Tolerance Landscapes in Thermal Ecology

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

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 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 and a ramping rate of results on a higher thermal challenge than a starting temperature of and a rate of ). Because the intensity and duration of the thermal stress is determined by the interaction between starting temperatures and heating rates, their 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 as the independent and dependent variable, without and with measurement error, respectively (CTmax and z are then calculated from the slope and intercept, see main text). In ramping assays, both T and 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 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.

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.
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).

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:

.eqn S1

The solution of this differential equation will have the form , 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 to drop to levels corresponding to a 1% of corresponds to . For example, t < 5 min when , which can be contrasted against the total duration of a 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:

,eqn S2

where b () 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 , and virtually negligible in the field (see fig. 1 in Terblanche et al. 2011). Because warming rates in the field are generally low (unless the organism encounters 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.

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Appendix S1. Thermal death time parameters calculated from heat tolerance measurements

Species / Class / Stage / Habitat / LT / CTmax / z / r2 / Reference
Cydia pomonella / Insecta / last instar / terrestrial / 100 / 53.96 / 4.35 / 0.996 / Tang et al. 2007 Table 6.3
Plodia interpunctella / Insecta / last instar / terrestrial / 100 / 51.5 / 3.85 / 0.998 / Tang et al. 2007 Table 6.3
Amyelois transitella / Insecta / last instar / terrestrial / 100 / 54.58 / 3.85 / 0.987 / Tang et al. 2007 Table 6.3
Ceratitis capitata / Insecta / last instar / terrestrial / 100 / 51.23 / 3.33 / 0.999 / Tang et al. 2007 Table 6.3
Anastrepha ludens / Insecta / last instar / terrestrial / 100 / 50.17 / 3.45 / 0.997 / Tang et al. 2007 Table 6.3
Tribolium castaneum / Insecta / last instar / terrestrial / 100 / 52.34 / 2.44 / 0.993 / Tang et al. 2007 Table 6.3
Bactrocera latifrons / Insecta / egg / terrestrial / 100 / 50.14 / 2.98 / 0.947 / Armstrong et al. 2009 Table 5
Ceratitis capitata / Insecta / egg / terrestrial / 100 / 50.22 / 3.16 / 0.986 / Armstrong et al. 2009 Table 5
Bactrocera cucurbitae / Insecta / egg / terrestrial / 100 / 49.24 / 3.03 / 0.994 / Armstrong et al. 2009 Table 5
Bactrocera dorsalis / Insecta / egg / terrestrial / 100 / 50.01 / 3.21 / 0.997 / Armstrong et al. 2009 Table 5
Bactrocera latifrons / Insecta / third instar / terrestrial / 100 / 50.66 / 3.7 / 0.997 / Armstrong et al. 2009 Table 6
Ceratitis capitata / Insecta / third instar / terrestrial / 100 / 50.25 / 3.03 / 0.979 / Armstrong et al. 2009 Table 6
Ceratitis capitata / Insecta / third instar / terrestrial / 100 / 49.71 / 3.17 / 0.977 / Armstrong et al. 2009 Table 6
Bactrocera cucurbitae / Insecta / third instar / terrestrial / 100 / 50.67 / 3.87 / 0.998 / Armstrong et al. 2009 Table 6
Bactrocera dorsalis / Insecta / third instar / terrestrial / 100 / 50.66 / 3.06 / 0.971 / Armstrong et al. 2009 Table 6
Stegobium paniceum / Insecta / first instar / terrestrial / 50 / 61.57 / 6.47 / 0.936 / Abdelghany et al. 2010 Table3
Cataglyphis rosenhaueri / Insecta / adult / terrestrial / 100 / 53.53 / 3.92 / 0.935 / Cerda and Retana 2000 Fig3
Cataglyphis velox / Insecta / adult / terrestrial / 100 / 60.03 / 6.26 / 0.959 / Cerda and Retana 2000 Fig3
Drosophila subobscura / Insecta / adult / terrestrial / 50 / 41.4 / 3.93 / 0.988 / Maynard-Smith 1957 Fig1
Cimex lectularius / Insecta / adult / terrestrial / 100 / 48.84 / 4 / 0.995 / Pereira et al. 2009 Fig2
Anopheles gambiae / Insecta / egg / aquatic / 100 / 48.59 / 3.04 / 0.991 / Huang et al. 2006 Table1
Drosophila melanogaster / Insecta / third instar / terrestrial / 50 / 44.05 / 3.4 / 0.998 / Feder et al. 1997 Fig7
Deleatidium sp / Insecta / larvae / aquatic / 50 / 48.84 / 7 / 0.997 / Quinn et al. 1994 Table1
Sephlebia dentata / Insecta / larvae / aquatic / 50 / 44.23 / 5.48 / 0.999 / Quinn et al. 1994 Table1
Aoteapsyche colonica / Insecta / larvae / aquatic / 50 / 37.91 / 3.18 / 0.992 / Quinn et al. 1994 Table1
Pyconocentria evecta / Insecta / larvae / aquatic / 50 / 59.58 / 9.3 / 0.964 / Quinn et al. 1994 Table1
Deleatidium autumnale / Insecta / nymph / aquatic / 50 / 40.06 / 4.24 / 0.991 / Cox and Rutherford 2000 Fig2
Trogoderma granarium / Insecta / larvae / terrestrial / 100 / 60.01 / 4.22 / 0.911 / Cotton 1950 in Strang1992
Sphaerium novaezelandiae / Bivalvia / adult / aquatic / 50 / 44.99 / 3.84 / 0.994 / Quinn et al. 1994 Table1
Argopecten purpuratus / Bivalvia / adult / aquatic / 50 / 47.15 / 6.01 / 0.92 / Urban 1994 Fig2
Semele corrugata / Bivalvia / adult / aquatic / 50 / 49.04 / 5.87 / 0.985 / Urban 1994 Fig2
Semele solida / Bivalvia / adult / aquatic / 50 / 50.28 / 6.91 / 0.937 / Urban 1994 Fig2
Gari solida / Bivalvia / adult / aquatic / 50 / 43.8 / 5.39 / 0.988 / Urban 1994 Fig2
Donax vittatus / Bivalvia / adult / aquatic / 50 / 38.39 / 2.87 / 0.902 / Ansell et al. 1980 Fig1A tacc=20
Donax semistriatus / Bivalvia / adult / aquatic / 50 / 39.34 / 2.71 / 0.854 / Ansell et al. 1980 Fig1B tacc=20
Donax trunculus / Bivalvia / adult / aquatic / 50 / 45.03 / 3.55 / 0.957 / Ansell et al. 1980 Fig1C tacc=20
Tellina fabula / Bivalvia / adult / aquatic / 50 / 33.53 / 2.02 / 0.889 / Ansell et al. 1980a Fig1A tacc=20
Tellina tenuis / Bivalvia / adult / aquatic / 50 / 40.13 / 2.68 / 0.868 / Ansell et al. 1980a Fig1B tacc=20
Tellina tenuis / Bivalvia / adult / aquatic / 50 / 42.78 / 3.28 / 0.96 / Ansell et al. 1980a Fig1C tacc=20
Cardium glaucum / Bivalvia / adult / aquatic / 50 / 41.31 / 2.04 / 0.921 / Ansell et al. 1981 Fig1A tacc=20
Cardium tuberculatum / Bivalvia / adult / aquatic / 50 / 40.83 / 2.99 / 0.911 / Ansell et al. 1981 Fig1B tacc=20
Cardium edule / Bivalvia / adult / aquatic / 50 / 49.71 / 5.3 / 0.975 / Ansell et al. 1981 Fig1C tacc=20
Ameiurus nebulosus / Actinopterygii / adult / aquatic / 50 / 36.4 / 1.35 / 0.987 / Brett 1956 Fig2
Semotilus atromaculatus / Actinopterygii / adult / aquatic / 50 / 35.86 / 1.9 / 0.969 / Brett 1956 Fig2
Rhinichthys atratulus / Actinopterygii / adult / aquatic / 50 / 34.57 / 1.32 / 0.984 / Brett 1956 Fig2
Salmo salar / Actinopterygii / adult / aquatic / 50 / 32.52 / 1.78 / 0.988 / Brett 1956 Fig2
Salvelinus frontinalis / Actinopterygii / adult / aquatic / 50 / 31.94 / 2 / 0.993 / Brett 1956 Fig2
Oncorhynchus tshawytscha / Actinopterygii / adult / aquatic / 50 / 30.15 / 1.34 / 0.955 / Brett 1956 Fig2
Cristivomer namaycush / Actinopterygii / adult / aquatic / 50 / 29.36 / 1.47 / 0.993 / Brett 1956 Fig2
Trematomus bernacchii / Actinopterygii / adult / aquatic / 50 / 16.99 / 3.1 / 0.972 / Somero and DeVries 1967 Table1
Trematomus hansoni / Actinopterygii / adult / aquatic / 50 / 16.96 / 3.03 / 0.932 / Somero and DeVries 1967 Table1
Trematomus borchgrevinki / Actinopterygii / adult / aquatic / 50 / 17.87 / 3.73 / 0.974 / Somero and DeVries 1967 Table1
Salvelinus confluentus / Actinopterygii / juvenile / aquatic / 50 / 34.87 / 2.83 / 0.999 / Selong et al. 2011 Fig1
Fundulus parvipinnis / Actinopterygii / adult / aquatic / 50 / 42.14 / 1.65 / 0.991 / Doudoroff 1945 Fig2
Girella nigricans / Actinopterygii / young / aquatic / 50 / 38.15 / 2.09 / 0.995 / Doudoroff 1945 Fig2
Atherinops affinis / Actinopterygii / young / aquatic / 50 / 34.59 / 0.82 / 0.967 / Doudoroff 1945 Fig2

Appendix S2. Thermal death time parameters calculated from cold tolerance measurements

Species / Class / Stage / Habitat / LT / CTmin / z’ / r2 / Reference
Tribolium castaneum / Insecta / all / terrestrial / 50 / -85.17 / 17.09 / 0.916 / Fields 1992 Fig1
Cryptolestes ferrugineus / Insecta / all / terrestrial / 50 / -100.96 / 20.60 / 0.992 / Fields 1992 Fig1
Sitophilus granarius / Insecta / all / terrestrial / 50 / -35.26 / 8.25 / 0.988 / Fields 1992 Fig1
Alphitobius diaperinus / Insecta / adult / terrestrial / 50 / -33.05 / 9.36 / 0.934 / Renault et al. 2004 Fig2
Lasioderma serricone / Insecta / egg / terrestrial / 50 / -23.05 / 7.07 / 0.995 / Imai and Harada Table1
Lasioderma serricone / Insecta / larvae / terrestrial / 50 / -33.03 / 9.21 / 0.921 / Imai and Harada Table1
Lasioderma serricone / Insecta / pupae / terrestrial / 50 / -26.44 / 7.36 / 0.874 / Imai and Harada Table1
Lasioderma serricone / Insecta / adult / terrestrial / 50 / -24.35 / 6.47 / 0.966 / Imai and Harada Table1
Stegobium paniceum / Insecta / adult / terrestrial / 50 / -22.19 / 6.02 / 0.961 / Abdelghany et al. 2010 Table4
Callosobruchus maculatus / Insecta / pupae / terrestrial / 50 / -27.94 / 6.42 / 0.958 / Loganathan et al. 2011 Tables4,5
Callosobruchus maculatus / Insecta / egg / terrestrial / 50 / -32.58 / 9.25 / 0.966 / Loganathan et al. 2011 Tables4,5
Oryzaephilus surinamensis / Insecta / adult / terrestrial / 100 / -107.16 / 23.03 / 0.965 / Mathlein 1961 in Strang 1992
Sitophilus granarius / Insecta / adult / terrestrial / 100 / -36.12 / 7.11 / 0.937 / Back and Cotton1924 in Strang 1992
Sitophilus granarius / Insecta / egg / terrestrial / 100 / -59.23 / 12.65 / 0.915 / Mathlein 1961 in Strang 1992
Sitophilus granarius / Insecta / larvae / terrestrial / 100 / -48.78 / 9.79 / 0.96 / Mathlein 1961 in Strang 1992
Sitophilus oryzae / Insecta / adult / terrestrial / 100 / -38.98 / 8.98 / 0.965 / Back and Cotton1924 in Strang 1992
Tribolium castaneum / Insecta / all / terrestrial / 100 / -35.28 / 7.70 / 0.934 / Cotton 1950 in Strang 1992
Tribolium confusum / Insecta / all / terrestrial / 100 / -34.31 / 7.37 / 0.917 / Cotton 1950 in Strang 1992
Tineola bisselliella / Insecta / egg / terrestrial / 100 / -47.32 / 9.73 / 0.965 / Back and Cotton 1927 in Strang 1992
Tineola bisselliella / Insecta / larvae / terrestrial / 100 / -49.18 / 8.71 / 0.878 / Back and Cotton 1927 in Strang 1992
Anagasta kuhniella / Insecta / all / terrestrial / 100 / -40.23 / 7.21 / 0.952 / Cotton 1950 in Strang 1992
Plodia interpunctuella / Insecta / all / terrestrial / 100 / -34.94 / 6.11 / 0.95 / Cotton 1950 in Strang 1992

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