No physiologist would find surprising that performance in general and thermal tolerance in particular, changes as a function of an individual’s physical condition. This would explain, for instance, why flies in the static treatment of Mitchell & Hoffmann (2010) were able to cope with 38 °C for over 30 min while most individuals in the ramping treatment were knocked down at lower temperatures, resulting in an average CTmax of 36·9 °C and 37·5 °C for flies from Gordonvale and Melbourne respectively. Flies in the ramping treatment were exhausted or dehydrated when approaching their ‘basal target’ CTmax, hence the general decrease in average CTmax in longer trials (e.g. fig. 1 in Chown et al. 2009) probably reflects a real biological phenomenon with potentially important consequences in nature. However, effects of physical condition impinge on considerably more serious problems when attempting to obtain causal variance estimates of thermal tolerance limits or to study the effects of thermal acclimation on critical thermal limits. Subsequently, we illustrate these issues with a Gedankenexperiment.
Assume that we genetically engineer D. melanogaster isogenic flies to produce mutant alleles of target genes that affect only desiccation rates during the course of a heat resistance assay. Assume also that CTmax under optimal physical conditions is 40 °C and that it decreases as individual flies become dehydrated at a linear rate of 0·05 °C per 1% of total water reserve lost. This is a reasonable scenario because CTmax = 40·1−0·047 × (1% water lost) according to Chown et al’s. (2009) experimental data and our estimated fraction of total metabolism spent in desiccation resistance assays with Q10 = 2·5 (Table 1). Incidentally, Huey et al. (1992, p. 492) noted that ‘if heating rate is slow and if evaporative water loss is very high, then insects could be knocked down by desiccation, not by heat’; and Parsons (1980) had already shown that desiccated flies tolerate lower temperatures than their hydrated counterparts.
Notice that in our hypothetical scenario no variation exists on CTmaxper se apart from that imposed by dehydration, hence all individuals with the same water content should have identical CTmax. However, individuals will exhibit different CTmax in heating assays simply because they lose water at different rates (Fig. 4). Consequently, one could erroneously conclude that the observed variation in CTmax has a genetic basis when in reality it is due to variation in desiccation rates, which by definition is orthogonal to CTmax because no genetic variation exists for upper thermal limits in our engineered flies (Falconer & Mackay 1996). This might seem as a trivial point, but it is actually important because this environmental source of phenotypic variation in CTmax scales up with experimental time (i.e. decreasing ΔT; Fig. 4).
Figure 4. CTmax as a function of metabolic rates from numerical results assuming 100 D. melanogaster flies with: (a) (upper panels) fixed ‘basal’ CTmax = 40 °C and genetic variation for metabolic rates sampled from a normal distribution with (mean ± SD) 4·2 ± 0·1 mL O2 g−1 h−1 at 18 °C; or (b) (lower panels) genetic variation for basal CTmax also sampled from a normal distribution with parameters 40 °C ± 0·25 °C and metabolic rates fixed at 4·2 mL O2 g−1 h−1 at 18 °C. CTmax is assumed to decrease as individuals flies become dehydrated at a linear rate of 0·05 °C per 1% of total water reserve lost. Plotted are the metabolic rates in four ramping experiments with T0 = 20 °C and heating rates ΔT = 0·06, 0·1, 0·25 or 0·5 °C min−1, with time of the assay increasing with decreasing heating rate. Phenotypic variance in CTmax is environmental (right upper panel) or genetic (right lower panel).
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Let us now turn the problem on its head, and ask what would happen if the phenotypic variance of CTmax was solely due to (additive) genetic variation (i.e. assume that our Gedankenexperiment makes use of D. melanogaster isogenic flies targeted for genes that affect only CTmax). In this scenario, all individuals loose water at exactly the same rate and, therefore, observed variation in CTmax at any given hydric condition reflects primarily genetic differences across individuals (e.g. individuals with a CTmax corresponding to 41 °C and 39 °C in optimal conditions would exhibit a CTmax of 40·5 °C and 38·5 °C, respectively, after losing 10% of their water reserves). Numerical results show that in this case the variance in CTmax decreases with the duration of the assay, resulting in a positive association between heating rates and the genetic variance in CTmax (Fig. 4). For example, in an assay with T0 = 20 °C and ΔT = 0·06 °C min−1 a fly with a ‘basal optimum’ CTmax = 41 °C would be knocked down after 309 min at a recorded temperature of 38·5 °C, having lost 50·2% of its water reserves. Another fly with an optimal CTmax = 39 °C, on the other hand, would be knocked down at 36·9 °C after 282 min, having lost 41·8% of its water content. Consequently, the genetically determined 2 °C difference in basal optimum CTmax drops to a 1·6 °C difference simply as a result of the slow heating rate, illustrating how the genetic variation in CTmax changes with experimental conditions. We emphasize that this pattern reflects a decrease in (additive) genetic variance in the strict sense, and not an effect of genetic correlation γ < 1 across CTmax measured in different environmental conditions (see Falconer 1952; Falconer & Mackay 1996, ch. 19). In fact, in our simulations the observed genetic correlation across environments remains consistently high (γ ≈ 1).
As shown in Fig. 4, the thermal ramping rate affects the genetic and environmental components underlying the phenotypic variance of CTmax in opposite directions. Considering that other factors such as thermal acclimation, variation in energy and water reserves, and measurement error also contribute to the phenotypic variation in CTmax, it is not surprising that similar protocols with different species (or vice versa) may result in contrasting outcomes. For instance, Chown et al. (2009) reported a decrease in phenotypic variances in CTmax with heating rates for the ant Linepithema humile, and the opposite trend for D. melanogaster (see their figs 2 and 3). In contrast, Mitchell & Hoffmann (2010) showed that the phenotypic variation in knockdown time of D. melanogaster was three times higher in the ramping than in the static treatment. In the tsetse fly, Glossina pallidipes, tests of homoscedasticity indicate that the phenotypic variance in CTmax was independent of the ramping protocol, but visual inspections suggest that the variance might be actually lower at higher heating rates (fig. 1a in Terblanche et al. 2007). Succinctly, no clear association between phenotypic variation and experimental protocol seems to emerge from empirical studies.
Nonetheless, the obvious implication of the previous numerical exercises is that both heritability (h2 = σ2g/(σ2g + σ2e); Falconer & Mackay 1996) and ‘evolvability’ (i.e., , where μ is the average; Houle 1992) of CTmax are expected to decrease at lower heating rates. Although the relative magnitudes of genetic (σ2g) and environmental (σ2e) variances will obviously depend on real values, we suspect h2 should drop as heating rates decrease, primarily because of its disproportional impact on the environmental component. For instance, in our numerical results σ2e at a heating rate Δ = 0·06 °C min−1 corresponds to ∼27 times σ2e at ΔT = 0·5 °C min−1, whereas σ2g at ΔT = 0·06 °C min−1 is ∼0·67 that at ΔT = 0·5 °C min−1 (Fig. 4). Employing these values and assuming that the contribution of σ2g and σ2e are equal at ΔT = 0·5 °C min−1, h2 would drop to 0·024 at ΔT = 0·06 °C min−1. It is also important to notice that the decrease in the adaptive potential of CTmax with decreasing ΔT (Fig. 4) is also evident in evolvability estimates, which also drop by ∼15% from the fastest to the slowest heating rates (this figure is quite consistent for different initial parameter values although it can slightly increase with a higher ‘basal’ CTMAX). The scarce empirical available evidence supports this observation (Mitchell & Hoffmann 2010): narrow sense h2 for knockdown times were relatively high and significant under static conditions (mean ± SE: h2 = 0·22 ± 0·07 and h2 = 0·14 ± 0·05 for Gordonvale and Melbourne D. melanogaster populations, respectively), but were not significantly different from zero in ramping conditions (differences between protocols are listed in Table 1). Gilchrist & Huey (1999) observation that knockdown temperatures in D. melanogaster is heritable and responds to selection partly supports our predictions, given that these authors employed a ramping protocol with fast heating rates (∼1 °C min−1). It remains to be seen whether a similar experiment employing low heating rates would result in the same output.
Although we have assumed two extreme situations in the Gedankenexperiment (i.e. σ2g = 0 for CTmax in the first scenarios and σ2e = 0 in the second) for illustrative purposes, there is ample evidence for the presence of genetic variation in both desiccation resistance and thermal limits in Drosophila populations (reviewed in Hoffmann & Harshman 1999; Hoffmann, Sørensen & Loeschcke 2003); albeit the seemingly lower capacity for genetic and plastic responses in CTmax compared with CTmin (Chown 2001; Hoffmann 2010). Moreover, the repeatability and heritability of standard metabolic rate is relatively high in several species of insects (Marais & Chown 2003; Terblanche, Klok & Chown 2004; Nespolo, Castañeda & Roff 2007), including D. melanogaster (Williams, Rose & Bradley 1997). In addition, desiccation and starvation resistance are genetically uncorrelated to metabolic rates in Drosophila (Djawdan, Rose & Bradley 1997; Hoffmann & Harshman 1999), hence our conclusion that the environmental component of the phenotypic variance for CTmax scales up with decreasing heating rates is probably applicable to real scenarios.
The preceding scenario also allows inquiring on the effect of heating rates on thermal acclimatory responses. Briefly, assume that, at temperatures above 25 °C (the optimum for D. melanogaster), CTmax increases in response to ramping conditions acclimation as
where t(i) is time at the ith minute after ambient temperature in the water-bath increased over 25 °C, and CTmax|t(0)| = 40 °C as above. We therefore make the implicit assumption that environment temperature (not heating rate) is the clue to trigger the thermal acclimatory responses.
Assuming T0 = 20 °C and that flies’ physical condition is constant throughout the experiment (i.e. no desiccation occurs and, hence, CTmax|t(i)| remains equal to CTmax|t(0)| when ambient temperature is ≤25 °C and thereafter increases as given by eqn 4 when >25 °C), CTmax at the end of the assays would increase from 40·24 °C with ΔT = 0·5 °C min−1 to 42·39 °C with ΔT = 0·06 °C min−1; that is, a non-trivial net beneficial effect of 2·15 °C with the slowest heating rate. However, when desiccation effects are considered as in our first Gedankenexperiment (i.e. CTmax|t(i)| continuously decreases below CTmax|t(0)| because of desiccation effects when ambient temperature is ≤25 °C, and thereafter this decrease is somewhat compensated because of the thermal acclimatory responses given by eqn 4 when ambient temperature >25 °C), the resulting CTmax are 39·88 °C with ΔT = 0·5 °C min−1and 39·22 with ΔT = 0·06 °C min−1. What this numerical exercise shows is that desiccation can potentially overshadow thermal acclimation effects owing to short-term responses of individuals to changing temperatures (see also Woods & Harrison 2002) and, more importantly, that a drop in CTmax with slower heating rates does not necessarily rule out the ‘beneficial acclimation hypothesis’ (Leroi, Bennett & Lenski 1994), which has some empirical support (Chung 1997; Nyamukondiwa & Terblanche 2010; but see Huey et al. 1999).
Actually, in Drosophila pre-treatment or pre-exposure to a non-lethal high temperature enables survival at even higher temperatures (Levins 1969; Loeschcke, Krebs & Barker 1994; Dahlgaard et al. 2002), and a similar response is documented for low temperatures (i.e. pre-exposure at non-lethal low temperatures enables survival at even lower temperatures; Kelty & Lee 1999, 2001) thus suggesting that beneficial thermal acclimation does indeed happen. Parenthetically, when assessing CTmin in ramping protocols and flies’ metabolic costs were probably of little concern (Fig. 1), Chown et al. (2009) detected an important effect of beneficial acclimation: flies kept at 15 °C had a CTmin that was ∼2·5 °C below that of their corresponding counterparts raised at 25 °C.