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Fig. 1. An illustration of the effect of temperature (t) and
three different diets on rate of development (R) of larvae within
the linear range of the relationship between R and t. The larvae
are isomorphic, and at each temperature (t1, t2, t3), 1/6 of the
total time spent on the three diets is spent on diet 1, 1/2 on diet
2, and 1/3 on diet 3. Larvae on all three diets have a common
lower developmental threshold (LDT).
average body mass increment per day) was therefore calculated
as GR=PM×D-1. Standardized growth rate SGR (average body
mass increment per day degree) was calculated as
SGR=PM×SET-1. SGR compensated for differences in growth
rate caused by temperature and revealed the variation caused by
food. In food utilization experiments, dry mass of ingested food
(F), dry mass of excrement (E) and dry body mass increments
(I) were calculated. These values were used to calculate the
indices of food assimilation, efficiency of food conversion
ECI=I×F-1 and metabolic efficiency ECD=I×(F–E)-1. Relative
growth rate was calculated as RGR=exp((lnWf–lnWi)×d-1)×Wi-1
where Wi is initial mass and Wf final mass of an individual
larva in the feeding experiment, and d is duration of the experiment (days) (Barbehenn et al., 1999). Means are accompanied
by ± SE throughout the paper.
change in temperature (Fig. 1). Therefore, within the range of
the linear relationship between development rate R and temperature t, the consequence of rate isomorphy is common LDT for
larvae on all diets, in spite of different development rates on
each diet. The prediction of rate isomorphy, namely uniform
LDT accompanied by proportional variation of SET, was tested
by designating the arcsin proportion of the time spent on particular diet as the response variable, and temperature and diet as
factors. The data were analysed by two-way ANOVA with temperature and diet as fixed effects. The existence of rate isomorphy was inferred from a zero change in the development
time proportion at changing temperature, and the existence of
variation in SET from differences in the development time proportions on individual diets. A zero change in the development
time proportion at different temperature accompanied by differences in the proportions on individual diets indicated rate isomorphy. Different development time proportions on individual
diets accompanied by variation in the proportions at different
temperatures violated the assumptions of rate isomorphy.
RESULTS
Thermal constants of development. The duration of
larval development decreased and development rate
increased with increasing temperature (Tables 1 and 2).
Mortality was generally high, and was not correlated with
temperature or kind of food. This might be caused by diseases introduced to laboratory cultures by food contaminated in the open. Thermal constants were calculated for
development on 11 host plant species of which 9 permitted complete larval development at 3 temperatures
while with 2 host plant species development was completed at 2 temperatures. Experimental LDT for all species were similar (9.3–11.0°C, average 9.9 ± 0.2°C)
(Table 2). As development rate was largely affected by
food, larvae fed with leaves of some host plant species
extended their development time by up to 3 times compared that found with optimum food. Consequently, the
variation in SET was large and the slow growing larvae
Testing for “rate isomorphy”. Rate isomorphy implies no
change in the proportion of time spent on a particular diet with
TABLE 1. Number of pupated individuals (N), per cent mortality (M), larval development time (D) and fresh pupal mass (W) of
larvae kept at 3 constant temperatures and fed with leaves of 13 host plant species.
Temperature (°C)
Host plant
15.0
20.3
26.7
N
M
D
W
N
M
D
W
N
M
D
W
A. millefolium
6
67
36.3±1.2
336±33
6
67
18.3±0.2
307±6
13
28
11.8±0.2
254±6
A. retroflexus
4
78
56.9±0.5
86a
7
61
24.4±0.7
227±4
15
17
14.5±0.3
187±7
C. arvense
8
56
34.2±0.4
352±14
5
72
19.4±0.2
318±8
9
50
10.7±0.2
272±9
G. pratense
5
72
47.2±1.9
258±28
9
50
20.2±0.3
324±4
7
61
14.5±0.5
249±7
M. maritima
0
100
--
--
9
50
23.8±0.4
182±8
6
67
14.8±0.9
191±17
M. sativa
1
94
42.0
202
3
83
20.3±0.6
226±15
11
39
11.8±0.2
183±10
P. sativa
4
78
41.9±2.6
305±43
3
83
16.9±0.1
354±10
6
67
11.7±0.2
289±10
P. major
9
50
39.5±0.3
350±15
5
72
19.6±0.2
339±7
10
44
12.5±0.3
287±7
R. pseudoacacia
0
100
--
--
0
100
--
--
3
83
27.5±0.9
117±13
S. babylonica
1
94
64.9
--
0
100
--
--
11
39
20.6±0.6
195±11
S. nigra
0
100
--
--
0
100
--
--
10
44
14.1±0.3
227±9
T. officinale
11
39
36.4±1.0
375±9
24
4
17.4±0.1
335±4
8
56
10.3±0.2
284±8
U. dioica
13
28
35.6±0.4
362±6
20
20
18.7±0.2
329±4
15
17
11.2±0.1
265±5
a – other pupae malformed
243
Fig. 2. The influence of food quality, the water content (t(8) = –3.034, p = 0.016) and N content (t(8) = –1.957, p = 0.086) of host
plant leaves on SET of the larval development (R2 = 0.614, F(2,8) = 6.367, p = 0.022). Data for each host plant is represented by one
point.
fed with S. babylonica leaves had 2.3 times greater SET
(353 dd) than larvae fed with T. officinale (167 dd) (Table
2).
Rate isomorphy. Proportion of the total development
time spent on a particular diet significantly interacted
with temperature and type of diet (ANOVA: F = 9.236; df
= 16, 225; p < 0.001). At particular temperatures, the proportion significantly varied with diet (Table 3). This confirms that the SET is very plastic and changes with food
quality. The proportion did not significantly vary with
temperature for larvae reared on Medicago sativa,
Pastinaca sativa and Taraxacum officinale (Table 4). It
means that on these diets, the variation of SET is proportional with changing temperature. The larvae fed by these
diets have a common LDT and their development is thus
isomorphic. The development time proportion varied with
temperature on other diets. Larval development thus violated rate isomorphy. However, the variation in larval
development time on particular diets at different temperatures (Table 4) was much less than the variation on different diets at any given temperature (Table 3). The
violation of rate isomorphy thus appeared to be generally
negligible and the differences in LDT for larvae reared on
different diets were small compared to differences in SET
TABLE 2. Food quality as indicated by per cent water (WC) and total N content (NC) in leaves, regression constants a, b (development rate = a × temperature + b), thermal constants SET (dd) and LDT (°C) calculated from experimental data, and SET recalculated under assumption of “rate isomorphy” principle (SETrec).
Host plant
WC
NC
a (×103)
b (×102)
LDT
SET
SETrec
A. millefolium
A. retroflexus
C. arvense
G. pratense
M. maritima
M. sativa
P. sativa
P. major
R. pseudoacacia
S. babylonica
S. nigra
T. officinale
U. dioica
Average
81.4
79.2
84.9
78.8
85.9
77.3
80.5
82.5
68.8
71.9
82.1
84.5
80.0
2.50
3.75
2.77
3.75
3.54
4.64
2.86
2.14
3.17
2.16
3.57
3.12
4.02
4.886
4.397
5.509
4.060
4.000
5.216
5.201
4.688
–4.535
–4.833
–5.587
–3.729
–3.915
–5.516
–5.149
–4.471
9.3±0.2
11.0±0
10.1±0.8
9.2±1.2
9.8
10.6±0.3
9.9±0.9
9.5±0.1
205
227
182
246
250
192
192
213
188
257
182
227
2.833
–2.709
9.6
353
5.995
5.250
–6.308
–5.154
10.5±0.2
9.8±0.3
9.9±0.2
167
190
219.7±14.7
244
205
192
202
177
185
201.7±7.3
Fig. 3. Proportion of water content (W) in the food in relation
to efficiency of food conversion (ECI = 0.0068W – 0.4514, R2 =
0.645, p < 0.001) and metabolic efficiency (ECD = –0.0141W –
0.9047, R2 = 0.694, p < 0.001). Each point represents an experiment replicate, a group of 5 larvae.
(Table 2). The data for 9 diets where development rate
was established in 3 experimental temperatures were
recalculated assuming rate isomorphy. The recalculated
LDT was 10.0°C (identical with the average LDT calculated as the arithmetical mean of the experimental data for
these foods). The recalculated SETrec differed by up to 30
dd from SET calculated from experimental data (Table 2).
Effect of food quality. The SET increased with
decreasing water content and decreasing nitrogen content
of food (Fig. 2). Multiple regression analysis indicated a
significant contribution of variation in food dry matter
content (t(8) = 3.152, p = 0.014) while the effect of
nitrogen content was below the limit of statistical significance (t(8) = –2.011, p = 0.079). The increase of SET was
paralleled by decreasing efficiency of food assimilation
TABLE 3. ANOVA of the proportion (angular transformation)
of the total development time spent on different diets at 15,
20.3 and 26.7°C.
Temperature
(°C)
15
Source of
variation
Df
SS
MS
Among diets 8 0.0365 0.00456
Within diets 51 0.00629 0.000123
F
P
37.02 < 0.001
20.3 Among diets 8 0.0237 0.00296
63.49 < 0.001
Within diets 73 0.00341 0.0000467
26.7 Among diets 8 0.0382
Within diets 85 0.0105
0.00477 309.70 < 0.001
0.000123
Fig. 4. Sum of effective temperatures SET for development of
larvae on 4 host plants (from above: A. retroflexus, G. pratense,
C. arvense and T. officinale) in relation to the efficiency of food
conversion ECI (SET = –406.3ECI + 264.8, R2 = 0.515, p <
0.001) and metabolic efficiency ECD (SET = –210.4ECD +
261.4, R2 = 0.584, p < 0.001). Meaning of points as in Fig. 3.
which also was largely determined by food quality. ECD
and ECI (Fig. 3) decreased with decreasing water content
in food. SET established on 4 host plants were consequently significantly correlated with ECI and ECD (Fig.
4). Food ingestion and RGR were also negatively influenced by decreasing water content of the food and RGR
significantly increased with ECD and ECI (Fig. 5). By
contrast, the effect of temperature on larval metabolism
was not significant when data were pooled across foods.
Food consumption, growth rate, as well as metabolic efficiency ECD and efficiency of food conversion ECI (Fig.
6) did not significantly change with temperature.
Body growth. Pupal mass increased with temperature
and, within each temperature, decreased with the length
of development time (Fig. 7). Pupal mass was thus determined by growth rate GR which significantly increased
with temperature (Fig. 8). Recalculation of data to SGR
which removed the effect of temperature revealed that
pupal mass increased with SGR and the increase was
typical for particular food types (Fig. 8). The increasing
SET was inversely proportional to decreasing SGR (Fig.
9).
DISCUSSION
Constraints on LDT. The prediction of uniform LDT
derived from the assumption of rate isomorphy (RI) was
confirmed only on 3 from 9 diets where development was
completed in all temperatures. It is not surprising because
we had available only 3 experimental temperatures. Even
245
Fig. 5. Relative growth rate RGR (mg.mg-1.d-1) in relation to
efficiency of food conversion ECI (RGR = 0.169lnECI + 1.509,
R2 = 0.539, p < 0.001) and metabolic efficiency. The significance of the RGR vs. ECD relationship was not tested because
of autocorrelation. Meaning of points as in Fig. 3.
if LDTs are calculated from data collected over a range of
ecologically relevant temperatures, and the regression of
development rate on temperature is linear, the accuracy of
the estimates is affected by errors in the estimates of the
Fig. 6. Efficiency of food conversion ECI (R2 = 0.060, p >
0.05) and metabolic efficiency ECD (R2 = 0.034, p > 0.05) in
relation to temperature (°C). Meaning of points as in Fig. 3.
development rate (Campbell et al., 1974). The low precision of LDTs is obvious from their large standard errors
(Table 2).
The largest departure from expected proportions
assuming the existence of rate isomorphy is at the lowest
TABLE 4. ANOVA of the proportion (angular transformation) of the total development time spent at different temperatures on individual diets.
Diet
Source of variation
Df
SS
MS
F
P
Achillea millefolium
Among temperatures
Within temperatures
2
22
0.00119
0.00194
0.000596
0.0000883
6.746
0.005
Amaranthus retroflexus
Among temperatures
Within temperatures
2
23
0.00282
0.00396
0.00141
0.000172
8.189
0.002
Cirsium arvense
Among temperatures
Within temperatures
2
19
0.00290
0.00124
0.00145
0.0000654
Geranium pratense
Among temperatures
Within temperatures
2
18
0.00299
0.00325
0.00150
0.000181
8.279
0.003
Medicago sativa
Among temperatures
Within temperatures
2
12
0.000344
0.000782
0.000172
0.0000651
2.639
0.11
Plantago major
Among temperatures
Within temperatures
2
21
0.000714
0.00195
0.000357
0.0000929
3.841
0.04
Pastinaca sativa
Among temperatures
Within temperatures
2
10
0.00126
0.00171
0.00063
0.000171
3.68
0.06
Taraxacum officinale
Among temperatures
Within temperatures
2
39
0.000473
0.00300
0.000236
0.0000770
3.075
0.06
Urtica dioica
Among temperatures
Within temperatures
2
45
0.00249
0.00234
0.00124
0.0000520
246
22.15
23.95
< 0.001
< 0.001
Fig. 7. The relationship between pupal mass and development
duration at different temperatures. 15°C: pupal mass = 0.71 –
0.0098 development duration; 20.3°C: pupal mass = 0.63 –
0.017 development duration; 26.7°C: pupal mass = 0.34 –
0.0077 development duration. F = 100.4; df = 5, 262; p <<
0.001; R2 = 65.7%. Each point represents 1 individual.
or the highest temperatures (Jarošík et al., in prep.). There
are three reasons why these temperatures may violate rate
isomorphy. At low temperature there may be differential
mortality. The individuals with the fastest development
complete their development early while the rest succumb
to adverse conditions, the more so if their development is
prolonged. The second reason is an imprecise measuring
of developmental time at high temperatures. As developmental time decreases with temperature, the number of
observations per stage also decreases if monitoring is
made at constant intervals at low and high temperatures.
The third reason is crucial from a statistical point of view.
An important determinant of the slopes of the linear
regressions, from which the LDTs are inferred, are the
highest and the lowest values (see Crawley 1993, p.
78–82). Therefore, a relatively small bias in the developmental rates measured at the highest or the lowest temperatures will cause a large shift in the LDT.
The common LDT for A. gamma larvae calculated
using data for 11 host plant species was 9.9 ± 0.2°C, by
2.3°C higher than the LDT calculated for a UK popula-
Fig. 9. Standardized growth rate (mg/dd) in relation to SET
for different host plants (data pooled over temperatures).
Regression for average value for each host plant: growth rate =
2.9 – 0.0073 SET. F = 16.80; df = 1, 9; p < 0.003; R2 = 65.1%.
Acronyms as in Fig. 8, meaning of points as in Fig. 7.
Fig. 8. Above: The relationship between pupal mass and
growth rate (GR) at different temperatures. 15°C: pupal mass =
99.2 + 25.9 GR; 20.3°C: pupal mass = 99.2 + 12.8 GR; 26.7°C:
pupal mass = 99.2 + 7.3 GR. F = 889.3; df = 3, 264; p << 0.001;
R2 = 91.0%. Below: The relationship between pupal mass and
standardized growth rate SGR (pooled over temperatures) at different host plants. F = 22.1; df = 21, 234; p << 0.001; R2 =
66.5%. Increase in pupal mass is host-plant specific (F = 2.982;
df = 11, 245; p < 0.001). TOFI – T. officinale, MSAT – M.
sativa, PMAJ – P. major, MMAR – M. maritima, CARV – C.
arvense, PSAT – P. sativa, ARET – A. retroflexus, SBAB – S.
babylonica, UDIO – U. dioica, AMIL – A. millefolium, GPRA –
G. pratense. Meaning of points as in Fig. 7.
tion of this species (Hill & Gatehouse, 1992) which was
7.7°C (male) and 7.6°C (female) (Table 5). The difference, tested using SD calculated for the UK data (Janáþek
et al., in litt.), was not significant (t2,4 = 1.434, p > 0.05).
In fact it is smaller than variation observed between populations of other species studied by more than one author,
e.g. Heliothis armigera (Hübner) (LDT between 8.6–
12.9°C), Heliothis virescens (F.) (7.6–11.8°C), or Trichoplusia ni (Hübner) (9.0–14.7°C) (Table 5). The difference was apparently caused by variation of methods used
in the two studies. Data on variation of LDT between
populations were available for 12 noctuid species (Table
5). If we exclude the outlier data for populations of A.
ipsilon (Hufnagel), Pseudaletia unipuncta (Haworth) and
Spodoptera frugiperda (Smith) because of the large
extent of variation in the differences between local populations, which were in the order of 1.7–5.7°C (mean = 3.9
± 0.4°C). In general differences between the studies of
different authors were greater than the differences
“within” the studies.
Dixon et al. (1997) extended the idea of rate isomorphy
(existence of a LDT constraint) to higher taxonomic
247
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