Ecological Research

, Volume 21, Issue 1, pp 107–116

Modeling population dynamics of a tea pest with temperature-dependent development: predicting emergence timing and potential damage

Authors

    • Center for Ecological ResearchKyoto University
    • Department of Ecology and Evolutionary BiologyPrinceton University
  • Takayuki Ohgushi
    • Center for Ecological ResearchKyoto University
  • Satoru Urano
    • Laboratory of Pest Management SystemsNational Agricultural Research Center for Kyushu Okinawa Region
  • Koichiro Uchimura
    • Kagoshima Tea Experiment Station
Original Article

DOI: 10.1007/s11284-005-0099-9

Cite this article as:
Satake, A., Ohgushi, T., Urano, S. et al. Ecol Res (2006) 21: 107. doi:10.1007/s11284-005-0099-9

Abstract

The tea leaf roller, Caloptilia theivora Walsingham (Lepidoptera: Gracillariinae), is one of the serious pests of tea plants in Japan. To understand the mechanism of seasonal occurrence of this insect pest, we developed a population dynamics model that explicitly incorporates the temperature-dependent development of the pest. The model predictions were compared with observed captures in pheromone traps at the experimental site of the Kagoshima Tea Experiment Research Station in Japan. The results showed that the emergence timing of the insect pest observed in the field was determined primarily by temperature. The relationship between the timing of adult emergence and the leaf damage level was also studied using a logistic regression model. The infestation level decreased as the interval between the adult peak emergence date and the date of tea plucking increased, implying that asynchrony between plant phenology and emergence of the insect pest is a critical factor reducing damage level. We examined how the damage level changes according to global warming. Increased temperature made the timing of insect appearance forward and enhance asynchrony of plant–pest phenology. Therefore, reduction of damage level by the insect pest is expected under global warming.

Keywords

Tea pestTemperature-dependent developmentPopulation dynamicsSynchrony of plant–pest phenologyGlobal warming

Introduction

The tea leaf roller, Caloptilia theivora Walsingham (Lepidoptera: Gracillariinae), is a serious pest of tea plants in Japan (Minamikawa and Ueda 1996). This insect pest largely deteriorates the quality of manufactured tea. Leaf damage is caused by the fourth and fifth instars, which make triangular-shaped leaf shelters, contaminating young leaves (Kodomari 1975). There is significant deterioration of both the flavor and taste of tea made with infested leaves, which causes a serious economic problem for the tea industry in Japan.

From the mid-20th century, in order to understand the population dynamics of this insect pest, an annual emergence pattern of adult insects has been monitored by light and/or pheromone traps at several experimental sites widely distributed in Japan (Kagoshima Plant Protection Association 1994). These monitoring programs have provided details of the phenology of C. theivora, but underlying mechanisms that regulate the seasonal occurrence of this species and the relationship between the leaf damage level and adult trap catch remain largely unknown.

Knowledge of the phenology of C. theivora is likely to allow the prediction of the timing of appearance of each developmental stage, which can provide a well-timed control method. A key factor regulating the life history pattern of insect pests is temperature. Because insects are cold blooded, the developmental rates of their life stages are strongly dependent on temperature. In general, the cooler the temperatures, the slower the developmental rate of insects, and as the temperature increases so does the developmental rate until the temperature increases sufficiently to inhibit developmental processes (Gilbert and Raworth 1996). Based on these observations, day-degree (or heat unit) models that assume a linear relationship between temperature and development have been widely used to estimate insect development (Taylor 1981; Pruess 1983; Higley et al. 1986). The nonlinear relationships have also been applied to represent convex features of temperature-dependent development of insects (Stinner et al. 1975; Logan et al. 1976; Sharpe and DeMichele 1977).

Timing of appearance of the insect pest varies, depending on differences in temperature throughout the years, which makes the pest’s forecasting and management difficult. One way to promote our understanding of the phenology of C. theivora is to develop a population dynamics model that explicitly incorporates temperature-dependent development. Indeed models for temperature-dependent development of insect pests have been widely used as decision-support tools to improve the efficiency of pest management, such as accurate forecasting (Graf et al. 1999; Milonas et al. 2001; Yonow et al. 2004) and effective applications of pesticides and viral pathogen (Inoue and Ohgushi 1976; Martin 2001). In addition, there is increased awareness of computerized decision-making tools that incorporate models of insect phenology [DESSAC (Brooks 1998) and MORPH (Walton 1998)].

This study represents a comprehensive attempt to model C. theivora population dynamics using field temperature data. We built a mathematical model in which individuals are categorized according to their life-cycle stages, and the developmental transition is simply described in relation to temperature. The model predicts the seasonal occurrences of all life stages of the insect. We compared the prediction with the observation at the study site of the Kagoshima Tea Experiment Research Station in Chiran, Kagoshima, Japan. Based on the results of the model and data analysis, we predict a possible alteration of damage by the insect pest under global warming.

Materials and methods

Biological background

The tea leaf roller overwinters as pupa and emerges in spring. Adults emerging from overwintering pupae constitute an overwintering flight to oviposit on the underside of young leaves of a tea plant (Minamikawa and Ueda 1996). Caterpillars hatch, bore into the young leaves, and start feeding. Fourth and fifth instar larvae make triangular shaped leaf shelters by rolling young leaves. The larvae further grow to pupate, and adults emerging from these pupae constitute the next generations. The number of generations per year ranges from four to seven, depending on site-specific climatic conditions, especially temperature (Kodomari 1976).

This insect pest seriously reduces the quality of manufactured tea due to a frass contamination of larvae in leaf nests. If harvest of tea leaves shows a 3% mix rate of contaminated leaves, significant damage is recognized. The leaf damage by first, second, and third instars, which are in the leaf mining stage, rarely influence a growth and yield of tea plant. Significant decrease in tea quality is caused by the fourth and fifth instars in the leaf rolling stage (Kodomari 1975).

Data description and analysis

Daily samples of the insect pest populations were collected from the tea garden owned by the Kagoshima Tea Experiment Station in Chiran, Kagoshima, Japan, using pheromone traps during the period March 1996 to November 2003. Monitoring is still ongoing but we used the data from these 8 years for analysis. At the study site, one pheromone trap was settled, covering a plot of 27 acres in a plantation field of a tea plant race “Yabukita.” Yabukita is the most popular cultivar used in the tea production in Japan because of its high yielding and cold resistance (Hakamada 2003). There were 28 missing values from daily data over the 8 years. These missing spaces were linearly interpolated.

In addition to the pheromone trap catch data, the daily maximum and minimum temperatures were automatically monitored at the study plot using agricultural meteorological equipment (NASCON-2000). These temperature data are used to estimate the developmental rate of each life-cycle stage of the insect pest, as explained later.

Infestation level by larvae was monitored three times per year. The survey was conducted closely according to the tea plucking season. Infestation level was checked by counting the number of infested buds among all buds produced by tea plants at eight plots of size of 50×25 cm during the period of 1996–2003. The Ministry of Agriculture, Forestry and Fisheries of Japan designed the census procedure. These plots were located within the study site where the pheromone trap catch census was took place. To investigate the relationship between the timing of adult emergence and the infestation level, we used a logistic regression model and examined how the infestation level is a function of the interval between the peak date of adult emergence and the date of tea plucking. The peak date of adult emergence was estimated from the pheromone trap data. We considered that the tea plucking dates are consistent with the dates when infestation level was monitored. We used the number of days between the two occasions as an independent variable for the logistic regression. This analysis was applied only to the data from the second tea plucking season that indicate a sufficiently high level of infestation, as described later.

Model

The model describes the dynamics of the life cycle of the insect pest based on daily temperature. We represent the pest abundance by the number of females. We assume that there is neither emigration nor immigration. The life cycle of the insect pest can be divided into four developmental stages: egg, larva, pupa, and adult. Individuals at each stage are grouped into cohorts, and age of each cohort is given by tracing the number of days since the transitions to the current developmental stage (Fig. 1). Let E(t, i) be the number of eggs of age i at time t, L(t, i), P(t, i), and A(t, i) be that for larvae, pupae, and adults, respectively. The population dynamics is described by stage-specific survivorship and fecundity. The stage-specific survivorship values, given by se, sl, sp, and sa, are the probabilities of individual survival from age i to i+1 at each developmental stage of egg, larva, pupa, and adult, respectively. The fecundity, f, is assumed to be constant with age and is multiplied by the probability of offspring survival during their first day of life. Note that we count only newborn female offspring per adult female per year. We assume that the survival rate is constant with time and that population size is large enough to neglect demographic stochasticity. The population dynamics are formulated as
$$ \begin{array}{*{20}l} {{E(t + 1,1) = f{\sum\limits_{i = 1}^{\omega _{{\text{a}}} } {A(t,i)} }} \hfill} & {{} \hfill} \\ {{E(t + 1,i + 1) = s_{{\text{e}}} [1 - q_{{\text{e}}} (t,i)]E(t,i)} \hfill} & {{{\text{for}}\;i = 1,2, \ldots ,\omega _{{\text{e}}} - 1} \hfill} \\ {{L(t + 1,1) = {\sum\limits_{i = 1}^{\omega _{{\text{e}}} } {q_{{\text{e}}} (t,i)E(t,i)} }} \hfill} & {{} \hfill} \\ {{L(t + 1,i + 1) = s_{{\text{l}}} [1 - q_{{\text{l}}} (t,i)]L(t,i)} \hfill} & {{{\text{for}}\;i = 1,2, \ldots ,\omega _{{\text{l}}} - 1} \hfill} \\ {{P(t + 1,1) = {\sum\limits_{i = 1}^{\omega _{{\text{l}}} } {q_{{\text{l}}} (t,i)L(t,i)} }} \hfill} & {{} \hfill} \\ {{P(t + 1,i + 1) = s_{{\text{p}}} [1 - q_{{\text{p}}} (t,i)]P(t,i)} \hfill} & {{{\text{for}}\;i = 1,2, \ldots ,\omega _{{\text{p}}} - 1} \hfill} \\ {{A(t + 1,1) = {\sum\limits_{i = 1}^{\omega _{{\text{p}}} } {q_{{\text{p}}} (t,i)P(t,i)} }} \hfill} & {{} \hfill} \\ {{A(t + 1,i + 1) = s_{{\text{a}}} A(t,i)} \hfill} & {{{\text{for}}\;i = 1,2, \ldots ,\omega _{{\text{a}}} - 1.} \hfill} \\ \end{array} $$
(1)
where ωa, ωe, ωl, and ωp are the maximum lengths of life span of adults, eggs, larvae, and pupae, respectively. qe(t, i) is the probability that eggs of age i transfer into the larval stage at time t. Similarly, ql(t, i) and qp(t, i) are the probabilities of larva to pupa and pupa to adult transfer. The law of effective cumulative temperature determines these transition probabilities.
Fig. 1

Schematic diagram of demographic components of the tea leaf roller. Numbers represent the age of each cohort. ωe, ωl, ωp, and ωa are the maximum life spans of eggs, larvae, pupae, and adults, respectively. se, sl, sp, and sa are the probabilities of individual survival from age i to i+1 at a developmental stage of egg, larva, pupa, and adult. f is fecundity (see text for details)

Developmental transition from the current to the next stage is assumed to occur when the day-degrees accumulated above the lower threshold temperature for development (i.e., developmental zero) exceeds the effective cumulative temperature, which is called “the law of effective cumulative temperature” (Inoue and Ohgushi 1976; Ikemoto and Takai 2000). Therefore, the temperature exposed to the pest population critically influences the duration time of each developmental stage. The probability of the developmental transition of individuals at stage x (x represents either eggs, larvae, or pupae) of age i to the next stage is formalized by
$$ q_{x} (t,i) = \left\{ {\begin{array}{*{20}c} {1} & {{{\text{if }}{\sum\limits_{k = 0}^i {D_{x} (t - k)} } \ge Q_{x} }} \\ {0} & {{{\text{if}}{\sum\limits_{k = 0}^i {D_{x} (t - k)} } < Q_{x} }} \\ \end{array} } \right., $$
(2)
where t is the calendar date. Dx (t) is the day-degrees on date t and Qx is the effective cumulative temperature needed for transition of individuals from stage x to the next. Day-degrees, Dx (t), accumulated above the developmental zero are estimated by means of the daily maximum and minimum temperatures using a “sine-wave” method (Baskerville and Emin 1969; Allen 1976). This method is based on the fact that daily temperature patterns closely resemble a sine-wave function and determine the amount of day-degrees by calculating the amount of area under the temperature curve and above the developmental zero. Since developmental rate may be low when temperature is very high, the upper temperature limit for development may exist. However, no reports have provided quantitative information of such an upper temperature limit on C. theivora. In the following calculation, we have used the developmental zero and the effective cumulative temperature used in previous studies (Table 1).
Table 1

Parameter values given in Eqs. 1 and 2

Parameters

Parameter values

References

Developmental zeros (°C)

 From egg to larva

12.3

Furuno (1982)

 From larva to pupa

4.2

Furuno (1982)

 From pupa to adult

9.4

Furuno (1982)

Cumulative temperatures (°C)

 From egg to larva

29

Furuno (1982)

 From larva to pupa

292

Furuno (1982)

 From pupa to adult

203

Furuno (1982)

Daily survival rates

 Adult sa

0.78

Estimated from Matsuhira (2001)

 Egg se

0.8–0.98

N/A

 Larva sl

0.8–0.98

N/A

 Pupa sp

0.8–0.98

N/A

Daily fecundity of female adults

 f

15

Estimated from Matsuhira (2001)

Simulation procedure

The parameter values used for simulation runs are shown in Table 1. There are no data available for daily survival rates of eggs, larvae, and pupae. Therefore, we prepared a set of parameters with which we examined how sensitively our conclusions depend on our choice of the parameter values (Table 1).

The major target of our simulation study was to generate within-year dynamics of the pest insect with a given pattern of initial emergence, rather than to predict the among-years dynamics. We adopted such a simulation strategy because (1) no accurate information is available on the mechanism constituting overwintering generations and (2) practically the most important point is to predict the peak occurrence of first and second generations that have the potential to cause economical damage on tea production (Kodomari 1976). Toward that end, we gave independent initial condition for each simulation—the daily number of trapped individuals from March to April in each observed year was used as an overwintering generation that initiates each simulation run. Then simulations were implemented until the flight of the second generation was over, i.e., in mid July.

Results

Observed pest population dynamics

Seasonal occurrence of adult populations during the period 1996 to 2003 is illustrated in Fig. 2. The original data were smoothed by a simple moving average of order two to clearly show the trend and smooth out the “noisy” fluctuations (Bloomfield 1976). In most years at least six generations occur within 1 year. The peak emergence date of adult insects (arrows in Fig. 2) and population size varied considerably among years. Peak emergence dates were visually determined. When multiple peaks with similar population sizes were included within a same generation, the first peak was chosen. The observed peak dates of the first and second generations varied from 10 May to 3 June for the first and from 13 June to 3 July for the second (Fig. 2), showing that the maximum time interval between peaks of emergence in different years was almost 3 weeks (arrows in Fig. 3).
Fig. 2

Observed numbers of trapped adult individuals. Arrows the peak emergence dates of the first and the second generations. Dotted lines dates of the second tea plucking (we have no data from 1999)

Fig. 3

Predicted peak emergence dates plotted against those observed. a First generation; b second generation. Arrows the maximum time differences between observed peak emergence dates

The annual variability in peak emergence dates is likely to be a reflection of annual variation of temperature. Monthly average of temperature varies across years (Fig. 4a). If developmental rate is an increasing function of temperature, the time to peak emergence date will become shorter as temperature during the developing season increases, resulting in a negative relationship between the time to peak emergence date and the temperature. To test the prediction, we plot the intervals between the peak dates of the overwintering and the first generations against the temperature averaged over those intervals. The interval between the peaks of the overwintering and the first generations approximates the time to peak emergence of the first generation. The result showed that the time to peak emergence date of the first generation is negatively correlated with the averaged temperature during the developing season when the 1999 data were excluded (Fig. 4b). We also plot the time to peak emergence date of the second generation along the temperature averaged over the interval between the peak dates of the first and the second generations, and found a significantly negative relationship between the two variables (Fig. 4c). The results imply that emergence of the insect pest is mainly temperature driven, although the potential impacts of other factors still remain to explain the deviation observed in the first generation in 1999.
Fig. 4

a The profile of temperature transition across years. The monthly averages of March (open circles), April (solid circles), May (triangles), and June (squares) temperatures in 1996–2003. b The plot of the time to peak emergence date of the first generation along the averaged temperature. Solid line the linear regression model that excludes the data in 1999, which has intercept and slope of 124.1 (SE=36.0, P<0.01) and −4.2 (SE=2.0, P<0.05). c The plot of the time to peak emergence date of the second generation along the averaged temperature. Solid line the linear regression model that has intercept and slope of 167.0 (SE=25.8, P<0.001) and −5.6 (SE=1.1, P<0.001)

The averaged infestation level was highest at the second tea plucking season (first tea plucking: 0.003%, SD=0.002; second: 6.4%, SD=0.05; third: 0.003%, SD=0.003). Low infestation level at the first tea plucking is likely to be attributed to the small population size (Fig. 2). On the contrary, the pesticide application prior to tea plucking might explain low infestation level at the third tea plucking. The infestation level at the second tea plucking was high and was negatively correlated with the interval between the date of peak emergence of the first generation and that of second tea plucking (Fig. 5), which means that the infestation level decreases as the adult peak emergence date occurs much earlier than the tea plucking season. Deterioration of tea quality is recognized when the proportion of infested leaves is larger than 3% (Kodomari 1975). Thus, the results suggest that to keep the infestation level below 3%, the peak date of adult emergence should be at least 28 days earlier than the tea plucking (safety zone is shown in Fig. 5).
Fig. 5

The proportion of buds infested as a function of the interval between the peak date of adult emergence and the date of tea plucking. Solid line the logistic regression model that has intercept and slope of 0.92 (SE=0.98, N/A) and −0.16 (SE=0.04, P<0.05). Dotted line the 3% infestation criterion above which significant decrease of tea quality is recognized. Gray region the safety zone in which the infestation level is less than 3%

Prediction model

The predicted seasonal occurrence of the pest insect and observed temperature curve in 1996 are shown in Fig. 6. Overlapping was observed between appearance periods of several developmental stages within and between generations (Fig. 6a). Developmental period of each stage shortened as maximum and minimum temperature increased throughout the season (Fig. 6a, b).
Fig. 6

a Predicted seasonal occurrence of the tea leaf roller population in 1996. Lines predicted stage durations, solid circles the predicted peak emergence date of each stage. Parameter values: se=0.92, sl=0.92, and sp=0.90. b Daily maximum (open circles) and minimum (solid circles) temperatures

Peak emergence date is a good measure to compare the predicted and observed dynamics of the pest population, because it is very robust to a change of unknown demographic parameters (survival rate of egg, larva, and pupa) while population size is considerably influenced by slight changes in these parameter values (data are not shown). Thus, we verified the model prediction by comparing the predicted and observed peak emergence dates of the first and the second generations.

The observed and predicted population dynamics of the pest are shown in Fig. 7. As shown in Figs. 3 and 7, the predicted peak emergence dates are mostly in agreement with those observed, although there were large deviations in 1999 (−15 days for the first generation and −7 days for the second generation) and in the first generation in 2003 (7 days) as shown in Fig. 3. Except for years of 1999 and 2003, the difference fell within the period of 4 days. This predicting ability of the simple mechanistic model with the temperature-dependent development suggests that temperature can be a main factor in controlling the emerging timing of the tea pest in the field.
Fig. 7

Predicted and observed population dynamics of the tea leaf roller over 8 years from 1996 to 2003. Solid lines the predicted moth numbers, dotted lines the trapped moth numbers. Solid and dotted arrows the predicted and observed peak emergence dates for the first and the second generations, respectively. Parameter values: se=0.90, sl=0.92, and sp=0.90

To investigate the impact of global warming on the emergence timing of the tea pest, we simulated the model under the situation in which a certain amount of increment is incorporated in the data of daily maximum and minimum temperatures. Temperature data over 8 years (1996–2003) were used for this simulation. Using each of the simulated population dynamics of the pest, we estimated the peak emergence date of adults of the first and the second generations and then took the average over the 8 years. As temperature increased, the averaged peak emergence date of adult insects occurred earlier (Fig. 8a). The shift was more enhanced in the second generation than in the first, which is because the shift in emergence timing of the first generation further put forward the emergence timing of the second.
Fig. 8

a The forwarded shift of the peak emergence date of adult insects under global warming. Solid and open circles the averaged shift predicted in the first and second generations, respectively. Parameter values: se=0.90, sl=0.92, and sp=0.90. b Averaged infestation level predicted by the model under global warming. Dotted line the observed infestation level without any temperature increment

Using the expected shift on emergence timing (Fig. 8a) and the logistic regression model that estimates infestation level (Fig. 5), we predicted the possible change of damage level by the insect pest under global warming. We assume that plant phenology is independent of temperature. Plant phenology may vary depending on temperature, but the temperature-dependent change of the phenology of Yabukita remains largely unknown. Therefore, we fixed the tea plucking date even under global warming and then calculated the intervals between the estimated peak dates of adult emergence and the dates of tea plucking. The infestation level decreased gradually as temperature increased (Fig. 8b). A 3°C rise of temperature resulted in an almost 3% decline in damage, which was nearly close to the damage-free criterion (i.e., 3% infestation criterion). This decline of infestation level would be explained by asynchrony between the timing of larval hatch and that of leaf flush as explained later.

Discussion

The long-term pheromone trap data of the tea pest (C. theivora) monitored in Chiran, Kagoshima, Japan, demonstrated that the timing of peak appearance of adult populations varied considerably among years—the maximum time differences of peak emergence dates were as large as 3 weeks. The population dynamics model of C. theivora that explicitly describes a temperature-dependent development clearly showed that the emergence timing of the insect pest observed in the field is determined primarily by temperature, although the potential impacts of other factors, e.g., sensitivity to photoperiod and precipitation, still remain.

Thus, we concluded that by measuring temperature, managers of tea gardens could roughly predict the emergence timing of each of the developmental stages of C. theivora. Knowledge of when each of the developmental stages is present in the field should allow the prediction of when the infestation level will be highest. The logistic regression model for infestation level demonstrated that the infestation level was high (almost two times as large as the damage-free criterion) when the adult population had a peak about 18 days earlier than the date of tea plucking (Fig. 5). The infestation level decreased as the interval between the peak date of adult emergence and date of tea plucking increased, and finally it became sufficiently small as to meet the damage-free criterion (Fig. 5). This can be interpreted by considering the extent to which plant–pest phenology synchronizes. In general, it is pointed out that synchrony of larval hatching and bud burst of host plants strongly affects larval survival (Komatsu and Akimoto 1995; Buse and Good 1996; Dougen et al. 1997). For example, leaf toughness that rapidly changes after bud burst significantly affects the establishment of young C. theivora larvae, hence the timing of oviposition has important fitness implications for this species. Oviposition of the first generation generally coincides with the production of new leaves of host plants. However, when adult moths emerge earlier than foliage flush season, offspring survival must be reduced, which results in low infestation levels. New leaf production of the tea plant normally occurs about 20 days earlier than the tea plucking season on average (K. Uchimura, personal communication). Therefore, the setting of safety criteria—the appearance of adult moths at least 28 days earlier than the tea plucking date (Fig. 5)—has a biologically realistic implication.

Global warming may change the population dynamics of pest species in various ways (Cammell and Knight 1992; Kareiva et al. 1993). For example, an increase in temperature may enhance the overwintering survival and thus increase the number of generations per year (Yamamura and Kiritani 1998), and shift the timing of insect appearance. Logan and Powell (2001) and Powell and Logan (2005) developed temperature-dependent models for insect phenology and demonstrated that global warming may alter adaptive seasonality of many cold-blooded organisms, as exemplified in the mountain pine beetle. In this study, we examined how the damage levels were altered by global warming. Temperature increases up to 3°C made the timing of insect appearance forward and enhance asynchrony between plant and pest phenology, which consequently led to the reduction of leaf damage (Fig. 8). This scenario can be applicable only to the situation in which host plant phenology is mostly independent of temperature. If the relationship between the plant phenology and temperature is investigated in detail, the assumption of the fixed phenology would be relaxed, and then more practical predictions for the damage level would be possible under global warming.

We conjecture that the large differences between the predicted and observed peak emergence dates in 1999 and 2003 (Fig. 3) were caused not only by additional environmental factors such as precipitation and photoperiod but also by man-made events such as pesticide spraying, which greatly alters the population size and potentially changes the emergence timing of the pest. Thus, an analysis incorporating the timing and the impact of pesticide spraying is needed to evaluate the model more accurately.

Several questions remain to be answered in this study. Although our study mainly focused on the emergence timing of the insect pest, population size at the time is of course an equally important measure to determine the infestation level. However, because of little information on demographic parameters, e.g., survival rate of egg, larva, and pupa, we could not analyze the relationship between infestation level and population size. Tea plucking and pesticide spraying that are carried out several times per year may influence the population dynamics of the pest insect, but there are no quantitative assessments of the impact of such man-made operations on the pest’s population dynamics. Therefore, an accurate estimation of unknown demographic parameters and the analysis incorporating the impact of man-made events will be important for the continued development of useful models.

Acknowledgments

This work was supported in part by a fellowship and a grant-in-aid from the Japan Society for the Promotion of Science (AS), the Ministry of Education, Culture, Sports, Science, Technology grant-in-aid for Scientific Research (A-15207003) (TO), and the 21st Century COE Program (A14) (TO). The authors thank Higuchi S, Iwasa Y, Matsumura M, Nakashizuka T, Shigesada N, Takasu F, and two anonymous reviewers for their helpful comments.

Copyright information

© The Ecological Society of Japan 2005