elucidating the temperature response of survivorship in insects

Elucidating the temperature response of survivorshipin insectsPriyanga Amarasekare*,1 and Romina Sifuentes1

1Department of Ecology and Evolutionary Biology, University of California Los Angeles, Los Angeles, California, 90095-1606USA

Summary

1. In ectotherms, survivorship is dependent on the environmental temperature. This depen-

dence 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 cumula-

tive (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 temper-

ature variation, stages/age classes that are highly sensitive to temperature exhibit monotoni-

cally 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 ecto-

therms 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.

Key-words: climate warming, development, life-history traits, survivorship, temperature

variation

Introduction

Studies of temperature effects on insect life-history traits

show that the temperature response of egg-to-adult survi-

vorship exhibits an inverted U- or ‘flat-topped’ shape, with

sharp thresholds at low and high temperatures and rela-

tively 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 dif-

ferential 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*Correspondence author. E-mail: [email protected]

� 2012 The Authors. Functional Ecology © 2012 British Ecological Society

Functional Ecology 2012 doi: 10.1111/j.1365-2435.2012.02000.x

become inactive at low and high temperatures. If the tem-

perature response of the cell cycle regulation is dictated by

the temperature response of enzymes involved in cell divi-

sion, the lower and upper limits for embryonic develop-

ment 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 sur-

vivorship 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 compos-

ite 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 differ-

ent life stages/age classes do not exhibit differential ther-

mal responses either because they live in similar habitats

and experience similar microclimates or because they expe-

rience 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 dif-

ferent life stages/age classes exhibit differential thermal

responses because of local and/or seasonal differences in

the environment, one would expect egg-to-adult survivor-

ship to be driven by life stages whose survival is most sen-

sitive 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 tempera-

ture 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 tem-

perature response of egg-to-adult survivorship in terms of

the temperature responses of age/stage-specific survivor-

ship. We test predictions of the framework with data for

insects. Investigating the temperature response of survivor-

ship in insects is important in its own right because insects

are among the most diverse of all ectothermic taxa, per-

forming critical roles as decomposers, herbivores, preda-

tors 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 num-

ber 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

CONCEPTUAL FRAMEWORK

The relationship between stage-specific and cumulative survivor-

ship is the key to elucidating the temperature response of cumula-

tive survivorship. Let nx be the number of individuals of age x.

Stage-specific survivorship (sx) is the proportion of individuals that

survive from age x � 1 to x, that is, sx ¼ nx=ðnx� 1Þ, and cumula-

tive survivorship (lx) is the proportion of individuals that survive

from birth to age x, that is, lx ¼ nx=n0. The relationship between lxand x is given by the survivorship curve (Pearl 1928). Recalling

from life table analysis (Roff 1992; Stearns 1992; Charnov 1993)

that lx ¼ Qxi¼0 si, we see that differential survivorship of different

stages/age classes can strongly affect cumulative survivorship. We

can quantify fitness in terms of viability as W ¼ �Qxmax

i¼0 si�1=xmax

where xmax is the generation time. Because effects of sx on lx are

multiplicative, the life stage/age class with the lowest survivorship

will have a disproportionately large effect on fitness.

Let d(x) represent the per capita mortality rate (instantaneous

risk of death) of individuals of age x. Then

lx ¼ e�R x

0dðyÞdy

(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, dðxÞ ¼ ða=bÞðx=bÞa�1 (Gurney &

Nisbet 1998), where b is the scale parameter, which corresponds to

the critical age at which d(x) = a/b, and a is the shape parameter

that describes how d(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 infor-

mation in a life table (Pinder, Weiner & Smith 1978). For instance,

with d(x) defined as above, lx ¼ Qxi¼0 si ¼ e�ðx=bÞa . 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) deter-

mines 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,

lxðTÞ ¼ QxTi¼0 siðTÞ, 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 [@sxðTÞ=@T]. 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 survi-

vorship 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 [lxðTÞ] will have an inverted

U shape, the width of which is determined by the stage/age class

with the narrowest temperature tolerance.

� 2012 The Authors. Functional Ecology © 2012 British Ecological Society, Functional Ecology

2 P. Amarasekare & R. Sifuentes

2. If life stages/age classes are differentially sensitive to tempera-

ture, that is, some stages/age classes have lower survivorship at

lower/higher temperatures, instantaneous risk of death will vary

with temperature. As a result, lxðTÞ will be unimodal with a maxi-

mum at the temperature that affords the highest survivorship to

the life stage/age class that is most sensitive to temperature varia-

tion. The width of lxðTÞ 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 sx increasing with increasing temperature, the

instantaneous risk of death should decrease with increasing tem-

perature, resulting in a left-skewed temperature response of lx.

Alternatively, if one or more stages/age classes exhibit lower survi-

vorship at higher temperatures with sx decreasing with increasing

temperature, instantaneous risk of death should increase with

increasing temperature, resulting in a right-skewed temperature

response of lx.

3. Differential responses of life stages/age classes to temperature

should be manifested as a qualitative change in the temperature

response of sx. 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 exhi-

bit an inverted U-shaped temperature response of sx. 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 lar-

val/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 tem-

perature responses of sx. If this is the case, then the temperature

response of sx should change from inverted U-shaped to mono-

tonic or saturating as the life cycle proceeds from egg to adult.

Because effects of sx on lx 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 lx (Fig. 1).

STUDY SPEC IES

We tested predictions about the temperature responses of sx and

lx with data from three Hemipteran species from tropical, Medi-

terranean 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 (8�200N) 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 tem-

peratures (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 (differ-

ence between maximum and minimum monthly temperature) is

3·3 �C.The Mediterranean species is the harlequin bug (Murgantia his-

trionica) from coastal southern California ð33�370800 N), which is a

specialist herbivore on Bladderpod (Isomeris arborea) ( Amarasek-

are 2000a, b). Its life cycle consists of eggs, five nymphal instars

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ge-s

peci

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vors

hip

Cum

ulat

ive

(egg

-to-a

dult)

sur

vivo

rshi

p

Temperature (°C)

(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

Stage 1 Stage 2 Stage 3 Cumulative

Fig. 1. Expectations about the multiplicative effects of stage-specific survivorship on cumulative survivorship. In each row, the first three

panels depict the survivorship of three life stages and the fourth panel depicts the cumulative survivorship across stages. When life stages

are relatively insensitive to temperature (top row), except at extremes of low and high temperatures that define limits to viability, survivor-

ship of all life stages exhibit an inverted U-shaped temperature response (panels a–c). As a result, cumulative survivorship also exhibits an

inverted U-shaped temperature response (panel d). When life stages are differentially sensitive to temperature such that survivorship of the

most sensitive stage increases with increasing temperature (middle row), stage-specific survivorship exhibits a qualitative change from an

inverted U shape in the less sensitive stages to a monotonic increase in the more sensitive stages (panels e–g). As a result, cumulative survi-

vorship exhibits a left-skewed temperature response with a maximum at the temperature that affords the highest survivorship to the most

sensitive stage (panel h). When the survivorship of the most sensitive stage decreases with increasing temperature (bottom row), stage-spe-

cific survivorship exhibits a qualitative change from an inverted U shape in the less sensitive stages to a monotonic decrease in the more

sensitive stages (panels i–k). As a result, cumulative survivorship exhibits a right-skewed temperature response with a maximum at the

temperature that affords the highest survivorship to the most sensitive stage (panel l).


Temperature response of survivorship 3

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, b, 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. Theamplitude of seasonal fluctuations in the mean temperature is

9·5 �C.The temperate species is the pea aphid (Acyrthosiphon pisum)

from York, England (53�5703000 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; Mor-

gan, Walters & Aegerter 2001). The experimental protocols used

in these studies are similar to ours and hence unlikely to confound

any species-specific differences observed.

QUANT IFY ING THE TEMPERATURE RESPONSE OF

SURV IVORSHIP

For all three species, we quantified the temperature sensitivity of

each life stage in terms of an effect size Es ¼ ln�sxmax

=sxmin

�where

sxminand sxmax

are, respectively, the minimum and maximum survi-

vorship within the temperature range that the life cycle can be

completed. When the temperature response of stage-specific survi-

vorship is monotonic or saturating, sxminand sxmax

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 Es � 0 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 tem-

perature) or negative direction (if survivorship decreases with

increasing temperature) for such stages.

We quantified temperature tolerance range of each life stage

(TL) as TL ¼ Tsxmax� Tsxmin

where Tsxmaxand Tsxmin

are, respec-

tively, the highest and lowest temperatures at which it could suc-

cessfully develop to the next stage. For instance, if eggs could

hatch to the first-instar stage within the temperature range 15–30 �C, but the first instar can develop into the second instar only

within the range 18–30 �C, the tolerance range of the egg stage is

15 while that of the first nymphal instar is 12.

DATA ANALYS IS

Temperature effects on survivorship

Temperature effects on stage-specific survivorship were analysed

by fitting data to (i) a generalized Gaussian model when the survi-

vorship 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: sxT ¼ sxTmaxe��jT�Topt j=b

�a

where sxT is the

stage-specific survivorship at temperature T, sxTmaxis the maximum

survivorship, which is attained at Topt, b determines the variability

in survivorship about the optimum and a determines whether the

temperature–survivorship relationship is leptokurtic (a ∈ [1,2]),

symmetric (a = 2) or platykurtic (a ∈ [2,∞]). The quadratic model

is given by sxT ¼ a þ bT þ cT2, which simplifies to

sxT ¼ a þ bT when the temperature response is quasi-linear. The

Gaussian and quadratic models were fitted using nonlinear regres-

sion (NLS package; R Development Core Team 2009). 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 lxT ¼ e�ðxT=bTÞaT to data using nonlinear

regression where lxT is the proportion of individuals that survive

from birth to age xT at temperature T, and aT and bT are, respec-

tively, the shape and scale parameters of the Weibull distribution

estimated at temperature T. Data were arcsine-square-root-trans-

formed prior to fitting the model. The sign of the shape parameter

(aT) determines whether the instantaneous risk of death increases

or decreases with age, and its variation with temperature

determines whether lx 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 devel-

opment. We quantified temperature effects on stage duration

by fitting data to the Boltzmann–Arrhenius function: dðTÞ ¼dTR

eAd

�ð1=TRÞ�ð1=TÞ

�where d(T) is the stage duration at temperature

T (in �K), dTRis the stage duration at a reference temperature TR

and Ad is the Arrhenius constant. The Arrhenius constant

measures the temperature sensitivity of stage duration, that is, the

greater is the magnitude of Ad, 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 rela-

tive 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 9 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 9 Stage.

Results

TEMPERATURE EFFECTS ON STAGE DURAT ION

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 ANO-

VA 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 9 Stage interaction, that

is, the fraction of time spent at each stage, is unaffected by

temperature (Temperature: F = 0,P = 1; Temperature 9

Stage: F = 0·5,P = 0·85).

TEMPERATURE EFFECTS ON SURV IVORSHIP

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 deter-

mines 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 quali-

tative 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 survivor-

ship (Fig. 3k–p).

Mediterranean species (Murgantia histrionica)

Temperature sensitivities of life stages differed greatly, sug-

gesting strong stage-specific responses to temperature vari-

ation (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

Life stageFraction of total developmental period Developmental period (days)

Tem

pera

ture

sen

sitiv

ity (A

rrhe

nius

con

stan

t)

Tem

pera

ture

(C)

Tropical species(C. shadabi)

Mediterranean species(M. histrionica)

Temperate species(A. pisum)

(c)(b)(a)

(f)(e)(d)

(i)(h)(g)

. . . .

. . . .

. . . .

Fig. 2. Effects of temperature on the development of tropical (Clavigralla shadabi, first row), Mediterranean (Murgantia histrionica, middle

row) and temperate (Acyrthosiphon pisum, bottom row) species. Panels in the left column depict the temperature sensitivity (quantified as

the Arrhenius constant) of development for each life stage. Panels in the middle column depict temperature effects on the fraction of time

spent in each stage. Panels in the right column depict temperature effects on the total developmental period (egg to adult).



instantaneous risk of death decreases with increasing tem-

perature (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 tem-

perature 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 mono-

tonic 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).

General findings

Across all species, the earliest life stage (egg stage in tropi-

cal 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.

Life stage Life stage Age (scaled) Temperature (° C)

Tem

pera

ture

sen

sitiv

ity

Tem

pera

ture

tole

ranc

e

Egg-

to-a

dult

surv

ivor

ship

Slop

e of

sur

vivo

rshi

p cu

rve

(a)

surv

ivor

ship

Egg-

to-s

tage

su

rviv

orsh

ip

Temperature (°C)

Eggs N1 N2 N3 N4 N5

18 C32 C

23 C

20 C

30 C

(d)(c)(b)(a)

(e) (f) (g) (h) (i) (j)

(k) (l) (m) (n) (o) (p)

Fig. 3. Temperature responses of stage-specific and egg-to-adult survivorship of the tropical species (Clavigralla shadabi). Panel (a) depicts

the temperature sensitivity of life stages [Es ¼ ln�sxmax

=sxmin

�; see text for details]. Note that all stages exhibit temperature sensitivities

close to zero, suggesting similarly low sensitivity to temperature variation. Panel (b) depicts the temperature tolerance of life stages. The

first nymphal instar exhibits the lowest tolerance and hence determines the temperature range over which the life cycle can be completed.

Panel (c) depicts survivorship curves at different temperatures. The slope of the survivorship curve (as quantified by the shape parameter a

of the Weibull distribution; see Conceptual framework for details) exhibits no discernible relationship with temperature (linear regression:

slope = �0·007 ± 0·027, P = 0·81, intercept = 0·95 ± 0·69, P = 0·24; model fit: F = 0·06, P = 0·81, n = 6 temperatures). This is confirmed

by analyses of the temperature response of stage-specific survivorship (panels e–j), which show an inverted U shape in the egg (nonlinear

regression: sxTmax¼ 1�0 � 0�02; P\ 0�01; a ¼ 3�46 � 1�08; P\ 0�0001; b ¼ 8�65 � 0�65; P\ 0�05; Topt ¼ 25�21 � 0�51;P\ 0�0001; n ¼ 8

temperatures) and first nymphal stages (sxTmax¼ 1�0 � 0�03; P\ 0�01; a ¼ 5�75 � 0�21;P\ 0�001; b ¼ 7�34 � 0�22;P\ 0�0001;Topt ¼

26�05 � 0�51; P\ 0�0001; n ¼ 8 temperatures), a saturating response in the second nymphal stage (sxTmax¼ 1�0 � 0�03; P\ 0�05;

a ¼ 9�32 � 0�23; P\ 0�001; b ¼ 12�41 � 10�24; P\ 0�13; Topt ¼ 27�31 � 0�99; P\ 0�0001; n ¼ 8 temperatures), and temperature invari-

ant survivorship in third to fifth nymphal stages (linear regression, slope indistinguishable from zero, P > 0·05, n = 8 temperatures). As

expected, cumulative (egg-to-nymph and egg-to-adult) survivorship exhibits an inverted U-shaped temperature response (panels k–p).



The early nymphal stages (first to third), which exhibited

the greatest temperature sensitivity and the lowest temper-

ature tolerance, were the most likely to exhibit a monoton-

ically 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 VAR IABLE TEMPERATURES ON

SURV IVORSHIP

We have tested predictions from our conceptual frame-

work with survivorship data taken under constant temper-

atures. 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 cumula-

tive survivorship,that is, lxðTÞ ¼ QxTi¼0 siðTÞ, can be evalu-

ated under any kind of variable temperature regime. For

instance, if we want to consider the effects of seasonal vari-

ation on lxðTÞ of a particular species, we can make temper-

ature 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, lxðmðtÞÞ ¼ QxmðtÞi¼0 siðmðtÞÞ

and we can investigate the effects of seasonal temperature

variation in cumulative survivorship by fitting the model

lxðmðtÞÞ ¼ e�ððxmðtÞÞ=ðbmðtÞÞÞamðtÞto data using nonlinear

regression where lxðmðtÞÞ is the proportion of individuals

that survive from birth to age xmðtÞ when experiencing

the seasonal temperature regime given by m(t), and amðtÞand bmðtÞ are, respectively, the shape and scale parameters

of the Weibull distribution estimated under the same

temperature regime.

Life stage Life stage Age (scaled) Temperature (° C)

Tem

pera

ture

sen

sitiv

ity

Tem

pera

ture

tole

ranc

e

Egg-

to-a

dult

surv

ivor

ship

Slop

e of

sur

vivo

rshi

p cu

rve

(a)

surv

ivor

ship

Eggs N1 N2 N3 N4 N5

Egg-

to-s

tage

su

rviv

orsh

ip

Temperature (°C)

33 C18 C 24 C

21 C

27 C

29 C

(d)(c)(b)(a)

(e) (f) (g) (h) (i) (j)

(k) (l) (m) (n) (o) (p)

Fig. 4. Temperature responses of stage-specific and egg-to-adult survivorship of the Mediterranean species (Murgantia histrionica). Panel

(a) depicts the temperature sensitivity of life stages. Note that second and third nymphal stages exhibit the highest temperature sensitivity.

Second nymphal stage exhibits the narrowest temperature tolerance (panel b) and hence determines the temperature range over which the

life cycle can be completed. Panel (c) depicts survivorship curves at different temperatures. Note the very steep survivorship curves at

extreme temperatures (18 and 33 �C) and curves of decreasing slope as temperature increases. Panel (d) depicts shows that increasing tem-

perature causes a significant decrease in the slope of the survivorship curve (linear regression: slope = �0·28 ± 0·09, P < 0·05, inter-

cept = 8·16 ± 2·23, P < 0·05; model fit: F = 8·39, P = 0·04, n = 5 temperatures). Analyses of the temperature response of stage-specific

survivorship (panels e–j) show an inverted U shape in the egg (nonlinear regression: sxTmax¼ 1�0 � 0�02; P\ 0�01; a ¼ 19�76 � 4�8;

P ¼ 0�6; b ¼ 9�44 � 1�0; P\ 0�0001; Topt ¼ 24�65 � 1�5; P\ 0�0001; n ¼ 8 temperatures) and first nymphal stages (sxTmax¼

1�0 � 0�01; P\ 0�05; a ¼ 8�272 � 1�13; P\ 0�001; b ¼ 8�48 � 0�38; P\ 0�01; Topt ¼ 24�51 � 1�35; P\ 0�0001; n ¼ 8 temperatures),

a monotonic increase in the second (linear regression: slope = 0·025 ± 0·001, P < 0·0001, intercept = �0·005 ± 0·23, P = 0·93, n = 5 tem-

peratures), third (slope = 0·05 ± 0·01, P < 0·001, intercept: �0·75 ± 0·24, P = 0·037) and fourth nymphal stages (slope = 0·04 ± 0·009,P < 0·01, intercept = �0·34 ± 0·23, P = 0·24; n = 5 temperatures), and a saturating response in the fifth nymphal stage (nonlinear regres-

sion: sxTmax¼ 0�8885 � 0�023; P\ 0�01; a ¼ 6�08 � 1�2; P\ 0�05; b ¼ 6�41 � 0�11; P\ 0�001; Topt ¼ 24�67 � 0�5; P\ 0�01; model

fit: F = 952·33, P = 0·001, n = 5 temperatures). As expected, cumulative (egg-to-nymph and egg-to-adult) survivorship exhibits a left-

skewed temperature response (panels k–p).



Discussion

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 sur-

vivorship 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 dur-

ing which survivorship is maximal. Although both types of

temperature responses are frequently observed, the mecha-

nisms 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 survi-

vorship should be invariant at intermediate temperatures

nor why it should be left- or right-skewed.

Here we have developed a framework that can poten-

tially 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 nar-

row 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 survi-

vorship should exhibit a left- or right-skewed response

depending on whether the survivorship of the stage(s) most

)delacs(egAegatsefiL

Tem

pera

ture

sen

sitiv

ity

Tem

pera

ture

tole

ranc

e

Egg-

to-a

dult

surv

ivor

ship

Slop

e of

sur

vivo

rshi

p cu

rve

(a)

Life stage

surv

ivor

ship

2N1N N3 N4 PRD

Nym

ph-t

o-st

age

surv

ivor

ship

Temperature (°C)

Temperature (°C)

27 C

17 C

12 C

20 C

(a) (b) (c) (d)

(e) (f) (g) (h) (i)

(j) (k) (l) (m) (n)

Fig. 5. Temperature responses of stage-specific and egg-to-adult survivorship of the temperate species (Acyrthosiphon pisum). The second

nymphal instar exhibits the greatest temperature sensitivity (panel a). All stages have similar temperature tolerance (panel b) and the tem-

perature tolerance of the first nymphal stage determines the temperature range over which the life cycle can be completed. The survivor-

ship curves become steeper as the temperature increases (panel c) and the slope of the survivorship exhibits a marginally significant

increase with increasing temperature (panel d; linear regression: slope = �0·03 ± 0·007,P = 0·06, intercept = �0·02 ± 0·15,P = 0·56; model

fit: F = 15·13, P = 0·06, n = 4 temperatures). The strong trend suggests that the lack of significance is likely due to the small number of

temperatures studied. Analyses of the temperature response of stage-specific survivorship (panels e–j) show an invariant response in the

first nymphal stage (linear regression: slope = 0·0 ± 0·0, P = 0·13, intercept = 1�0 � 10�28;P\ 0�0001 ; model fit: F = 5·8, P = 0·09, n = 5

temperatures) and a monotonic decrease in the second nymphal stage (linear regression: slope = �0·02 ± 0·01, P = 0·12, inter-

cept = 1·0 ± 0·25, P < 0·05, n = 5 temperatures), and all subsequent stages (third nymphal stage: slope = �0·008 ± 0·003, P = 0·06, inter-cept = 1·0 ± 0·01, P < 0·05; fourth nymphal stage: slope = �0·008 ± 0·004, P = 0·09, intercept = 1·0 ± 0·04, P = 0·2; pre-reproductive

adult stage: slope = �0·003 ± 0·002, P = 0·19, intercept = 1·0 ± 0·05, P = 0·25; n = 5 temperatures). As expected, cumulative (nymph-

to-nymph and nymph-to-adult) survivorship exhibits a right-skewed temperature response (panels k–p).



sensitive to temperature increases or decreases with

increasing temperature.

We tested these predictions with three Hemipteran spe-

cies 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 survivor-

ship 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 tempera-

ture effects on survivorship. When different life stages exhi-

bit 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 differ-

ent microclimates or seasonal environments (e.g. species

with long generation times in which different stages

develop during different seasons), viability will be deter-

mined 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 envi-

ronment in which temperature fluctuations are minimal

while the Mediterranean and temperate species inhabit

environments characterized by strong seasonal fluctua-

tions. However, given the fact that we studied only a single

species from each latitude, these expectations are specula-

tive 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 crite-

ria (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 tempera-

ture tolerance. Mobile, free-living stages that are unpro-

tected 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 tem-

peratures, thus increasing overall survivorship and ensur-

ing 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 ecto-

therms 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 survivor-

ship (and hence lifetime fitness) if the mean habitat tem-

perature 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 survivor-

ship 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 tem-

perature 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 rela-

tive to the time scale of temperature variation (e.g. diurnal,

seasonal) are likely to be more adversely affected by cli-

mate warming because they would be unable to avoid peri-

ods 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 fluctua-

tions (IPCC 2007). Because stage-specific survivorship has

a multiplicative effect on egg-to-adult survivorship and

lifetime fitness, effects of increasing temperature fluctua-

tions 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.

Acknowledgements

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.



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Received 16 October 2011; accepted 26 March 2012

Handling Editor: Robbie Wilson

Supporting Information

Additional Supporting Information may be found in the online

version of this article:

Appendix S1. Experimental protocols for quantifying stage-specific

and egg-to-adult survivorship.

Appendix S2. Temperature responses of developmental stages.

As a service to our authors and readers, this journal provides sup-

porting information supplied by the authors. Such materials may

be re-organized for online delivery, but are not copy-edited or

typeset. Technical support issues arising from supporting informa-

tion (other than missing files) should be addressed to the authors.



elucidating the temperature response of survivorship in insects

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