fig2
Urban 1994 Fig2
Urban 1994 Fig2
Urban 1994 Fig2
Ansell et al. 1980 Fig1A tacc=20
Ansell et al. 1980 Fig1B tacc=20
Ansell et al. 1980 Fig1C tacc=20
Ansell et al. 1980a Fig1A tacc=20
Ansell et al. 1980a Fig1B tacc=20
Ansell et al. 1980a Fig1C tacc=20
Ansell et al. 1981 Fig1A tacc=20
Ansell et al. 1981 Fig1B tacc=20
Ansell et al. 1981 Fig1C tacc=20
Brett 1956 Fig2
Brett 1956 Fig2
Brett 1956 Fig2
Brett 1956 Fig2
Brett 1956 Fig2
Brett 1956 Fig2
Brett 1956 Fig2
Somero and DeVries 1967 Table1
Somero and DeVries 1967 Table1
Somero and DeVries 1967 Table1
Selong et al. 2011 Fig1
Doudoroff 1945 Fig2
Doudoroff 1945 Fig2
Doudoroff 1945 Fig2
Appendix S2. Thermal death time parameters calculated from cold tolerance measurements
Species
Tribolium castaneum
Cryptolestes ferrugineus
Sitophilus granarius
Alphitobius diaperinus
Lasioderma serricone
Lasioderma serricone
Lasioderma serricone
Lasioderma serricone
Stegobium paniceum
Callosobruchus maculatus
Callosobruchus maculatus
Oryzaephilus surinamensis
Sitophilus granarius
Sitophilus granarius
Sitophilus granarius
Sitophilus oryzae
Tribolium castaneum
Tribolium confusum
Tineola bisselliella
Tineola bisselliella
Anagasta kuhniella
Plodia interpunctuella
Class
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Insecta
Stage
all
all
all
adult
egg
larvae
pupae
adult
adult
pupae
egg
adult
adult
egg
larvae
adult
all
all
egg
larvae
all
all
Habitat
terrestrial
terrestrial
terrestrial
terrestrial
terrestrial
terrestrial
terrestrial
terrestrial
terrestrial
terrestrial
terrestrial
terrestrial
terrestrial
terrestrial
terrestrial
terrestrial
terrestrial
terrestrial
terrestrial
terrestrial
terrestrial
terrestrial
LT
50
50
50
50
50
50
50
50
50
50
50
100
100
100
100
100
100
100
100
100
100
100
CTmin
-85.17
-100.96
-35.26
-33.05
-23.05
-33.03
-26.44
-24.35
-22.19
-27.94
-32.58
-107.16
-36.12
-59.23
-48.78
-38.98
-35.28
-34.31
-47.32
-49.18
-40.23
-34.94
12
z’
17.09
20.60
8.25
9.36
7.07
9.21
7.36
6.47
6.02
6.42
9.25
23.03
7.11
12.65
9.79
8.98
7.70
7.37
9.73
8.71
7.21
6.11
r2
0.916
0.992
0.988
0.934
0.995
0.921
0.874
0.966
0.961
0.958
0.966
0.965
0.937
0.915
0.96
0.965
0.934
0.917
0.965
0.878
0.952
0.95
Reference
Fields 1992 Fig1
Fields 1992 Fig1
Fields 1992 Fig1
Renault et al. 2004 Fig2
Imai and Harada Table1
Imai and Harada Table1
Imai and Harada Table1
Imai and Harada Table1
Abdelghany et al. 2010 Table4
Loganathan et al. 2011 Tables4,5
Loganathan et al. 2011 Tables4,5
Mathlein 1961 in Strang 1992
Back and Cotton1924 in Strang 1992
Mathlein 1961 in Strang 1992
Mathlein 1961 in Strang 1992
Back and Cotton1924 in Strang 1992
Cotton 1950 in Strang 1992
Cotton 1950 in Strang 1992
Back and Cotton 1927 in Strang 1992
Back and Cotton 1927 in Strang 1992
Cotton 1950 in Strang 1992
Cotton 1950 in Strang 1992
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