1.In ectotherms, survivorship is dependent on the environmental temperature. This dependence can take the form of survivorship declining sharply at low and high temperatures and being relatively constant at intermediate temperatures (i.e. an inverted U-shaped or ‘flat-topped’ temperature response), or with survivorship exhibiting a maximum at an intermediate temperature (i.e. a unimodal temperature response). Data show that species differ in which response they exhibit, but there is no mechanistic explanation for why such differences exist.
2.Here we use a life-history-based approach to elucidate the temperature response of cumulative (egg-to-adult) survivorship. We focus on the fact that cumulative survivorship is a composite trait, arising from the multiplicative effects of stage-specific survivorship.
3.We show that the temperature response of cumulative survivorship depends on whether or not different life-history stages/age classes respond differentially to temperature. When all stages/age classes are similarly sensitive to temperature, cumulative survivorship exhibits an inverted U-shaped response. When different stages/age classes respond differentially to temperature variation, stages/age classes that are highly sensitive to temperature exhibit monotonically increasing/decreasing or saturating temperature responses, while stages/age classes that are relatively insensitive to temperature exhibit inverted U-shaped responses. Because the effects of stage/age-specific survivorship are multiplicative, the net result is a temperature response of cumulative survivorship that is unimodal and left-skewed (if the survivorship of the most sensitive stage/age class increases with increasing temperature) or unimodal and right-skewed (if the survivorship of the most sensitive stage/age class decreases with increasing temperature).
4.Tests of these predictions with data from insects lead to important insights about how ectotherms with different life-history patterns respond to temperature variation, information that is crucial in understanding how ectotherms with complex life cycles persist in the face of climate warming.
Studies of temperature effects on insect life-history traits show that the temperature response of egg-to-adult survivorship exhibits an inverted U- or ‘flat-topped’ shape, with sharp thresholds at low and high temperatures and relatively invariant survivorship at intermediate temperatures (Van der Have 2002; Angilletta 2009; Kingsolver 2009; deJong 2010). This pattern suggests that temperature has a nominal effect on survivorship except in determining the lower and upper limits for viability. It represents a strong deviation from the temperature responses of other life-history (e.g. fecundity and development) and performance (e.g. assimilation and locomotion) traits that are unimodal and often left-skewed (Angilletta 2009; Kingsolver 2009). It is also at odds with numerous studies demonstrating differential responses of life-history stages to temperature variation in insects and other ectotherms (e.g. Dempster 1983; Kingsolver 1989; Crozier 2004; Kingsolver et al. 2011; Potter, Davidowitz & Woods 2011).
Mechanistic explanations of the inverted U-shaped response of survivorship have invoked temperature effects on the cell cycle regulation (Van der Have 2002): inducers and suppressors of DNA transcription are proteins, which become inactive at low and high temperatures. If the temperature response of the cell cycle regulation is dictated by the temperature response of enzymes involved in cell division, the lower and upper limits for embryonic development should match those for embryonic survivorship. While this mechanism can potentially explain the sharp survivorship thresholds at low and high temperatures in terms of temperature effects on enzyme kinetics and enzyme denaturation (Johnson & Lewin 1946; Sharpe & DeMichele 1977; Schoolfield, Sharp & Magnuson 1981; Ratkowsky, Olley & Ross 2005), it cannot explain why survivorship should be invariant at intermediate temperatures (Van der Have 2002).
A potential solution to this mismatch lies in the fact that cumulative survivorship (the proportion of an initial cohort that survives to a particular age/stage) is a composite trait arising from the multiplicative effects of age/stage-specific survivorship (the proportion of individuals that survive from one life stage/age class to the next). If different life stages/age classes do not exhibit differential thermal responses either because they live in similar habitats and experience similar microclimates or because they experience similar seasonal environments (Kingsolver et al. 2011), one would expect egg-to-adult survivorship to be relatively insensitive to temperature within the temperature range the life cycle can be completed. Alternatively, if different life stages/age classes exhibit differential thermal responses because of local and/or seasonal differences in the environment, one would expect egg-to-adult survivorship to be driven by life stages whose survival is most sensitive to temperature variation. Such stages will therefore have a disproportionately large effect on lifetime fitness and play a key role in the ability of organisms to adapt to variation in the thermal environment. Given that most ectothermic taxa have complex life cycles with distinct stages, understanding stage-specific responses to temperature variation in fitness components such as survivorship is critical in identifying the types of life-history strategies and thermal responses that allow ectotherms to withstand the effects of climate warming.
Here we develop a framework for elucidating the temperature response of egg-to-adult survivorship in terms of the temperature responses of age/stage-specific survivorship. We test predictions of the framework with data for insects. Investigating the temperature response of survivorship in insects is important in its own right because insects are among the most diverse of all ectothermic taxa, performing critical roles as decomposers, herbivores, predators and parasites in virtually every community. Temperature effects on insect life cycles, therefore, not only influence the persistence of particular insect species, but also the structure and function of communities by modifying their interactions with other species. Because they have distinct life stages (eggs, larvae/nymphs, adults), relatively short generation times and include a large number of well-studied species, insects provide ideal model organisms on which to build a broader framework for predicting ectotherm survivorship in thermally variable environments.
Materials and methods
The relationship between stage-specific and cumulative survivorship is the key to elucidating the temperature response of cumulative survivorship. Let be the number of individuals of age x. Stage-specific survivorship () is the proportion of individuals that survive from age x − 1 to x, that is, , and cumulative survivorship () is the proportion of individuals that survive from birth to age x, that is, . The relationship between and x is given by the survivorship curve (Pearl 1928). Recalling from life table analysis (Roff 1992; Stearns 1992; Charnov 1993) that , we see that differential survivorship of different stages/age classes can strongly affect cumulative survivorship. We can quantify fitness in terms of viability as where is the generation time. Because effects of on are multiplicative, the life stage/age class with the lowest survivorship will have a disproportionately large effect on fitness.
Let δ(x) represent the per capita mortality rate (instantaneous risk of death) of individuals of age x. Then
(see Gurney & Nisbet 1998 for the derivation). We can describe the relationship between the instantaneous risk of death and age using the hazard function of the Weibull distribution (Pinder, Weiner & Smith 1978), that is, (Gurney & Nisbet 1998), where b is the scale parameter, which corresponds to the critical age at which δ(x) = a/b, and a is the shape parameter that describes how δ(x) changes with x. The Weibull distribution provides a useful tool for analysing survivorship data because the shape and scale parameters summarize all the survivorship information in a life table (Pinder, Weiner & Smith 1978). For instance, with δ(x) defined as above, . When a > 1 instantaneous risk of death increases with age, when a < 1, it decreases with age, and when a = 1, it is invariant with respect to age. Whether a increases or decreases with age depends on whether earlier life stages/age classes exhibit lower/higher survivorship than later stages/age classes. Because the shape parameter (a) determines the form of the survivorship curve, it allows for comparisons of survivorship curves between different populations or of the same population under different environmental condidtions.
When survivorship is temperature dependent, that is, , instantaneous risk of death will be determined by how temperature affects the survivorship of different life stages/age classes. We can characterize the temperature responses of life stages/age classes in terms of two properties: temperature sensitivity and temperature tolerance. Temperature sensitivity is defined as the rate at which stage-specific survivorship changes with temperature . Temperature tolerance is defined as the width of the temperature range over which a particular life stage/age class can survive to develop to the next stage/age class.
Based on this information, we can make the following predictions.
1. If life stages/age classes do not differ in their temperature sensitivity, that is, all stages/age classes have similarly high survivorship within the temperature range that the life cycle can be completed, instantaneous risk of death should be invariant with respect to temperature. As a consequence, the temperature response of cumulative survivorship  will have an inverted U shape, the width of which is determined by the stage/age class with the narrowest temperature tolerance.
2. If life stages/age classes are differentially sensitive to temperature, that is, some stages/age classes have lower survivorship at lower/higher temperatures, instantaneous risk of death will vary with temperature. As a result, will be unimodal with a maximum at the temperature that affords the highest survivorship to the life stage/age class that is most sensitive to temperature variation. The width of will be determined by the life stage/age class with the narrowest temperature tolerance. For instance, if one or more stages/age classes have lower survivorship at lower temperatures, with increasing with increasing temperature, the instantaneous risk of death should decrease with increasing temperature, resulting in a left-skewed temperature response of . Alternatively, if one or more stages/age classes exhibit lower survivorship at higher temperatures with decreasing with increasing temperature, instantaneous risk of death should increase with increasing temperature, resulting in a right-skewed temperature response of .
3. Differential responses of life stages/age classes to temperature should be manifested as a qualitative change in the temperature response of . We expect immobile, nonfeeding stages that are adapted to withstand temperature extremes (e.g. embryos within eggs, pupae of free-living holometabolous insects) or are protected from them (e.g. parasitic larvae that develop within hosts) to exhibit an inverted U-shaped temperature response of . We expect life stages/age classes that are the first to feed and/or to be mobile and hence most vulnerable to temperature variation (e.g. early larval/nymphal stages that are small in size, have low mobility and lack thick exoskeletons that protect them from temperature extremes), to exhibit monotonically increasing or decreasing temperature responses of . If this is the case, then the temperature response of should change from inverted U-shaped to monotonic or saturating as the life cycle proceeds from egg to adult. Because effects of on are multiplicative, the net outcome of these different types of stage-specific temperature responses should be a unimodal, rather than an inverted U-shaped, temperature response of (Fig. 1).
We tested predictions about the temperature responses of and with data from three Hemipteran species from tropical, Mediterranean and temperate latitudes. Our goal was not an exhaustive analysis of survivorship data in a large number of species, but rather to validate our approach with a few well-studied species.
The tropical species is a pod-sucking bug (Clavigralla shadabi) from Benin (820N) that is a pest of cowpea (Vigna unguiculata). Its life cycle consists of eggs, five nymphal instars and adults. The first instar is the life stage with the lowest survivorship at all temperatures (Dreyer & Baumgartner 1996). The species experiences a mean annual temperature of 27·2 C (SE = 0·09) and a coefficient of variation (CV) of mean monthly fluctuations of 0·04. The amplitude of seasonal fluctuations in the mean temperature (difference between maximum and minimum monthly temperature) is 3·3 C.
The Mediterranean species is the harlequin bug (Murgantia histrionica) from coastal southern California N), which is a specialist herbivore on Bladderpod (Isomeris arborea) ( Amarasekare 2000a2000a, 2000bb). Its life cycle consists of eggs, five nymphal instars and adults. First-instar nymphs do not feed and remain aggregated around the eggs. The second instars do feed and are mobile, but they typically stay in the vicinity of the egg clutch. The third instar is the first stage to move to the other parts of the host plant. The second and third instars exhibit the highest mortality, which is likely because the former is the first feeding stage and the latter is the first mobile stage ( Amarasekare 2000a, 2000ab, 2000b, 2007). The harlequin bug experiences a mean annual temperature of 16·56 C (SE = 0·28) and a CV of mean monthly fluctuations of 0·21. The amplitude of seasonal fluctuations in the mean temperature is 9·5 C.
The temperate species is the pea aphid (Acyrthosiphon pisum) from York, England ( N), which is a pest of the pea plant (Pisum sativum). Apterus females give birth to nymphs, which go through four instars before becoming adults. The second instar is the stage with the lowest survivorship at all temperatures (Morgan, Walters & Aegerter 2001). The pea aphid experiences a mean annual temperature of 9·75 C (SE = 0·41) and a CV of mean monthly fluctuations of 0·50. The amplitude of seasonal fluctuations in the mean temperature is 13 C.
Survivorship data for the Mediterranean species come from experiments we conducted, which are described in Appendix S1. Data for the tropical and temperate species were obtained from previously published studies (Dreyer & Baumgartner 1996; Morgan, Walters & Aegerter 2001). The experimental protocols used in these studies are similar to ours and hence unlikely to confound any species-specific differences observed.
Quantifying the temperature response of survivorship
For all three species, we quantified the temperature sensitivity of each life stage in terms of an effect size where and are, respectively, the minimum and maximum survivorship within the temperature range that the life cycle can be completed. When the temperature response of stage-specific survivorship is monotonic or saturating, and correspond, respectively, to the lowest and highest temperature at which the life cycle can be completed. If all life stages are similarly sensitive to temperature, we expect for all stages. If some stages are more sensitive than others, we expect a significant deviation from zero in the positive (if survivorship increases with increasing temperature) or negative direction (if survivorship decreases with increasing temperature) for such stages.
We quantified temperature tolerance range of each life stage (TL) as where and are, respectively, the highest and lowest temperatures at which it could successfully develop to the next stage. For instance, if eggs could hatch to the first-instar stage within the temperature range 15–30C, but the first instar can develop into the second instar only within the range 18–30C, the tolerance range of the egg stage is 15 while that of the first nymphal instar is 12.
Temperature effects on survivorship
Temperature effects on stage-specific survivorship were analysed by fitting data to (i) a generalized Gaussian model when the survivorship exhibited an inverted U-shaped or saturating response, (ii) a quadratic model when survivorship exhibited a monotonic but nonlinear increase or decrease with temperature and (iii) a linear model when survivorship exhibited a linear or quasi-linear increase/decrease with temperature. The generalized Gaussian model is given by: where is the stage-specific survivorship at temperature T, is the maximum survivorship, which is attained at , β determines the variability in survivorship about the optimum and α determines whether the temperature–survivorship relationship is leptokurtic (α ∈ [1,2]), symmetric (α = 2) or platykurtic (α ∈ [2,∞]). The quadratic model is given by , which simplifies to when the temperature response is quasi-linear. The Gaussian and quadratic models were fitted using nonlinear regression (nls package; R Development Core Team 2008). Data were arcsine-square-root-transformed prior to analysis to stabilize variances (Sokal & Rohlf 1995).
Temperature effects on cumulative survivorship were analysed by fitting the model to data using nonlinear regression where is the proportion of individuals that survive from birth to age at temperature T, and and are, respectively, the shape and scale parameters of the Weibull distribution estimated at temperature T. Data were arcsine-square-root-transformed prior to fitting the model. The sign of the shape parameter () determines whether the instantaneous risk of death increases or decreases with age, and its variation with temperature determines whether increases or decreases with temperature. We used regression analysis (linear or nonlinear as appropriate) to investigate the relationship between the shape parameter and temperature.
Temperature effects on stage duration
Temperature can affect stage duration through its effects on development. We quantified temperature effects on stage duration by fitting data to the Boltzmann–Arrhenius function: where d(T) is the stage duration at temperature T (in ), is the stage duration at a reference temperature and is the Arrhenius constant. The Arrhenius constant measures the temperature sensitivity of stage duration, that is, the greater is the magnitude of , the steeper is the decrease in the stage duration (or equivalently, the increase in the developmental rate) with temperature.
We computed the fraction of the total development time spent at each life stage to determine whether stages differed in their relative duration as a function of temperature. If the development of some life stages is more sensitive to temperature than that of other stages, the fraction of the total developmental time spent at these stages should decrease faster with increasing temperature. This should increase stage-specific survivorship of such stages because the density-independent mortality during a given stage is lower when the stage duration is shorter. We analyzed stage duration data on the harlequin bug by using a two-way anova with the fraction of the total developmental time spent at each stage as the response variable, Temperature and Stage as the main effects and with repeated measures on Stage (glm package; R Development Core Team 2009). A repeated-measures anova is the appropriate design because stage durations are measured on the same cohort over time (Winer, Brown & Michels 1994). Data were arcsine-square-root-transformed prior to analysis to stabilize variances. A statistically significant Temperature × Stage interaction would indicate stage-specific responses in development. If the fraction of time spent in each stage is independent of temperature, one would expect a significant effect of Stage (that is, some stages have longer developmental periods than others) but not of Temperature or Temperature × Stage.
Temperature effects on stage duration
In all three species, duration of all life stages decreased monotonically with increasing temperature, with data providing a significant fit to the Boltzmann–Arrhenius function (see Appendix S2 for details). Although the total developmental time (egg to adult) declined with increasing temperature, the fraction of the time taken to develop from one stage to the next is approximately constant across temperature (Fig. 2). This suggests that temperature has a similar effect on all life stages in terms of accelerating development. Statistical analysis of this pattern was not possible for the tropical and temperate species because of the unavailability of raw data, but repeated-measures anova on data for the harlequin bug revealed a significant effect of Stage (F = 8028,P < 0·0001), that is, the fraction of time spent in a given stage increased as the life cycle proceeds from egg to adult, and nonsignificant effects of Temperature and Temperature × Stage interaction, that is, the fraction of time spent at each stage, is unaffected by temperature (Temperature: F = 0,P = 1; Temperature × Stage: F = 0·5,P = 0·85).
Temperature effects on survivorship
Tropical species (Clavigralla shadabi)
All life stages exhibited temperature sensitivities near zero (Fig. 3a), suggesting that stage-specific survivorship is unaffected by temperature within the temperature range studied for this species. As expected under this scenario, the instantaneous risk of death is invariant with respect to temperature (Fig. 3c,d). The first instar exhibits a narrower temperature tolerance than the egg stage and hence determines the width of the temperature response of egg-to-adult survivorship (Fig. 3b). Because all life stages exhibit similar temperature sensitivity, we do not observe a qualitative change in the temperature response of stage-specific survivorship (although there is the quantitative effect of survivorship at lower temperatures improving as the life cycle proceeds; Fig. 3e–j). The net result is an inverted U-shaped temperature response of egg-to-adult survivorship (Fig. 3k–p).
Mediterranean species (Murgantia histrionica)
Temperature sensitivities of life stages differed greatly, suggesting strong stage-specific responses to temperature variation (Fig. 4a). The second and third nymphal instars exhibited greater temperature sensitivities than stages that both preceded and followed them. For instance, egg and first nymphal stages exhibited uniformly high survivorship over all temperatures, while the second and third nymphal stages exhibited a monotonic increase in survivorship with increasing temperature. Because the survivorship of later stages is dictated by that of earlier stages, the fourth-instar stage also shows a monotonic increase in stage-specific survivorship, while the fifth instar shows a saturating response with survivorship approaching 1 except at the lowest temperature. As expected under this scenario, the instantaneous risk of death decreases with increasing temperature (Fig. 4c,d). The second instar exhibits a narrower temperature tolerance than the egg and first-instar stages, and hence, its tolerance determines the width of the temperature response of egg-to-adult survivorship (Fig. 4b). Differential responses of life stages to temperature are manifested as a qualitative change in the temperature response of stage-specific survivorship, from an inverted U shape for egg and first nymphal instar stages to a monotonic increase in the second- to fourth-instar stages (Fig. 4e–j). The net result is a left-skewed temperature response of egg-to-adult survivorship (Fig. 4k–p).
Temperate species (Acyrthosiphon pisum)
This species also exhibited strong stage-specific responses to temperature variation (Fig. 5). For instance, the first nymphal and pre-adult stages exhibited uniformly high survivorship, while the second nymphal stage exhibited a decline in survivorship with increasing temperature. The third and fourth instars show the same trend, albeit less strongly. The second nymphal stage exhibited the greatest temperature sensitivity (Fig. 5a). As expected under this scenario, the instantaneous risk of death increases with increasing temperature (Fig. 5c,d). Life stages do not differ in temperature tolerance, and hence, the tolerance of the egg stage determines the width of the temperature response of nymph-to-adult survivorship (Fig. 5b). Differential responses of life stages to temperature is manifested as a qualitative change in the temperature response of stage-specific survivorship, from a horizontal line in the first-instar stage to a monotonic decrease in the second- to fourth-instar stages (Fig. 5e–i). The net result is a right-skewed temperature response of egg-to-adult survivorship (Fig. 5j–n).
Across all species, the earliest life stage (egg stage in tropical and Mediterranean species, the first nymphal instar in the temperate species) exhibited the highest temperature tolerance and the lowest temperature sensitivity. These stages were, therefore, the most likely to exhibit an inverted U-shaped temperature response of survivorship. The early nymphal stages (first to third), which exhibited the greatest temperature sensitivity and the lowest temperature tolerance, were the most likely to exhibit a monotonically increasing or decreasing temperature response. Late nymphal and pre-reproductive adult stages exhibited lower temperature sensitivity, but their temperature tolerance was constrained by lower tolerance exhibited by the early nymphal stages. The key point is that the life stages that are the most sensitive to temperature variation act as a rate-limiting step in determining the temperature range over which the life cycle can be completed.
Effects of variable temperatures on survivorship
We have tested predictions from our conceptual framework with survivorship data taken under constant temperatures. This is because nearly all available data come from experiments conducted under constant temperature regimes and hence provide the only basis for comparing model predictions and data. The framework we have developed does not assume constant temperatures and is able to predict survivorship under fluctuating temperature regimes (e.g. diurnal, seasonal). In fact, the expression we have derived for the temperature dependence of cumulative survivorship,that is, , can be evaluated under any kind of variable temperature regime. For instance, if we want to consider the effects of seasonal variation on of a particular species, we can make temperature a function of time such that it varies seasonally, that is, T = m(t), where T is temperature, t is time and the function m(t) is a sinusoidal function that depicts seasonal variation in temperature. Then, and we can investigate the effects of seasonal temperature variation in cumulative survivorship by fitting the model to data using nonlinear regression where is the proportion of individuals that survive from birth to age when experiencing the seasonal temperature regime given by m(t), and and are, respectively, the shape and scale parameters of the Weibull distribution estimated under the same temperature regime.
There is increasing awareness that differential responses of life stages to temperature variation may be critical in understanding and predicting how ectotherms respond to perturbations in the thermal environment (Kingsolver 2009; Kingsolver et al. 2011). Studies of the temperature response of survivorship in insects present a puzzle. In some species, the temperature response of egg-to-adult survivorship exhibits an inverted U shape (e.g. Messenger & Flitters 1958; Cohet, Vouidibio & David 1980; Dreyer & Baumgartner 1996; Van der Have 2002), suggesting that temperature has a nominal effect on survivorship except in determining the lower and upper limits to survival. In other species, the temperature response is unimodal and left-skewed (e.g. Cohet, Vouidibio & David 1980; Van der Have 2002; Kingsolver et al. 2011) or right-skewed (e.g. Morgan, Walters & Aegerter 2001; Jandricic et al. 2010), suggesting that there is an optimal temperature range during which survivorship is maximal. Although both types of temperature responses are frequently observed, the mechanisms that give rise to them are not well understood. The existence of lower and upper temperature limits to viability can be explained in terms of temperature effects on enzymes involved in cell division (Van der Have 2002). However, this mechanism can neither explain why survivorship should be invariant at intermediate temperatures nor why it should be left- or right-skewed.
Here we have developed a framework that can potentially reconcile these conflicting observations. We focus on the fact that egg-to-adult survivorship is a composite trait resulting from the multiplicative effects of stage-specific survivorship. Thus, it is the temperature response of stage-specific survivorship that determines the temperature response of cumulative (egg-to-adult) survivorship. Life stages that exhibit high temperature sensitivity and/or narrow temperature tolerance have a disproportionately large effect on egg-to-adult survivorship and hence on lifetime fitness. Therefore, egg-to-adult survivorship will exhibit an inverted U shape only if all life stages exhibit similar responses to temperature variation. When life stages are differentially sensitive to temperature, egg-to-adult survivorship should exhibit a left- or right-skewed response depending on whether the survivorship of the stage(s) most sensitive to temperature increases or decreases with increasing temperature.
We tested these predictions with three Hemipteran species from different latitudes. In the tropical species, all life stages were similarly sensitive to temperature with egg-to-adult survivorship exhibiting an inverted U shape. In the Mediterranean species, the second and third nymphal stages, which were more temperature sensitive than the other stages, exhibited increasing survivorship with increasing temperature. As a result, egg-to-adult survivorship exhibited a left-skewed response with a maximum at the temperature that afforded the highest survivorship to the second and third instars. In the temperate species, the second nymphal instar, which was the most temperature stage-specific responses to sensitive, exhibited decreasing survivorship with increasing temperature. As a result, egg-to-adult survivorship exhibited a right-skewed response with a maximum at the temperature that afforded the highest survivorship to the second-instar stage.
These findings lead to important insights into temperature effects on survivorship. When different life stages exhibit similar responses to temperature variation, either because they occupy the same habitats and experience the same microclimates or because they experience the same seasonal environment (e.g. species with short generation times that can complete one or more generations within a season), viability is determined by the life stage with the narrowest temperature tolerance. When life stages differ in their temperature responses because they experience different microclimates or seasonal environments (e.g. species with long generation times in which different stages develop during different seasons), viability will be determined by the life stage(s) with the greatest temperature sensitivity and the narrowest temperature tolerance. In the insect species we examined, the tropical species exhibited similar stage-specific responses to temperature, while the Mediterranean and temperate species both exhibited strong differences between stages in their temperature responses. This may be because the tropical species inhabits an environment in which temperature fluctuations are minimal while the Mediterranean and temperate species inhabit environments characterized by strong seasonal fluctuations. However, given the fact that we studied only a single species from each latitude, these expectations are speculative at best. Indeed, the case studies we have presented are meant to be illustrative rather than exhaustive. They serve to validate the predictions of our framework and the criteria (e.g. temperature sensitivity and tolerance, relationship between the instantaneous risk of death and temperature) used to identify the stages most sensitive to temperature variation. Testing these predictions with a larger data set with more species from different latitudes is an important future direction.
Our findings shed light on how temperature variation may affect the persistence of insects and other ectotherms with complex life cycles. Immobile, nonfeeding stages that are adapted to withstand extreme temperature changes (e.g. egg and pupal stages) or are protected from them (e.g. parasitic larvae that develop within hosts) are likely to exhibit low temperature sensitivity and high temperature tolerance. Mobile, free-living stages that are unprotected from temperature variation are likely to exhibit greater temperature sensitivity, which allow them to take advantage of favourable conditions, that is, such stages perform better than expected under mild to moderate temperatures, thus increasing overall survivorship and ensuring that the majority of individuals in a cohort develop into reproductive adults. The earlier in the life cycle the stage with the lowest intrinsic survivorship occurs, the greater is the increase in overall survivorship in response to favourable conditions.
Our findings also lead to predictions about how ectotherms with different life-history patterns will respond to climate warming. First, species in which the survivorship of highly temperature-sensitive stages increases with increasing temperature (e.g. warm-adapted species) are likely to experience an increase in egg-to-adult survivorship (and hence lifetime fitness) if the mean habitat temperature were to increase, while species in which the survivorship of high-sensitivity stages decreases with increasing temperature (e.g. cold-adapted species) are likely to experience a reduction in egg-to-adult survivorship and lifetime fitness under such an increase. Second, species in which life stages do not differ in temperature sensitivity but do differ in temperature tolerance are likely to experience a decrease in egg-to-adult survivorship if it is the earlier stages (e.g. early larval or nymphal stages) that exhibit lower tolerance of high temperatures. In general, the life stage whose survivorship is most affected by temperature will determine how severe the effects of warming would be on the persistence of a given species. Species in which the most sensitive life stage is of short duration relative to the time scale of temperature variation (e.g. diurnal, seasonal) are likely to be more adversely affected by climate warming because they would be unable to avoid periods of extreme temperature that exceed the duration of critical life stages.
It is becoming increasingly clear that climate warming involves not just an increase in the mean temperature but also an increase in the magnitude of temperature fluctuations (IPCC 2007). Because stage-specific survivorship has a multiplicative effect on egg-to-adult survivorship and lifetime fitness, effects of increasing temperature fluctuations on population persistence are likely to be complex and nonlinear. Such effects can only be predicted using models of stage-structured population dynamics. The framework and data analyses presented here provide the basis for developing such predictive models.
This research was supported by NSF grant DEB-0717350 to P.A. We thank T. Dell, C. Johnson, K. Okamoto, S. Pawar, V. Savage and two anonymous reviewers for comments on the manuscript and C. Acosta for assistance with the experiments.