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.

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

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

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