Author's Accepted Manuscript

Are thermal constants constant? A test usingtwo species of ladybird

V. Jarošík, G. Kumar, Omkar, A.F.G Dixon

PII: S0306-4565(13)00133-2DOI: http://dx.doi.org/10.1016/j.jtherbio.2013.12.001Reference: TB1479

To appear in: Journal of Thermal Biology

Received date: 29 May 2013Accepted date: 10 December 2013

Cite this article as: V. Jarošík, G. Kumar, Omkar, A.F.G Dixon, Are thermalconstants constant? A test using two species of ladybird, Journal of ThermalBiology, http://dx.doi.org/10.1016/j.jtherbio.2013.12.001

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Are thermal constants constant? A test using two species of ladybird

The late V. JAROŠÍK1,2, G. KUMAR3, OMKAR3 & A. F. G. DIXON4, 5

1Department of Ecology, Faculty of Science, Charles University Prague, Viničná 7, CZ-128 44

Prague, Czech Republic and 2Department of Invasion Ecology, Institute of Botany Academy of

Sciences of the Czech Republic, CZ-252 43 Průhonice, Czech Republic, jarosik@cesnet.cz;

3Ladybird Research Laboratory, Department of Zoology, University of Lucknow, Lucknow- 226

007, India, dr_omkar@hotmail.com; 4Department of Biodiversity Research, Global Change

Research Centre AS CR, Na sádkách 7, 370 05 České Budějovice, Czech Republic, 5School of

Biological Sciences, University of East Anglia, Norwich, NR4 7TJ, U.K, a.f.dixon@uea.ac.uk

Corresponding author: Professor Anthony F. G. Dixon, School of Biological Sciences,

University of East Anglia, Norwich, NR4 7TJ, United Kingdom, Telephone: +44 (0) 1603

456161

Abstract

There is a controversy about whether the thermal constants, lower developmental threshold, rate

of development and corresponding degree days required for development, change when a species

is reared under different developmental conditions. We present a more precise way of measuring

these constants using the linear relationship between the rate of development and temperature.

First we use the equation proposed by Ikemoto and Takai (2000) to determine the linear phase of

development and then a generalised linear model having a different variance at low and high

temperatures, specific for each condition, to estimate the parameters of the linear relationship.

Using this method, we show that providing the difference in food quality is sufficiently great, an

aphidophagous ladybird develops significantly faster and starts developing at a significantly

lower temperature on a good than on a poor quality diet. Adaptive significance of the thermal

constants not remaining constant is discussed in terms of a trade-off between growth and rate of

development, when temperature and food quality varies.

Key words: lower developmental threshold, degree days, linear phase of development, food

quality, Menochilus sexmaxculatus, Propylea dissecta

1. Introduction

There are a large number of studies in which the thermal constants of insects, i.e., the

lower temperature threshold, rate of development and number of degree-days required for

development, are determined by rearing individuals at a range of different temperatures (see

Jarošík et al., 2011 for a recent review). The thermal constants can be used to forecast when in

the year various pest insects will become active and develop models to predict when they will

complete their development and fly off and infest other plants (e.g. Baskerville and Emin, 1969;

Campbell et al., 1974; Allen, 1976; Welch et al., 1978). More recently, these models have been

used as a component of risk analysis for predicting the establishment and spread of exotic pests

(e.g. Jarvis and Baker, 2001; Venette et al., 2010; Eyre et al., 2012).

The underlying assumption, however, is that the thermal constants are actually constant.

This is supported by many studies (e.g. Danilevsky, 1957, 1965; Tauber et al., 1986; Lamb et al.,

1987; Nechols et al., 1987; Lamb and MacKay, 1988; Mogi, 1992; Groeters, 1992) and the

existence of a general negative relationship between degree-days required for development and

the lower temperature threshold among species (Honěk and Kocourek, 1988, 1990; Trudgill and

Perry, 1994; Trudgill, 1995; Honěk, 1996a,b), indicating that adaptations of thermal constants

occur mainly at an inter-specific level (Honěk, 1996b). However, there are also contrary

examples suggesting that thermal constants of populations of a species can be adjusted to suit

local climatic conditions (Morris and Fulton, 1970; Morris, 1971; Umeya and Yamada, 1973;

Campbell et al., 1974; Rae and Death, 1991) and seasonal differences, namely the presence or

absence of diapause in the preceding developmental stages (Morris and Fulton, 1970b; Nechols

et al., 1983; Turnock et al., 1985; Saulich and Volkovich, 2004). There also exist a few studies

suggesting that food quality affects the thermal constants, namely in moths (Taylor, 1988; Honěk

et al., 2002) and aphids (Dixon et al., 2013).

The within species variation in thermal constants may not be a serious problem when

predicting when insects will become active or hatch at a specific geographical location.

Moreover, the within species variation in thermal constants related to specific local climatic

conditions or seasonal differences can be adaptive (Roff, 1980), though the trade-off action of

natural selection can keep the thermal parameters constant (Nechols et al., 1987; Tauber et al.,

1987; Groeters 1992). However, when considering insects that feed on plants or prey that differ

greatly in terms of food quality their ability to adapt to such a change by varying their thermal

constants is less apparent and could be important when predicting pest occurrence or

performance of a natural enemy.

The first question addressed here is therefore whether the assumption of constant within

species thermal constants is valid for species fed food of different qualities. This is examined

using two ladybird species. There are results for the ladybird Adalia bipunctata reared on an

artificial diet and aphids over a range of temperatures (Jalali et al., 2010). In this case, the

thermal constants for complete development did not differ on the two diets, which can be

attributed to the high quality of the artificial food. Consequently, there is still a need for a study

of the effect of varying food quality on the thermal constants of ladybirds. In this study, this is

achieved by feeding two species of aphidphagous ladybirds, Menochilus sexmaxculatus (F) and

Propylea dissecta (Mulsant), which have overlapping geographic ranges, on two species of

aphids that both sequester plant secondary substances for defence against predators (Dixon,

1998), but in terms of their food quality for the ladybirds were thought to differ.

The second question we address is the nature of the statistics required for determining

differences in thermal constants. Within a relevant range of temperatures of about 20 °C

(Charnov and Gillooly, 2003; Dixon et al., 2009), in which insects actually live, the relationship

between the rate of development and temperature is virtually linear (e.g. Sharpe and DeMichele,

1977). This enables easy calculation of the thermal constants using a linear regression (e.g.

Jarošík et al., 2002; Shi et al., 2010; Kuang et al., 2012). However, standard errors of the lower

temperature threshold and number of degree-days required for development calculated from this

linear relationship can be calculated only approximately (Campbell et al., 1974) and are usually

relatively large. This cannot be improved by treating the results for individuals reared at each

constant temperature as independent data points (Kipyatkov and Lopatina, 2010) because all

these individuals are nested within a particular temperature and thus are pseudo-replicates (e.g.

Hurlbert ,1984; Sokal and Rohlf, 1995). In addition, the values of the thermal constants depend

on establishing the temperature range over which the relationship between the developmental

rate and temperature is actually linear (Ikemoto and Takai, 2000). Consequently, many studies

supporting the view that the thermal constants for species are actually constant also report small

differences between populations within species. Whether these differences can be proved to be

statistically significant remains an open question.  

2. Materials and methods

2.1 Stock culture

Adults of Propylea dissecta and Menochilus sexmaculatus (Coleoptera: Coccinellidae)

were collected from agricultural fields around the city of Lucknow, India (26º50`N, 80º54`E),

paired separately in Petri dishes (14.5 x 1.5 cm) and then placed in an Environmental Test

Chamber (ETC) kept at 27±1ºC, 65±5% relative humidity (RH) and a 14L: 10D photoperiod.

Half of the pairs of each ladybird species were provided daily with an ad libitum supply of the

better quality aphid prey, Aphis craccivora Koch reared on hyacinth bean [Dolichos lablab (L.)

Sweet] and the other half with the poorer quality aphid prey, Lipaphis erysimi Kaltenbach reared

on mustard [Brassica rapa L. (= campestris L.)]. Eggs laid by each of these pairs were removed

and monitored at regular intervals until they hatched. The hatchlings were reared to the adult

stage in glass beakers (five per beaker) and fed daily an ad libitum supply of aphids similar to

their parents. These adults were paired and fed the same diet and kept under similar temperature

conditions to their parents, which was either 15±1ºC, 20±1ºC, 25±1ºC, 30±1ºC or 35±1ºC (± in

each case is the variance) . The eggs laid by these females were used in the following

experiments.

2.2 Experimental Protocol

Eggs of M. sexmaculatus collected from beetles kept at the different temperatures were

kept in ETCs at the same temperature as the adults, 65±5% relative humidity (RH) and a 14L:

10D photoperiod. These eggs were monitored twice a day and the time of hatching recorded.

Fifty larvae that hatched from these eggs were transferred within 3-4 hours in groups of 5 and

placed in Petri dishes, each of which constituted a replicate. The larvae in five of the batches of

five larvae, like their parents, were provided with an ad libitum supply of either A. craccivora or

L. erysimi, together with host plant leaves, until the larvae pupated. One batch of five larvae fed

on each of the two aphids was reared at either: 15°, 20º, 25º, 30º or 35ºC. A total of ten such

replicates were reared at each of the five temperatures under each prey regime. Every twenty

four hours the Petri dishes were cleaned and the larvae provided with fresh aphids and leaves.

Mean values recorded for the five larvae in each Petri dish constituted a replicate. The duration

of development and the number of larvae that survived to the end of each instar, pre-pupal and

pupal stages were recorded. The adults that emerged from the pupae were weighed on an

electronic balance (Sartorius CP225-D) within 24 h of emergence. This experiment was repeated

using P. dissecta fed the same two species of aphid. The results were used to calculate the

percentage that pupated, developmental rate (1/D), mean duration of larval development, growth

index, which is the percentage of the larvae that pupate divided by the mean duration of larval

development (Zhang et al., 1993), and average weights of adult beetles (Tables A.1-A.4).

2.3 Statistical analysis

Developmental characteristics of the two ladybird species, each reared on the two aphid

species (Tables A1-4), were compared based on the duration of their total developmental period

(egg to adult) using three thermal constants: developmental rate (R), i.e. reciprocal values of

durations of development (D; measured in days); lower developmental threshold (t), i.e.

temperature at which development ceases (°C); and sum of effective temperatures (k), i.e. the

amount of heat above the lower developmental threshold necessary for complete development

(degree-days °D).

Within the linear range between the developmental rate (R) and temperature (T), the relationship

between R and T can be described by a linear equation:

R = a + bT (1)

In this equation, a is the intercept and b the slope of the line. From equation (1), the lower

developmental threshold is t =-a/b, and the sum of effective temperatures k = 1/b (e.g. Campbell

et al., 1974). Thus, when developmental rate R is plotted against temperature T, the lower

developmental threshold t corresponds to the intercept of the line with the temperature x-axis,

and the reciprocal value of its slope b to the sum of effective temperatures k (e.g. Jarošík et al.,

2004).

The linear equation (1) was used to test whether the developmental rate (R) and the lower

developmental threshold (t) differed on the low and high quality aphid food, separately for each

ladybird species. This was done using ANCOVAs by regressing R on temperature T, with a

different intercept a and a different slope b for each diet. Parameters of these models were

inspected for significance using deletion tests (e.g. Crawley, 1993). Differences in the

developmental rates R when reared on low and high quality prey were indicated by significantly

(P < 0.05) different slopes of R on T. When the slopes differed significantly, differences in the

lower developmental thresholds t’s were tested by shifting the x-axis along until the origins of

the regression lines were at the t values. This was done by subtracting the values of lower

developmental thresholds from temperature values, following Crawley (1993, p. 276-7). Using

this method, the t values corresponded to the intercepts of the lines (a’s), which were tested by

comparing the 95% confidence intervals of the intercepts (Dixon et al., 2005).

Ikemoto and Takai (2000) suggest a different way of estimating the lower developmental

threshold t and sum of effective temperatures k within the linear range between the duration of

development D and temperature T:

DT = k + tD (2)

In this equation, the intercept is the predicted value of the sum of effective temperatures k and

the slope the lower developmental threshold t. Because both these values on the y- and x-axis,

respectively, are subject to errors, equation (2) is solved using reduced major axis (Kermack and

Haldane, 1950, Sokal and Rohlf, 1995 p. 541-549) and cannot be directly used for comparing

regression slopes and intercepts using deletion tests in ANCOVAs. However, the plot of DT on

duration of development D using equation (2) is a better way of establishing the linear range of

temperature dependent development than a plot of developmental rate R on temperature T using

equation (1) (Ikemoto and Takai, 2000). We therefore used the plot of DT on D to assess the

linear range of the temperature dependent development. Whether the deletion of those values that

indicate a non-linear relationship improved the linear fit of the temperature dependent

development was tested by comparing the ranges of the confidence intervals of t and k before

and after omitting these points. The established linear range for each ladybird and diet was then

used to evaluate the differences in developmental rates R and lower developmental thresholds t

using ANCOVAs and using equation (1), as described above.

Ikemoto and Takai (2000) suggest that although fitting equation (1) within the linear

range of the relationships assuming homogeneous variance in error structure is usually fairly

satisfactory, the points in the upper and lower part of the line have unequal weights, which yield

estimates of the line that are unreliable. To remove this potential bias, we fitted ANCOVAs

based on equation (1) using eight models differing in error variance structure (Zuur et al., 2009,

p. 72-106). This was done by using the gls function in the R-package nlme (Pinheiro et al.,

1993). In these models, the error variance of the residuals was related to the value of the

explanatory variable temperature T, which in these models is the variance covariate; in some

models, this variance covariate is also specific for the categorical explanatory variable, i.e. in this

case for each aphid as a representative of a particular food quality. Full ANCOVA models with

different error variance structures were compared based on AIC and likelihood ratio (L) tests

with the original full ANCOVA model assuming homogeneous error variance, using the

maximum likelihood restricted method. The model with the overall lowest AIC value was then

simplified by deletion tests, using L tests and the maximum likelihood method, and the final

model with heterogeneous error variance compared with the final model assuming homogeneous

variance by using the restricted maximum likelihood method (Diggle et al., 2002). All models

were checked by plotting standardized residuals against fitted values, temperature T and aphid

species representing food quality. Calculations were done in R 2.9.2 (R Development Core

Team 2009).

3. Results

3.1 The quality of Aphis craccivora and Lippaphis erysimi as food for Menochilus sexmaculatus

and Propylea dissecta

In terms of the average adult weights of the two ladybirds reared at the five temperatures,

A. craccivora is a better quality prey than L. erysimi (two-sample t-test: t = 6.641, df = 32, P <

0.0001). The average weights of those reared on the better quality aphid in both cases were only

26 and 20% greater. That is, although the two aphids differ similarly in terms of their food

quality for these two ladybirds the difference in performance measured in this way is only 6%,

which is not very large. If one measures the difference in quality in terms of the growth index,

the difference is again significant (t = 2.189, df = 15, P < 0.05), but the difference in performance

is 26 and 10% greater, respectively, which indicates the difference in the quality of the two

aphids for these ladybirds measured in this way was much greater for M. sexmaculatus than P.

dissecta (Table A.5).

3.2 The effect of prey quality on the thermal constants of Menochilus sexmaculatus and Propylea

dissecta

Plots of the developmental rate on temperature (Fig. 1 A and C) indicate a slight non-

linearity in the temperature dependent development of M. sexmaculatus and P. dissecta. It was

difficult, however to determine the points within the range of temperatures from 15 to 35 °C that

are responsible for the deviations from linearity. On the other hand, the plots of the product of

the duration of development and temperature on the duration of development (Fig. 1 B and D)

clearly indicate that the values recorded at the highest temperature, 35 °C, for M. sexmaculatus

and lowest temperature, 15 °C, for P. dissecta could be responsible for these deviations. For P.

dissecta, the widths of the confidence intervals of the lower developmental threshold and sum of

effective temperatures were narrower when the temperature dependent development was

evaluated after omitting the value recorded for the lowest temperature, 15 °C, than for the whole

temperature range. On the other hand, the confidence intervals for M. sexmaculatus are on

average narrower for the whole temperature range than after omitting the values recorded at the

highest temperature, 35 °C. Consequently, the developmental characteristics of M. sexmaculatus

were evaluated for the whole temperature range of 15 to 35 °C and of P. dissecta for the range 20

to 35 °C.

Using the model assuming homogeneous error variance, the developmental rate of M.

sexmaculatus was significantly (F = 5.644; df = 1, 7; P < 0.05) faster on the better quality aphid,

A. craccivora than the poorer quality aphid, L. erysimi. Consequently, the sum of effective

temperatures k, the reciprocal value of the developmental rate, was lower when fed on A.

craccivora (k = 226.9 °D) than on L. erysimi (k = 247.7 °D). Comparing the 95% confidence

intervals (CI) for intercepts moved to coincide with the values of the lower developmental

thresholds, t, the value of t was significantly lower for M. sexmaculatus reared on A. craccivora

(t = 8.58 °C; CI = 8.55 - 8.60) than on L. erysimi (t = 9.30 °C; CI = 9.28 - 9.32). Using the

models with heterogeneous error variance, the best model based on the AIC values was that in

which the non-homogeneous error variance was described as “constant plus power of the

variance covariate” and in which the variance covariate, i.e. the explanatory variable temperature

T, had a specific error structure for each aphid diet. As in the model assuming homogeneous

error variance, the developmental rate of M. sexmaculatus was significantly (L = 4.997; df = 1; P

< 0.05) faster when fed on the better quality aphid, A. craccivora (k = 228.5 °C) than the poorer

quality aphid, L. erysimi (k = 249.7 °D) and the lower developmental threshold based on 95% CI

was significantly lower for M. sexmaculatus reared on A. craccivora (t = 8.63 °C; CI = 8.60 -

8.66) than on L. erysimi (t = 9.19 °C; CI = 9.17 - 9.21). In the likelihood ratio test, the model

assuming homogeneous error variance did not differ significantly from the best model with

heterogeneous error variance (L = 0.441; df = 4; NS).

For the ladybird P. dissecta, developmental rates, sum of effective temperatures and

lower developmental thresholds recorded on the two aphid diets did not differ significantly,

neither for the model assuming homogeneous error variance (common values on both aphid

diets: sum of effective temperatures k = 238.7 °D; lower developmental threshold t = 10.98 °C;

95% confidence interval CI = 10.96 - 11.00) nor for the best model with the “constant plus

power of the variance covariate” residual error structure (k = 280.9 °D; t = 8.25 °C; CI = 8.24 -

8.26). As for M. sexmaculatus, the predictions of the model assuming homogeneous error

variance did not differ significantly from those of the best model with heterogeneous error

variance (L = 5.802; df = 4; NS).

4. Discussion

Development in insects tends to be viewed either mainly in terms of growth in size or the

rate of development. Although they can be treated as separate processes, size in insects and

ultimately their fitness is a consequence of the relative effect of temperature on their growth and

developmental rates. For example, the generally smaller size of individuals of insects that are

reared at high temperatures than those reared at low temperatures is that increase in temperature

has a proportionally greater effect on their rate of development than on their growth rate.

Similarly, the generally larger size of those reared on a high quality diet than on a low quality

diet is that increase in food quality has a greater proportional effect on their growth rate than on

their developmental rate (Dixon et al., 1982, Dixon, 2000; Dixon and Hopkins, 2010). That is, an

increase in food quality affects both the rates of development and growth of insects and the

extent to which it affects their adult size. Thus, like size the value of thermal constants of a

species, which although adaptive in terms of the temperature conditions they experience during

their development (Honĕk, 1996a, b), might also be affected by food quality.

The aphidophagous ladybird M. sexmaculatus developed significantly faster and starts

developing at a significantly lower temperature on the better quality diet of A. craccivora than on

the poorer quality diet of L. erysimi. The developmental rate and lower developmental threshold

of P. dissecta, however, did not differ significantly on these two diets. It is likely that the reason

for this is that the difference in the quality of the two diets for the two ladybirds is not the same,

as the percentage differences in the adult weights and growth indices on the better of the two

diets were greater for M. sexmaculatus than P. dissecta. That is, in terms of the argument

developed in the preceding paragraph the temperature at which an insect can start developing and

growing is a function (F [TQ]) of the relative effects of both temperature (T) and food quality

(Q). If the difference in food quality is small then any effect this might have on F [TQ] is likely

to be obscured by the accuracy with which the lower developmental threshold can be measured.

However, once an insect starts developing it is less clear why food quality should affect sum of

effective temperatures.

The model with heterogeneous error variance, “constant plus power of the variance

covariate”, in which the variance covariate is the explanatory variable temperature with a

specific error structure for each aphid diet, is best if the variance covariate has values close to

zero (Pinheiro and Bates, 2000). Values close to zero in this case would be those recorded close

to the lower developmental threshold. In addition, this model also enables a larger residual

spread as temperature increases. This model thus solves the problem of an unreliable estimation

of the regression line of developmental rate on temperature due to unequal weights of the points

in the upper and lower part of the line (Ikemoto and Takai, 2000).

However, the results for the model supposing homogeneous error variance and the best

model with the heterogeneous error variance also confirm Ikemoto and Takai (2000) proposition

that fitting the linear model supposing homogeneous error variance, though biased, is usually

fairly satisfactory. For both ladybird species, the models with homogeneous and heterogeneous

residual error variance resulted in exactly the same conclusions and did not differ significantly in

likelihood ratio tests. For M. sexmaculatus, also the differences in the values of the sum of

effective temperatures k and lower developmental thresholds t between the model assuming

homogeneous error variance and that with heterogeneous error variance were negligible, on both

aphid diets (A. craccivora: k = 226.9 and t = 8.58 vs. k = 228.8 and t = 8.63; L. erysimi: k = 247.7

and t = 9.30 vs. k = 249.7 and t = 9.19). However, for P. dissecta the improved heterogeneous

error structure of the model caused a substantial change in the values of the sum of effective

temperatures (k = 238.7 vs. k = 280.9) and the lower developmental thresholds (t = 10.98 vs. t =

8.25). Thus, the use of the classical regression model assuming homogeneous variance in error

structure can, in some cases, give biased estimates of the sum of effective temperatures and the

lower developmental threshold. Consequently, to remove biases when assessing the relationship

between the developmental rate and temperature, the suggested best model with heterogeneous

variance, “constant plus power of the variance covariate” where the variance covariate, i.e. the

explanatory variable temperature T, has a specific error structure for each categorical response

variable, should be the preferred option.

Interesting, but not unexpected, is that the difference in the quality of the two aphids for

the two ladybirds used in this study was not the same with the species that was the poorest in

terms of food quality for both ladybirds was poorer for M. sexmaculatus than P. dissecta. In

addition, in terms of the effect of the difference in the food quality of the two aphids on the

thermal constants of the ladybirds only those of M. sexmaculatus were significantly affected.

This indicates that the order of the difference in food quality has to be sufficiently large that any

inaccuracies in the measurement of the rates of development do not obscure its effect on the

thermal constants.

The results of this study indicate that providing the difference in food quality is

sufficiently great then the thermal constants, in particular the lower developmental threshold, do

not remain constant. Similar results are reported for aphids (Dixon et al., 2013) and Lepidoptera

(Taylor, 1988; Honĕk et al., 2002) so it is likely that this is a general phenomenon in insects and

other ectothermic organisms. However, there is a need for more detailed studies using food of

markedly different qualities and rearing the animals at many more temperatures within the range

over which the relationship between developmental rate and temperature is linear and for the

results to be more critically analyzed as suggested above.

Acknowledgements

V.J. acknowledges grant no. 206/09/0563 (Czech Science Foundation) and the

institutional resources of the Czech Ministry of Education, Youth and Sports. Omkar and GK

thank the Department of Higher Education, Government of UP, Lucknow, India for financial

support in the form of funding for a Centre of Excellence. AFGD acknowledges financial

support from grant No. CZ.1.05/1.1.00/02.0073 of the MSMT.

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Text to Figure

Figure 1. Temperature dependent development of the ladybirds Menochilus sexmaculatus (A and

B) and Propylea dissecta (C and D) reared on two aphid species, Aphis craccivora and Lippaphis

erysimi. Plots of developmental rate on temperature (A and C) using equation (1) and of the

product of the duration of development and temperature on the duration of development (B and

D) using equation (2) are presented. Arrows in Figs 1B and 1D mark the points responsible for

non-linearity; these points were omitted when the linear range of the temperature dependent

development was examined. Note that the points in the lower left hand corners in B and D

correspond to the highest, and those in the upper right hand corners to the lowest temperatures.

0

0.02

0.04

0.06

0.08

0.1

0.12

10 20 30 40

Develop

men

tal rate (1/day)

Temperature (°C)

A. Menochilus sexmaculata

Aphis craccivora

Lippaphis erysimi

250

300

350

400

450

500

550

600

650

0 10 20 30 40

Duration x Tempe

rature

Duration of development (days)

B. Menochilus sexmaculata 

Aphis craccivora

Lippaphis erysimi

 

 

 

 

0

0.02

0.04

0.06

0.08

0.1

0.12

10 20 30 40

Develop

men

tal rate (1/day)

Temperature (°C)

C. Propylea dissecta

Aphis craccivora

Lippaphis erysimi

250300350400450500550600650700

0 10 20 30 40

Duration x Tempe

rature

Duration of development (days)

D. Propylea dissecta 

Aphis craccivora

Lippaphis erysimi

 

Highlights • We present a more precise way of measuring developmental thermal constants 

• We show that thermal constants are not constant 

• Development is faster and starts at a lower temperature on a good quality diet 

• This finding indicates an important trade‐off between growth and rate of development 

• It can also have practical consequences when using phenological models   

Table A.1 Developmental durations (days) of the egg and immature stages of Menochilus. sexmaculata and results of two-way ANOVA showing influence of temperature and aphid species. Temp. Aphid

species Egg Immature stage Total

developmental period

1st 2nd 3rd 4th Pre-pupa

pupa

15˚C A. craccivora

6.80±0.20

3.20±0.03

4.00±0.04

4.30±0.02

5.60±0.03

1.50±0.11

7.60±0.05

33.00±0.19

L. erysimi

7.70±0.15

4.07±0.04

4.64±0.03

5.35±0.05

6.50±0.05

2.20±0.05

8.70±0.06

39.16±0.20

20˚C A. craccivora

4.5±0.17

2.37±0.03

2.87±0.08

3.57±0.03

3.96±0.04

1.28±0.13

5.45±0.12

24.00±0.22

L. erysimi

4.90±0.10

2.82±0.04

3.18±0.04

3.77±0.03

4.13±0.04

1.59±0.01

5.74±0.04

26.13±0.12

25˚C A. craccivora

2.50±0.17

1.32±0.05

1.70±0.02

1.80±0.02

1.90±0.08

0.90±0.03

2.60±0.07

12.72±0.24

L. erysimi

3.20±0.13

1.86±0.05

2.04±0.03

2.16±0.02

2.50±0.03

1.06±0.03

3.40±0.04

16.22±0.19

30˚C A. craccivora

1.90±0.10

1.07±0.03

1.20±0.04

1.40±0.03

1.55±0.02

0.70±0.04

2.11±0.03

9.93±0.09

L. erysimi

2.10±0.10

1.35±0.02

1.30±0.02

1.45±0.03

1.70±0.02

0.96±0.02

2.15±0.02

11.01±0.10

35˚C A. craccivora

1.80±0.13

1.00±0.03

1.10±0.04

1.20±0.02

1.40±0.02

0.50±0.02

2.00±0.03

9.00±0.16

L. erysimi

2.00±0.00

1.07±0.03

1.21±0.05

1.39±0.02

1.54±0.03

0.79±0.07

2.00±0.04

10.00±0.11

Temp. F- value, P- value (df)

554.29, 0.0001 (4, 90)

1769.52, 0.0001 (4, 90)

1892.47, 0.0001 (4, 90)

5788.86, 0.0001 (4, 90)

4302.20, 0.0001 (4, 90)

165.08, 0.0001 (4, 90)

4267.90, 0.0001 (4, 90)

9034.30, 0.0001 (4, 90)

Aphid sp.

F- value, P- value (df)

31.29, 0.0001 (1, 90)

364.06, 00001 (1, 90)

118.01, 0.0001 (1, 90)

414.18, 0.0001 (1, 90)

215.94, 0.0001 (1, 90)

102.51, 0.0001 (1, 90)

150.51, 0.0001 (1, 90)

678.58, 0.0001 (1, 90)

Interaction

F- value, P-

2.63, 0.039 (4, 90)

33.47, 0.0001 (4, 90)

12.51, 0.0001 (4, 90)

94.83, 0.0001 (4, 90)

33.53, 0.0001 (4, 90)

7.35, 0.0001 (4, 90)

35.86, 0.0001 (4, 90)

81.16, 0.0001 (4, 90)

value (df)

Values are mean ±S.E. Table A.2 Developmental attributes of Menochilus. sexmaculata and results of two-way ANOVA showing influence of temperature and aphid species. Temp. Aphid

species Pupation (%)

Adult emergence (%)

Developmental rate

Growth index

Weight of male (mg.)

Weight of female (mg.)

15˚C A. craccivora

58.00±4.67

54.00±4.27

0.030±0.00017

3.49±0.28

7.45±0.04

8.50±0.04

L. erysimi

56.00±2.67

50.00±3.33

0.026±0.00013

2.80±0.13

5.77±0.04

6.81±0.06

20˚C A. craccivora

66.00±5.21

64.00±4.99

0.042±0.00039

5.17±0.41

8.20±0.05

9.11±0.08

L. erysimi

62.00±3.59

60.00±4.22

0.038±0.00018

4.46±0.26

6.21±0.04

7.29±0.02

25˚C A. craccivora

78.00±5.54

78.00±5.54

0.079±0.00154

11.61±0.82

9.45±0.05

10.18±0.04

L. erysimi

68.00±4.42

68.00±4.42

0.062±0.00070

7.94±0.52

7.42±0.05

8.53±0.05

30˚C A. craccivora

72.00±5.33

68.00±6.11

0.101±0.00094

13.79±1.02

8.80±0.04

9.49±0.05

L. erysimi

64.00±4.00

62.00±4.67

0.091±0.00082

11.03±0.69

6.51±0.10

7.60±0.05

35˚C A. craccivora

64.00±5.16

60.00±5.16

0.112±0.00211

13.62±1.06

7.00±0.06

8.07±0.06

L. erysimi

60.00±2.98

54.00±3.06

0.100±0.00112

11.52±0.57

5.81±0.09

6.49±0.06

Temp. F- value, P- value (df)

4.22, 0.004 (4, 90)

6.14, 0.0001 (4, 90)

1983.55, 0.0001 (4, 90)

118.14, 0.0001 (4, 90)

386.00, 0.0001 (4, 140)

437.46, 0.0001 (4, 140)

Aphid sp. F- value, P- value (df)

5.22, 0.020 (1, 90)

5.58, 0.0001 (1, 90)

152.65, 0.0001 (1, 90)

23.86, 0.0001 (1, 90)

2423.26, 0.0001 (1, 140)

2511.90, 0.0001 (1, 140)

Interaction

F- value, P- value (df)

0.69, 0.599 (4, 90)

0.51, 0.730 (4, 90)

27.17, 0.0001 (4, 90)

1.47, 0.217 (4, 90)

25.51, 0.0001 (4, 140)

2.53, 0.043 (4, 140)

Values are mean ±S.E.

Table A.3 Developmental durations (days) of the egg and different immature stages of Propylea dissecta and results of two-way ANOVA showing influence of temperature and aphid species. Temp. Aphid

species Egg Immature stage Total

developmental period

1st 2nd 3rd 4th Pre-pupa

pupa

15˚C A. craccivora

7.00±0.00

4.00±0.05

4.60±0.03

5.20±0.04

5.97±0.04

2.00±0.01

8.20±0.04

36.97±0.10

L. erysimi

7.30±0.15

4.43±0.05

4.80±0.02

5.40±0.04

6.00±0.04

2.05±0.09

8.50±0.03

38.48±0.12

20˚C A. craccivora

5.40±0.16

3.20±0.05

3.40±0.06

3.80±0.03

4.40±0.04

1.53±0.02

5.90±0.06

27.63±0.26

L. erysimi

6.50±0.17

3.52±0.02

4.30±0.05

4.65±0.03

5.30±0.03

1.60±0.07

7.30±0.02

33.17±0.25

25˚C A. craccivora

2.90±0.10

1.59±0.03

1.74±2.03

2.03±0.03

2.37±0.02

0.86±0.04

3.10±0.04

14.59±0.12

L. erysimi

3.20±0.13

1.80±0.03

2.00±0.03

2.20±0.04

2.50±0.05

1.10±0.09

3.25±0.04

16.05±0.26

30˚C A. craccivora

2.20±0.13

1.30±0.02

1.40±0.03

1.77±0.03

2.02±0.05

0.74±0.06

2.56±0.02

11.99±0.20

L. erysimi

2.40±0.16

1.30±0.03

1.50±0.04

2.00±0.04

2.21±0.02

1.07±0.10

2.50±0.02

12.98±0.17

35˚C A. craccivora

1.90±0.10

1.01±0.03

1.20±0.03

1.40±0.04

1.65±0.02

0.70±0.05

2.05±0.04

9.91±0.12

L. erysimi

2.00±0.00

1.19±0.05

1.35±0.01

1.40±0.02

1.63±0.02

0.82±0.08

2.10±0.03

10.50±0.09

Temp. F- value, P- value (df)

677.75, 0.0001 (4, 90)

2616.33, 0.0001 (4, 90)

3742.40, 0.0001 (4, 90)

4451.71, 0.0001 (4, 90)

5231.34, 0.0001 (4, 90)

121.06, 0.0001 (4, 90)

1100, 0.0001 (4, 90)

8975.72, 0.0001 (4, 90)

Aphid sp.

F- value, P- value (df)

25.00, 0.0001 (1, 90)

91.85, 0.0001 (1, 90)

203.05, 0.0001 (1, 90)

165.47, 0.0001 (1, 90)

108.40, 0.0001 (1, 90)

14.06, 0.0001 (1, 90)

249.43, 0.0001 (1, 90)

310.35, 0.0001 (1, 90)

Interaction

F- value, P-

5.00, 0.001 (4, 90)

8.79, 0.0001 (4, 90)

42.12, 0.0001 (4, 90)

41.34, 0.0001 (4, 90)

50.89, 0.0001 (4, 90)

1.53, 0.202 (4, 90)

129.50, 0.0001

61.18, 0.0001 (4, 90)

value (df)

(4, 90)

Values are mean ±S.E.

Table A.4 Developmental attributes of Propylea dissecta and results of two-way ANOVA showing influence of temperature and aphid species. Temp. Aphid

species Pupation (%)

Adult emergence (%)

Developmental rate

Growth index

Weight of male (mg.)

Weight of female (mg.)

15˚C A. craccivora

54.00±3.06

52.00±3.27

0.027±0.00007

2.73±0.15

6.56±0.05

7.17±0.07

L. erysimi

52.00±4.42

48.00±6.11

0.026±0.00008

2.52±0.21

5.50±0.05

6.16±0.05

20˚C A. craccivora

64.00±4.00

60.00±4.22

0.036±0.00035

4.32±0.27

6.79±0.07

7.70±0.05

L. erysimi

60.00±2.98

58.00±3.59

0.030±0.00023

4.70±0.23

5.83±0.06

6.55±0.05

25˚C A. craccivora

76.00±4.00

74.00±4.27

0.069±0.00056

9.83±0.52

7.96±0.21

8.70±0.14

L. erysimi

72.00±3.27

70.00±3.33

0.062±0.00095

8.47±0.38

6.31±0.04

7.08±0.07

30˚C A. craccivora

66.00±3.06

64.00±4.00

0.084±0.00134

10.17±0.47

7.08±0.05

7.82±0.06

L. erysimi

62.00±3.59

60.00±2.98

0.077±0.00104

8.84±0.51

5.72±0.04

6.63±0.05

35˚C A. craccivora

64.00±4.00

58.00±3.59

0.101±0.00128

12.17±0.76

6.12±0.05

6.90±0.10

L. erysimi

62.00±3.59

56.00±4.00

0.095±0.00081

11.11±0.64

5.09±0.06

5.81±0.07

Temp. F- value, P- value (df)

8.30, 0.0001 (4, 90)

7.99, 0.0001 (4, 90)

1490.76, 0.0001 (4, 90)

181.15, 0.0001 (4, 90)

92.93, 0.0001 (4, 140)

118.56, 0.0001 (4, 140)

Aphid sp. F- value, P- value (df)

2.23, 0.139 (1, 90)

1.91, 0.0001 (1, 90)

70.74, 0.0001 (1, 90)

5.53, 0.021 (1, 90)

536.42, 0.0001 (1, 140)

633.62, 0.0001 (1, 140)

Interaction

F- value, P- value (df)

0.12, 0.975 (4, 90)

0.09, 0.984 (4, 90)

5.34, 0.001 (4, 90)

1.41, 0.236 (4, 90)

6.15, 0.0001 (4, 140)

4.94, 0.001 (4, 140)

Values are mean ±S.E.

Table A5 Results of Two-way-ANOVA showing difference in average adult weights and average growth indices of M. sexmaculatus and P. dissecta reared on A. craccivora and L. erysimi.

Menochilus sexmaculatus Propylea dissecta Temp. Aphi

d species

Average adult wt.

Average growth index

Overall difference (%) in average adult wt.

Overall difference (%) in average growth index

Temp. Aphid species

Average adult wt.

Average growth index

Overall difference (%) in average adult wt.

Overall difference (%) in average growth index

15˚C Ac 7.98±0.00

3.49±0.28

26.40 26.17 15˚C Ac 6.86±0.07

2.73±0.15

20.05 10.68

Le 6.29±0.10

2.80±0.13

Le 5.83±0.07

2.52±0.21

20˚C Ac 8.65±0.10

5.17±0.41

20˚C Ac 7.24±0.09

4.32±0.27

Le 6.75±0.10

4.46±0.26

Le 6.19±0.08

4.70±0.23

25˚C Ac 9.82±0.08

11.61±0.82

25˚C Ac 8.33±0.14

9.83±0.52

Le 7.97±0.11

7.94±0.52

Le 6.70±0.08

8.47±0.38

30˚C Ac 9.15±0.07

13.79±1.02

30˚C Ac 7.45±0.08

10.17±0.47

Le 7.06±0.12

11.03±0.69

Le 6.17±0.09

8.84±0.51

35˚C Ac 7.54±0.11

13.62±1.06

35˚C Ac 6.51±0.09

12.17±0.76

Le 6.15±0.08

11.52±0.57

Le 5.45±0.08

11.11±0.64

Temp. F-, P- value (df)

138.97, 0.0001 (4, 290)

118.14, 0.0001 (4, 90)

Temp. F-, P- value (df)

81.85, 0.0001 (4, 290)

181.15, 0.0001 (4, 90)

Aphid sp.

F-, P- value (df)

836.70, 0.0001 (1, 290)

23.86, 0.0001 (1, 90)

Aphid sp.

F-, P- value (df)

456.08, 0.0001 (1, 290)

5.53, 0.021 (1, 90)

Interaction

F-, P- value (df)

3.64, 0.006 (4, 290)

1.47, 0.217 (4, 90)

Interaction

F-, P- value (df)

4.11, 0.0003 (4, 290)

1.41, 0.236 (4, 90)