# Environmental Entomology

### Editor-in-Chief

E. Alan Cameron

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## Development and Survival of the Diamondback Moth (Lepidoptera: Plutellidae) at Constant and Alternating Temperatures

Shu-Sheng Liu, Fei-Zhou Chen, Myron P. Zalucki
221-231 First published online: 1 April 2002

## Abstract

Survival and development time from egg to adult emergence of the diamondback moth, Plutella xylostella (L.), were determined at 19 constant and 14 alternating temperature regimes from 4 to 40°C. Plutella xylostella developed successfully from egg to adult emergence at constant temperatures from 8 to 32°C. At temperatures from 4 to 6°C or from 34 to 40°C, partial or complete development of individual stages or instars was possible, with third and fourth instars having the widest temperature limits. The insect developed successfully from egg to adult emergence under alternating regimes including temperatures as low as 4°C or as high as 38°C. The degree-day model, the logistic equation, and the Wang model were used to describe the relationships between temperature and development rate at both constant and alternating temperatures. The degree-day model described the relationships well from 10 to 30°C. The logistic equation and the Wang model fit the data well at temperatures <32°C, but only the Wang model described the decline in development rate at temperatures >32°C. Under alternating regimes, all three models gave good simulations of development in the mid-temperature range, but only the logistic equation gave close simulations in the low temperature range, and none gave close or consistent simulations in the high temperature range. The distribution of development time was described satisfactorily by a Weibull function. These rate and time distribution functions provide tools for simulating population development of P. xylostella over a wide range of temperature conditions.

• Plutella xylostella
• development time
• survival
• temperature
• rate function

The diamondback moth, Plutella xylostella (L.), is a major pest of cruciferous crops worldwide (CAB International 2000). Its pest status has risen rapidly since the 1960s when large-scale application of chemical insecticides was started in vegetable crops (Talekar and Shelton 1993). With its ability to develop high levels of resistance to chemical and biological insecticides, P. xylostella has become very difficult to manage in many parts of the world (Talekar and Shelton 1993). To develop improved strategies for managing P. xylostella, numerous studies of its population dynamics have been conducted in various localities from cool temperate to tropical regions (Harcourt 1986, Talekar 1992).

The duration of development from egg to first reproduction is one of the most important life-history parameters influencing numerical changes in insect populations (Lewontin 1965), and the rates of development under natural conditions are largely determined by temperature. Thus, precise knowledge of the relationship between temperature and rate of development is essential to the formulation of phenological models or studies of population dynamics. In the past 60 yr, many studies have been conducted to provide valuable information on the temperature-dependant development of P. xylostella (Table 1). However, scrutiny of the relevant literature indicated that more detailed knowledge of development and survival of P. xylostella in relation to temperature seemed desirable, especially at low and high temperatures. Such detailed information will be useful particularly for monitoring and population studies of P. xylostella in temperate and cool temperate regions, where this insect has become a more important pest in recent years (Talekar and Shelton 1993), and where climates are characterized by extreme temperatures (Commonwealth Scientific and Industrial Research Organization and CRC for Tropical Pest Management 1997).

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The purpose of this study was to examine the development rate of P. xylostella at controlled temperatures over a wide temperature range, and to derive mathematic functions that can be tested for their ability to simulate the development of P. xylostella populations over a wide range of natural temperature conditions.

## Materials and Methods

### Insects and Plants.

Plutella xylostella was originally collected from a brassica vegetable crop field in an eastern suburb of Hangzhou, China, in 1996. The stock culture of P. xylostella was reared on potted common cabbage, Brassica oleracea variety capitata (cultivar ‘Jing-feng No. 1') and maintained at 25-30°C as described in Wang et al. (1999).

Rearing cages for the test insects consisted of a clear, cylindrical plastic container (14.5 cm high, with a 9-cm-diameter top and 13-cm-diameter base). The top was covered with a fine stainless steel mesh gauze for ventilation. A cabbage leaf was fixed in the cage by inserting its petiole through a hole in the center of the cage base. The cage was placed onto a 500-ml glass bottle containing water and the petiole of the cabbage leaf was inserted in the water to maintain freshness.

### Treatments at Constant Temperature.

Eighteen constant temperatures were set up and maintained in small environmental cabinets (internal volume = 150 or 250 liters) in which the temperature was controlled within ± 0.5°C of the set value. Lighting in each of the cabinets was provided by eight vertically installed 30-W fluorescent tubes on both sides. A photoperiod of 12 h per day was controlled by time clocks in all cabinets. Levels of relative humidity were maintained within the range of 60-90% by providing free water in trays in some of the cabinets when necessary. Temperature and relative humidity in each of the cabinets were recorded continuously with thermohygrographs or Tinytag electronic data loggers. To help control experimental errors from nontemperature factors, treatments of different temperatures were allocated randomly to different cabinets.

Experiments at each of the temperatures were initiated with newly deposited eggs (0-3 h old), produced at 20°C by mated moths reared at 25°C. The numbers of eggs used to start each of the temperature treatments varied from 98-182 at the low temperatures (4-16°C), and 37-75 at temperatures >16°C (Table 2). The test eggs and subsequent larvae were placed on cabbage leaves in the rearing cage. The leaves were replaced with fresh ones as necessary. Upon pupation of the insects, pupae were placed singly in 2 by 8-cm glass tubes. Test insects were observed twice daily, at 0800 and 2000 hours, respectively, to record hatching, deaths, larval exuviae, pupation, and adult emergence.

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### Treatments at Low and High Constant Temperatures.

Results obtained in the early part of this study showed that P. xylostella could not achieve complete development from egg to adult emergence at temperatures <8°C or >32°C (see Table 2). To quantify the partial development of eggs at 4 and 6°C, 15 cohorts of newly deposited eggs (0-3 h old), produced at 16°C and consisting of ≈50 eggs each, were placed at each temperature. After various days of incubation at the low temperatures, the eggs were transferred to 16°C to observe their survival and subsequent development time. To quantify the partial development of eggs at the high temperatures of 36, 38, and 40°C, 15 cohorts of newly deposited eggs (0-3 h old), produced at 28°C and consisting of ≈50 eggs each, were placed at each of these temperatures. After various hours of incubation at the high temperatures, the eggs were transferred to 28°C to observe their survival and subsequent development time.

To observe the development of individual instars and pupae at 4 and 6°C, cohorts were reared at 16°C until either at the start of the test instar or approaching the end of the previous instar. They were then transferred to 4 or 6°C to observe their survival and development at these low temperatures. For example, to observe the development of the first instar at 4°C, eggs were reared at 16°C to larval hatching and then transferred to 4°C. If a test cohort completed development of an instar at a low temperature, it was maintained at that temperature to observe development of the next instar. Similar procedures were used to observe the development of instars and pupae at 34, 36, 38, 40, and 42°C, except that the test cohorts were reared at 28°C to the desired phase of development before being transferred.

### Treatments at Alternating Temperature Regimes.

Experiments were conducted to provide data for testing whether mathematic functions derived from constant temperature data could adequately describe development rates under alternating conditions. An alternating temperature regime consisted of two constant temperatures per day. Photoperiod and relative humidity were the same as those at constant temperatures. After consulting the data obtained at constant temperatures, three types of regimes were designed in which a temperature from the middle of the developmental range was alternated with: (1) a low temperature where complete development from egg to adult emergence was not observed; (2) another temperature within the middle range where complete development was observed; and (3) a high temperature where complete development was not observed. For each regime, the higher temperature was synchronous with the photophase. Experiments for each of the 14 regimes tested were started with 45-85 newly deposited eggs (0-3 h old at 20°C). Procedures of rearing and observations were the same as at constant temperatures.

### Data Analysis.

Three models were chosen to describe the relationships between temperature and development rate, which is the reciprocal of development time.

#### Model 1: Degree-Day Model.

In this model, the development rate V (T) is a linear function of temperature, T (°C): $$mathtex$$V(T) = - \frac{t} {k} + \frac{1} {k}T\,\,\,[1]$$mathtex$$ where t and k are the low development threshold (°C) and the thermal constant (degree-days), respectively.

Recently, Ikemoto and Takai (2000) argued that there are serious statistical problems with the use of equation 1 to derive t and k. They proposed the following formula: $$mathtex$$(DT) = k + tD\,\,\,[2]$$mathtex$$ where D is the observed mean development time at temperature T (°C). They developed a procedure of plotting DT against D to exclude the data points at low and high temperatures from the linear regression. Their procedure was followed, and equation 2 was used to derive t and k in the analysis.

#### Model 2: Logistic Equation.

The logistic equation describes a sigmoid curve expressed as: $$mathtex$$V(T) = K/(1 + \exp (a - bT))\,\,\,[3]$$mathtex$$ where K, a and b are regression parameters fitted to the data of mean development rates V (T) at the various constant temperatures T (°C) (Andrewartha and Birch 1954).

#### Model 3. Wang Model.

The model is a nonlinear equation formulated by Wang et al. (1982). $$mathtex$$V(T) = \frac{H} {{1 + \exp (- r(T - T_0))}}\left({1 - \exp \left({ - \frac{{T - T_L }} {\delta }} \right)} \right)\left({1 - \exp \left({ - \frac{{T_H - T}} {\delta }} \right)} \right)\,\,\,[4]$$mathtex$$ where V (T) is the mean development rate at temperature T (°C), H is the value of an assumed upper asymptote of the curve, r is the exponential increase rate, TO is the optimum temperature for development, TL and TH are, respectively, the minimum and maximum temperature boundaries, and δ is the boundary width at the lower and upper temperatures.

Arguments for selecting these models can be found in Liu and Meng (1999). The nonlinear estimation module (Gause-Newton iterative method) of STATISTICA (StatSoft 1995) was used to derive the parameters of equations 2 and 3. A BASIC program, based on the Marquardt techniques (Marquardt 1963), was used to fit equation 4 to various data sets (see Liu et al. 1995).

#### Modeling Distribution of Development Times.

Equations 2-4 describe the relationship between temperature and mean development rate of a cohort or a population, but insects have inherent, individual variation in development rate (Sharpe et al. 1977, Curry et al. 1978). To use the above models to simulate development of a P. xylostella population in the field, the distribution of development times needs to be considered. We used the following Weibull function to describe the distribution of development times (Wagner et al. 1984): $$mathtex$$F(x) = 1 - \exp (- ((x - \gamma)/\eta)^\varphi)\,\,\,[5]$$mathtex$$ where F (x) is the probability of complete development in a cohort at normalized time x, and γ, η, and ϕ are regression parameters. Equation 5 is based on the ‘same-shape property' theory described by Sharpe et al. (1977) and Curry et al. (1978). The procedures for normalizing development time for insects, as reported by Wagner et al. (1984), were followed with one modification. Using the procedure of Wagner et al. (1984), the observed values of the cumulative frequency distribution at each temperature are used to obtain the points of time when 1, 5, 10, 15, … , 90, 95, and 100% of the insects complete development, by linear interpolation between the observed points. This procedure standardizes the number of observations in each distribution to be used for the final regression to obtain the combined curve of normalized development times. We felt that the process of linear interpolation introduces errors and thus does not necessarily help to obtain a more realistic distribution curve of normalized development times. We thus calculated the values of cumulative relative frequency of complete development against normalized development time at each temperature only where observed values were available. These observed values at a range of chosen temperatures were all used in a regression analysis with equation 5, by the nonlinear estimation module (Gause-Newton iterative method) of Statistica (StatSoft 1995), to obtain an empirical curve of normalized development times.

## Results

### Survival and Development at Constant Temperatures.

Plutella xylostella achieved complete development from egg to adult emergence between 8 and 32°C (Table 2). The survival rates of the entire immature stage were above 60% between 12 and 28°C, but decreased rapidly both above and below this temperature range, dropping to zero at 6 and 34°C (Table 3). At the low temperatures, no egg hatch was observed at 4 or 6°C. At the high temperatures, 58% of eggs hatched successfully at 34°C but all died in the first instar; at 36°C, no egg hatch was observed (Tables 2 and 3).

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When eggs were incubated at 6 or 4°C, they could survive to a maximum of about 55 d (Fig. 1). When they were transferred to 16°C after various periods of incubation at these low temperatures, their development time at 16°C was reduced linearly with the increase of incubation periods at the low temperatures, and the reduction was greater with incubation at 6°C than with incubation at 4°C (Fig. 2). The data and the linear regression in Fig. 2 show that the subsequent development time of an egg at 16°C was reduced from about 7 d to about 3 d after 50 d of incubation at 6°C, indicating that some eggs completed ≈60% of their development at this low temperature. Indeed, dissection of the eggs after 55-60 d of incubation at 6°C revealed that some of the embryos had developed to a larva-form with well-defined head, body segments and appendages.

Fig. 1.

Percent survival of Plutella xylostella eggs after various durations of incubation at 4 or 6°C.

Fig. 2.

Mean development time of Plutella xylostella eggs at 16°C after various numbers of days of incubation at 4 or 6°C. Bars show standard deviations.

Eggs incubated at 36, 38, and 40°C could survive for a maximum period of 72, 48, and 24 h respectively (Fig. 3). When the eggs were transferred to 28°C after various periods of incubation at 36 or 38°C, their development times at 28°C were reduced linearly with the increase of incubation period at the high temperatures (Fig. 4). However, compared with incubation at 36°C, that at 38°C resulted in less reduction of subsequent development time at 28°C. Moreover, increased incubation periods at 40°C resulted in linear increase of subsequent development time at 28°C (Fig. 4). These results suggest that the upper temperature threshold for egg development is between 38 and 40°C.

Fig. 3.

Percent mortality of Plutella xylostella eggs after being kept at 36, 38, or 40°C for various durations.

Fig. 4.

Mean development time of Plutella xylostella eggs at 28°C after being kept at 36, 38, or 40°C for various durations. Standard deviations are smaller than the data symbols.

When newly hatched larvae (0-3 h) from eggs reared at 16°C were reared at 6°C, the percentages of individuals that developed to second, third, fourth instar and prepupa reached 79, 66, 43, and 4%, but none of them pupated. When late second instars from 16°C were reared at 6°C, 89, 47, and 47% of them developed to fourth instar, prepupa, and pupa, respectively. However, fresh pupae from 16°C transferred to 6°C did not develop to adult emergence. The mean development times of the instars at 6°C are listed in Table 4.

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When newly hatched larvae (0-3 h) from eggs reared at 16°C were reared at 4°C, 43 and 24% of them developed to the second and third instar, but none reached the fourth instar. When late second instars from 16°C were reared at 4°C, 78% of them developed to fourth instar, but none reached the prepupal stage. When late third instars from 16°C were reared at 4°C, 37 and 6% of them reached prepupal and pupal stage. As at 6°C, none of the fresh pupae transferred from 16 to 4°C developed to adult emergence. The mean development times of the instars at 4°C are listed in Table 4. The success or failure of development at 6 and 4°C showed that the threshold temperature for complete development was lower for larvae than for either eggs or pupae.

At the high temperatures, when newly hatched larvae (0-3 h) from 28°C were reared at 34°C, 45 and 20% of them developed to pupa and adult emergence respectively. When newly hatched larvae (0-3 h) from 28°C were reared at 36°C, 15% of them developed to pupa but none reached adult emergence. However, when late second instars from 28°C were reared at 36°C, 41 and 18% of them developed to pupa and adult emergence respectively. At 38°C, none of the newly hatched first instars transferred from 28°C reached the second instar. However, when late first instars from 28°C were reared at 38°C, 11% of them reached the third instar but all died in this stadium. When late second instars from 28°C were reared at 38°C, 35% of them reached the prepual stage. At 40°C, none of the late first instars from 28°C could develop to the end of the second instar. However, 14% of the late second instars from 28°C developed to the fourth instar but all died in this stadium; 8% of late third instars from 28°C developed to prepupae but none successfully pupated. Table 4 presents the mean development times of the stages and instars at the high temperatures and the lethal temperatures for complete development. The upper temperature threshold for complete development was highest for third and fourth instars, followed by second instar and pupa, and then egg (Table 4).

By consulting the data at both low and high temperatures, it could be inferred that the temperature ranges allowing complete development for egg, first instar, second instar, third instar, fourth instar, prepupa, pupae and whole immature stage were 8-34, 4-36, 4-38, 4-40, 4-40, 4-36, 8-36, and 8-32°C respectively (Tables 2 and 4). The low temperature limits for larval development were <4°C but could not be defined with our data. Within the temperature ranges that allowed development, duration of development decreased as temperature increased from 4 and 30°C, and then increased as temperature further increased (Tables 2 and 4). The data for pupae indicate that the duration of development in males was 1.11 ± 0.003 times that in females (Table 2).

Plotting the product of duration×temperature against temperature for various stages and instars helped to define the linear portion of the temperature-development rate curves (Fig. 5, Ikemoto and Takai 2000). The linear portions for all stages and instars could be defined in the range of 10-30°C. Linear regression of the data between 10-30°C with equation 2 resulted in all values of t falling in the range of 7.0-7.9°C, remarkably close for all stages and instars (Table 5). The corresponding values of k are also shown in Table 5.

Fig. 5.

Scatter diagrams and linear regression lines of the relationships between duration of development and the product of duration multiplied by temperature. Unfilled circles were excluded from linear regression.

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In fitting the data to model 2, the logistic equation, the data >32°C were excluded because a decline in development rate >32°C was apparent in all stages and instars. The parameter values of both the logistic equation and the Wang model are presented in Table 5. Both models fit the data well <32°C and the Wang model also fits the decline of development >32°C well (Table 5). For example, the fourth instar, which had the widest temperature range, and the whole immature stage from egg to adult emergence, are presented graphically (Fig. 6).

Fig. 6.

The relationships between temperature and development rate of Plutella xylostella, as described by the degree-day, logistic, and Wang models.

### Distribution of Development Time.

In normalizing the distributions of development times of an insect, the greater the accuracy of the measured distributions, the more similar the normalized distributions will be and the more closely they will align (Wagner et al. 1984). For this reason, we used the measured distributions of 8-22°C to obtain a normalized distribution (Fig. 7). The data >22°C were omitted because of relatively long intervals of observations at these temperatures that resulted in too few data points of each distribution. In all, 104 data points from the temperature range of 8-22°C were fitted to equation 5: $$mathtex$$F(x) = 1 - \exp (- ((x - 0.78)/0.23)^{5.76})$$mathtex$$ with R2 = 0.9849. The seven distributions fell into a single, well-defined distribution of development time after normalization (Fig. 7).

Fig. 7.

Distribution of observed (upper graph) and normalized (lower graph) development times of Plutella xylostella at seven constant temperatures.

### Survival and Development at Alternating Temperature Regimes.

With reference to the three types of alternating temperature regimes described earlier, the survival rates were higher under type (1) regimes, similar under type (2) regimes and lower under type (3) regimes, compared with those observed at the corresponding constant temperatures (Fig. 8).

Fig. 8.

Differences in percent survival from egg to adult emergence between cohorts reared under alternating temperature regimes and those reared under constant temperatures equivalent to the daily means of the alternating regimes. Positive values indicate higher, while negative values indicate lower survival under alternating regimes. Numbers in the figure indicate the three types of alternating temper-ature regimes defined in the text.

The comparison of development rates between constant and alternating temperatures was carried out as follows. We used the models derived from constant temperature data to estimate the proportion of development that would accumulate under an alternating regime, taking into account the proportions of time the insect spent at each of the temperatures. The estimated proportion of development per day was then compared with that observed under the alternating regime. As an example, for the cohort under the regime of 4:12°C (12:12 [L:D] h), the degree-day (DD) model predicts that 12 h at 12°C accumulates ([12 - 7.4°C] × 0.5 d =) 2.3 DD, and 12 h at 4°C accumulates no heat units. Dividing the 2.3 DD by the thermal constant of 268.2 DD yields 0.8576%, the predicted proportion of development per day. The observed proportion of development at this regime was 0.9756% (the reciprocal of 102.5 d, see Table 6), which is 1.1376 times that predicted by the degree-day model. In other words, the observed development rate is 13.76% faster than that predicted by the degree-day model (Table 6). The comparison with the curvilinear models was done in a similar manner. Using again the cohort at the regime of 4:12°C (12:12 [L:D] h) and the logistic equation as an example, the logistic equation predicts that 12 h at 12°C completes 0.8001% development and 12 h at 4°C completes 0.2074% development, accumulating 1.0075% development per day. The observed proportion of 0.9756% is 96.84% of the estimated. In other words, the observed development rate is 3.16% slower than that predicted by the logistic curve (Table 6). In the calculations, negative rates predicted by models at high temperatures were taken as zero, i.e., no development.

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No standard procedure was available for testing the significance of deviations of the observed development rates from those estimated by the models. The observed development times at the 13 alternating temperature regimes (Table 6) resulted in coefficients of variance ranging from 3.78 to 7.00%, with a mean of 5.46%. This mean coefficient of variance was subjectively taken as a criterion for showing the significance of the deviation. Thus, a deviation greater than ± 5.46% was taken as a significant difference in comparing the observed with simulated rates.

Table 6 shows that among the three models the logistic curve best simulated the development rates at alternating temperatures except at the high temperature regime including 38°C. The degree-day model did well for type (2) regimes, but tended to give underestimates for type (1) regimes and overestimates for type (3) regimes. The Wang model gave good simulations for type (2) regimes, tended to give underestimates for type (1) regimes and variable results for type (3) regimes.

## Discussion

Many experimental studies have shown that at both unfavorably low and high temperatures, the effects of temperature on survival and development are confounded with time (Howe 1967, Bursell 1974). Our results show that P. xylostella reared at constant temperatures could not develop from egg to adult emergence outside the temperature range of 8-32°C. However, complete development was possible for some individual instars and stages at temperatures below or above this range. Moreover, different stages and instars varied in their temperature limits for complete development, with the later instars having the widest ranges (Table 4). The data on partial development of eggs at both low and high temperatures indicated that this stage of the insect could achieve a substantial amount of development at unfavorable temperatures where complete development of eggs to hatch was not possible. This phenomenon of partial development of egg is analogous to the development of individual instars or stages at low or high temperatures in relation to complete development of the insect from egg to adult emergence. These data indicate that P. xylostella can accumulate a significant amount of development at temperatures outside 8-32°C under fluctuating temperatures, especially at the lower temperature range. This inference was confirmed by the results of modeling the development of P. xylostella at low and high alternating temperatures (Table 6).

Development occurring at unfavorable temperatures has also been demonstrated in several insects including Aphidius sonchi Marshall, Campylomma verbasci (Meyer), Lipaphis erysimi (Kaltenbach) and Myzus persicae (Sulzer) (Liu and Hughes 1984; Judd and McBrien 1994; Liu and Meng 1999,2000). When an insect remains active for long periods at low or high temperatures outside the linear portion of the temperature-development rate curve, modeling development time at these low and high temperatures by nonlinear models, often involving extrapolation of functions derived from constant temperature, becomes essential for more accurate predictions of population events in the field (Butler et al. 1976; Lysyk 1989; Judd and McBrien 1994; Liu and Meng 1999,2000).

Because P. xylostella is widely distributed from the tropics to cool temperate regions of the world (CAB International 2000), field populations in many regions can experience a substantial amount of development at temperatures <8°C or >32°C. For example, in Hangzhou (30.18° N, 120.07° N), China, the long-term mean monthly minimum temperature in January is 0.1°C and mean monthly maximum temperature in July is 32.0°C. The daily minimum temperature in January frequently drops below -2°C and daily maximum temperature in July frequently rises above 35°C, yet P. xylostella remains active throughout the year (Ke and Fang 1979, Chen 2000, Liu et al. 2000). In many localities in central and southern Japan, such as Okayama (Wakisaka et al. 1992) and Miyazaki (Uematsu and Yamashita 1999), where the long-term mean monthly minimum temperatures in January are 0-2°C and mean monthly maximum temperatures in August are 31-32°C (Commonwealth Scientific and Industrial Research Organization and CRC for Tropical Pest management 1997), P. xylostella occurs all year round (Koshihara 1986). In some south-central states of the United States, such as West Virginia, where the monthly mean temperature in December-January may approach zero and in July-August may exceed 30°C (Commonwealth Scientific and Industrial Research Organization and CRC for Tropical Pest management 1997), P. xylostella has been found feeding on crucifer crops throughout the year (Reid and Bare 1952).

The data obtained in this study suggest that in many localities, such as Hangzhou, it may be necessary to consider development in the temperature range from 0 to 40°C in predicting the population events of P. xylostella in the field. Our study has provided the necessary information and mathematic functions. Liu et al. (1995) showed that the intrinsic, instantaneous rate of development in relation to temperature generally remains the same under constant and fluctuating temperatures, and suggested that rate functions derived from constant temperature can be used effectively to predict population development in the field. Such an approach has been used successfully in studies of many insects (Judd and McBrien 1994; Lysyk 1989; Liu and Meng 1999,2000). That many populations of P. xylostella from tropical and temperate regions exhibit similar development responses to temperature (Umeya and Yamada 1973, Sarnthoy et al. 1989, Shirai 2000) suggests the likely applications of the temperature-development rate functions derived here to populations in other localities. To simplify the calculations involved in the simulation or prediction of P. xylostella in the field, the three models presented here can be chosen according to specific conditions: the degree-day model can be used for periods or localities where temperatures do not go outside the range of 10-30°C for a substantial amount of time; the logistic equation can be used when accumulation of temperature <10°C become substantial; and the logistic equation or the Wang model can be used when accumulation of temperature >30°C becomes substantial. By integrating the model of distribution of development times with the rate functions, the variations of population development time can also be modeled or predicted (Wagner et al. 1984,1985; Liu and Meng 1999,2000). The studies we have carried out in Hangzhou demonstrated that the models presented here could effectively simulate the population development of P. xylostella at natural temperatures ranging from -2 to 42°C (Chen 2002). Undoubtedly, rate of development of P. xylostella may be influenced by factors other than temperature, such as nutrition, humidity and photoperiod, which should not be neglected in the application of the models presented here. Although the evidence accumulated thus far indicates similar temperature-dependent development between many geographic populations of P. xylostella (Umeya and Yamada 1973, Sarnthoy et al. 1989, Shirai 2000), possible variability between geographic regions should be carefully examined, and if it exists, incorporated into modeling of population development in the field.

## Acknowledgments

This study was supported in part by the Australian Center for International Agricultural Research (ACIAR Project CS2/1998/089), and in part by the China National Natural Science Foundation (Project No. 39930120).

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