In this paper, we introduce a revised model to estimate the corrected initial number of each life stage in field life tables of insect pest populations, with a case example of the diamondback moth, Plutella xylostella L. (Lepidoptera: Plutellidae). To validate our revised model, we used life table data of P. xylostella from 9 field surveys conducted by the corresponding author in 1996. In these surveys, P. xylostella infestations had been monitored in fields of flowering Chinese cabbage, long white radish, butter cabbage, Shanghai pak choi, and Chinese kale to investigate the impact of different pest management methods on the pest populations. In the past, the numbers of individuals per life stage on any given sampling date were calculated based on sampling data of that particular date and an average temperature determined for the entire sampling period. In several cases, this approach produced unrealistic survival rates (above 100%) for certain life stages in the resulting life tables. This problem continued even after the model was adjusted by calculating the duration of each life stage based on the actual temperature measured on each sampling date (instead of using one average temperature for the entire period). With temperature being an important factor that (i) affects the development time of insect life stages and (ii) can be determined easily during field surveys, we previously hypothesized that including corrected initial numbers of each life stage on each sampling date based on an average of the temperature between the given sampling date and its preceding sampling date will result in realistic and precise life tables. Furthermore, to estimate accurate survival rates, we here hypothesized that (i) it is important to adjust and correct the numbers of life stages on a given sampling date by including the numbers of preceding life stages from a preceding sampling date (not from the given sampling date) in the model; and (ii) the development time of the preceding life stage will determine which sampling date needs to be included in the calculation. By re-constructing and comparing 9 life tables of P. xylostella populations according to the previous and the revised new model, we confirmed these hypotheses. The revised model will allow a precise and realistic evaluation of control efforts against diamondback moth and other insect pest infestations in agriculture.
The diamondback moth, Plutella xylostella L. (Lepidoptera: Plutellidae), is an important pest of vegetables worldwide, and it has caused more than 90% loss of crop yields (Talekar & Shelton 1993; Verkerk & Wright 1996). It is important to understand how various pest management strategies and tactics affect life table parameters of this pest. Field life tables have primarily been used to determine an insect's “life budget” by attempting to identify different causes of death and to measure life stage specific attrition (Carey 2001). Morris & Miller (1954) constructed a life table by using the numbers of the individuals in each life stage (egg, immature instars, and adult) of an insect species as cohorts for recording rates of mortality or survival. Based on this insect life table, Morris (1963) and Watt (1961, 1963) suggested the population growth trend index (I) and a mathematical population model as follows:
Where S: survival rate; E: egg; L: larva; P: pupa; A: adult; P♀: probability that the adult is a female; F: standard fecundity; PF: probability of achieving standard fecundity.
However, Pang and colleagues (see below) proposed that the life table could be expressed as a series of interacting survival factors for each life stage as specified in Equation 2.
Where S1, S2, S3 … Sk represent the survival rates of different life stages as functions of a certain factor, and other values are the same as in Equation 1 (Pang et al. 1981, 1984, 1995; Pang & Liang 1982, 1995).
By means of Equations 1 and 2, the effects of various treatments against different target insect pest species were studied successfully (Pang 1979; Pang et al. 1981, 1984, 1995; Pang & Liang 1982, 1995), including treatments against the diamondback moth (Wang et al. 1992; Shen 1997; Shen et al. 1998a,b; He et al. 2000a,b; Mo et al. 2000). However, by using the models according to Equations 1 and 2 in our own life table analyses, we sometimes obtained survival rates of certain life stages that were greater than 100% (Zhou et al. 2011) and hence were unable to publish important field data in the past.
The goal of this study was to make life tables of natural populations more precise and liable to better measure and predict the impact of pest management tactics on insect pest populations. Hence, we re-visited a large data set from a comprehensive field survey that we conducted in 1996, analyzed the data with the methods of Pang et al. (1995), and developed a revised model to calculate realistic life table data. To validate the new model, we re-analyzed data from previously published life tables (Shen 1997; Mo et al. 2000; Zhou et al. 2011).
Materials and Methods
In this study, we used data collected in 1996 during surveys of P. xylostella infestations in fields of flowering Chinese cabbage, long white radish, butter cabbage, Shanghai pak choi, and Chinese kale (Shen 1997; Mo et al. 2000; Zhou et al. 2011). These surveys were conducted in 8 fields of the Shenzhen Ecological Farm and in 1 nearby field of the Shun-He Farm in Shenzhen (22°39′59″N, 114°17′18″E), China. The 8 fields at Shenzhen Ecological Farm received no control, integrated control, or biological control methods, and the field at Shun-He Farm received chemical insecticides. Data from all 9 fields were used to validate the new model. One butter cabbage field without insect pest control at Shenzhen Ecological Farm served as an example in this paper to illustrate in detail our new approach to life table analyses. Over the course of 6 wk (from 31 Oct to 12 Dec), the fields were surveyed every 3 d according to the methods described by Pang et al. (1995) to determine the levels of infestation with P. xylostella. On each sampling date, at least 50 insects (eggs, larvae, or pupae of P. xylostella) were collected, and the developmental stages and their numbers were recorded. Leaves with insects were transferred into glass jars and transported to the nearby (about 1.5 km from the field plot) laboratory at Shenzhen Ecological Farm.
In the laboratory, collected eggs and 1st- and 2nd-instar larvae were transferred into 9 cm diameter Petri dishes at no more than 10 individuals per dish. The 3rd and 4th instars and pupae were kept singly. All insects were maintained at room temperature and provided with fresh vegetable leaves as necessary. They were inspected daily, and their development and mortality (including the cause of death) were recorded. After emergence of adults from the pupae, the sex was determined, and males and females were held in single pairs, each on a fresh vegetable leaf in a plastic tube. These adults were fed a 10% aqueous honey solution provided on a soaked cotton ball. Each day the leaf was replaced and the number of laid eggs was recorded until the female died. From each cohort of insects that had been collected on each field, at least 20 pairs were used to determine fecundity. Similar methods were used in all previous studies from which we used data for the model validation (Shen 1997; Mo et al. 2000; Zhou et al. 2011).
CONSTRUCTION OF A FIELD LIFE TABLE BY THE METHOD OF PANG ET AL
Table 1 shows the sampling data from the untreated butter cabbage field surveyed in 1996. Several steps were performed after collection of this data set. First, the data of eggs and larvae that could not develop into pupae were excluded from further life table calculations. Second, following the method of Pang et al. (1995), data of each life stage (i) were summarized by adding the numbers of each life stage collected on each sampling date to get the sum of individuals (Nis) of each stage (Table 2). Third, the duration (Ti) of each stage was determined based on the rate of development that was reported by Dan (1994) for P. xylostella when reared at the average field temperature recorded throughout the period of investigation (31 Oct to 12 Dec 1996). Fourth, an intermediate number of individuals (based on the expected duration of each life stage), Nim, for each life stage was determined as:
Plutella xylostella natural population survey data taken on a butter cabbage field without any control measures in Shenzhen, China, in 1996 (Shen 1997).
Where D is the interval (days) between field sampling dates; Ti is the duration (days) of each stage determined by the average temperature recorded throughout the entire field survey. Fifth, the corrected initial number of individuals of each “larval life stage,” Nib, was calculated as:
The initial numbers of eggs and pupae were replaced by their intermediate numbers. Next, the corrected survival rate, Si, in each life stage was calculated as:
Density (individuals/m2)a of a Plutella xylostella natural population in a butter cabbage field without any control measures as estimated by the method of Pang et al. (1995).
The diamondback moth stages could be infested by Beauveria bassiana, Plutella xylostella granulovirus (PxGV), Bacillus thuringiensis (Bt), or parasitoids, or could be killed by predators. The survival rate under each of these mortality factors was calculated with data from field investigations and laboratory observations for each stage. According to Equation 2, we could obtain an I-value and conduct the following 3 types of analyses (Pang 1979; Pang et al. 1981, 1984, 1995; Pang & Liang 1982, 1995).
Exclusion Analysis. If the factor “i” was excluded, the survival at this factor Si would equal 1, and the population growth trend index (I) would be changed to the exclusion index of population control (EIPC):
Interference Analysis. If the factor “j” was interfered (for example by a pest control treatment that would modify survival Sj to become Sj'), the population growth trend index (I) would be changed to the interference index of population control (IIPC):
Addition Analysis. If the factor “a” was added, the population growth trend index (I) would be changed to the addition index of population control (AIPC):
Shen et al. (1998a) discussed the sampling method to construct a life table of a natural population of P. xylostella and used data from Shen's published studies (Shen 1997; Shen et al. 1998a). However, during Shen's investigations, the temperature ranges resulted in deviation of the intermediate number of individuals (i.e., the number of individuals of a certain life stage between the sampling dates), sometimes “producing” greater numbers of 4th-instar larvae than 3rd-instar larvae. Therefore, Zhou et al. (2011) proposed improved methods of analysis, which we will introduce in the following section.
FIELD LIFE TABLE CONSTRUCTION BY THE METHOD OF ZHOU ET AL.
In contrast to Pang et al.'s method, Zhou et al. (2011) estimated Ti based on the actual temperature on each sampling date (obtained from hourly temperature data measured by the local Bureau of Meteorology), using the average temperature between two consecutive sampling dates, instead of using one average temperature calculated over the entire sampling period of the survey (Table 3). The initial number of individuals in each life stage was first estimated by Equations 3 and 4, and all other calculations were similar to Pang et al.'s method.
The duration of each life stage of Plutella xylostella according to development times reported by Dan (1994).a
Although Zhou et al.'s method produced relatively precise results, some life stage survival rates still were greater than 100% (Zhou et al. 2011). Zhou et al. (2011) calculated the initial number of individuals per life stage based on an adjusted intermediate number of individuals (adjusted Nim; Equation 3), but they relied on the observed and adjusted numbers of individuals per life stage on any given sampling date. However, we argue here that for calculating the corrected initial number of individuals (corrected Nib) in a life stage (Equation 4) on any given sampling date, it is important to use the adjusted intermediate number of individuals of the preceding life stage on the associated preceding sampling date on which the preceding life stage was present. For example, on 3 Nov, the adjusted intermediate number of eggs was 41.70/m2 (Table 4), that of L1+2 was 29.42/m2 (Table 4), the duration of the egg stage was 2.91 d (Table 3), and the duration of L1+2 was 2.76 d (Table 3). Thus, the corrected initial number (Equation 4) of L1+2 was (41.70 · 2.76 + 29.42 · 2.91) / (2.76 + 2.91) = 35.39/m2 by Zhou et al.'s method.
In contrast, we here propose to use the adjusted intermediate number of eggs and the expected duration of the egg stage from the associated preceding sampling date (31 Oct), which were 29.67/m2 (Table 4) and 2.88 (Table 3), respectively (according to the average temperature between 31 Oct and 3 Nov). Thus, the corrected initial number (Equation 4) of L1+2 was (29.67 · 2.76 + 29.42 · 2.88) / (2.76 + 2.88) = 29.54/m2 (Table 5) and lower than that calculated based on the method by Zhou et al. (2011).
A REVISED NEW METHOD OF CONSTRUCTING A LIFE TABLE
To test our hypothesis that using the adjusted intermediate number of individuals on an associated preceding sampling date (determined by the development time of the life stage in question) is important for calculating the corrected initial number of individuals in a life stage (Equation 4) on any given sampling date, we constructed new life tables from the sampling data that had been obtained from 9 natural populations of P. xylostella in Shenzhen by Shen (1997).
The corrected initial number of individuals (corrected Nib) in each life stage was calculated by Equation 4 (Nib = [Ti-1 · Nim + Ti · N(i-1)m] / [Ti + Ti-1]). How to calculate the terms Nim and N(i-1)m has been a key issue for constructing precise life tables. In Zhou et al.'s method, Nim and N(i-1)m on a given sampling date were calculated based on the survey data (i.e., numbers of individuals per life stage) from the same sampling date. In our revised new method, these values were calculated based on data from two associated sampling dates (i.e., the given date and a preceding date on which the preceding life stage was present). Similar to Zhou et al. (2011), the duration (Ti and Ti-1) of each life stage was based on the average of the temperatures recorded between the two associated sampling dates. We performed all calculation in Microsoft Excel software.
The corrected initial number (individuals/m2) of each life stage based on the development time identified in Table 3, estimated by Zhou et al. (2011) and by our revised new methoda
We re-constructed 9 life tables of diamondback moth natural populations based on previously published data and compared the results we obtained when using the different methods of life table analyses. The detailed results from these analyses are available upon request from the corresponding author. Here, we restrict our presentation to one natural population of P. xylostella surveyed in an untreated butter cabbage field (Table 1). Results from using Pang et al.'s method are presented in Table 2. The estimated durations of the different life stages based on temperature (Dan 1994) and the adjusted life table data according to Zhou et al. (2011) are listed in Tables 3 and 4, respectively. Table 5 shows the results obtained with the herein proposed revised life table analysis.
Corrected initial number (individual/m2)a of the Plutella xylostella natural population calculated by the revised new method.
Pang et al.'s method, for example, resulted in the survival rate of 4th instars as 123.6% (> 100%), which was not realistic (Table 2). According to Zhou et al.'s method, this survival rate, albeit lower (113.2%), was also above 100%. In a few other cases, Zhou et al. (2011) obtained survival rates above 100%. In contrast, our revised life table calculation produced realistic results with survival rates of all life stages being below 100% (Table 5). A revised field life table example is presented in Table 6.
Life table of the Plutella xylostella in a butter cabbage field without any control calculated by the revised new method.
The comparison of the main parameters of 9 life tables calculated by the different methods (Table 7) indicated that Pang et al.'s method produced one survival rate above 100%, whereas the revised new method produced survival rates below 100% for all life stages.
Chi and Liu (1985) and Chi (1988) presented a 2-sex life table, which has received considerable attention. Two-sex life table are especially suited for the construction and analysis of life tables of experimental populations. But this is a complex issue because of the relatively harsh requirements involved in the investigation of insect populations in the course of the formation of the field population life table. In fact it seems that very precise and very reliable field life tables have not been published. Nevertheless the insect field population life table method proposed by Pang (Pang 1979; Pang et al. 1981, 1984, 1995; Pang & Liang 1982, 1995) has proven to be very valuable based on applications of the method in China. Pang's method is fairly simple and involves only moderate human impact on surveyed natural insect populations.
A comparison of the parameters of 9 life tables calculated by Pang et al.'s method and the revised new methoda.
Our results demonstrated that the revised new method of calculating initial and intermediate numbers of life stages of an insect population between sampling dates during a population survey improved life table analyses. In the past, some life table analyses of insect pest populations monitored in the field resulted in estimated survival rates of certain life stages being greater than 100% (Zhou et al. 2011). We hypothesized that such unrealistic results could be caused by variable temperatures in the field that could influence the time of development of the insects. Although other biotic and abiotic factors (e.g., host plant variety, infection with pathogens, sunlight, and humidity) could affect the development time, temperature is very important and influences the duration as well as the survival of each life stage (Dan 1994; Dan et al. 1995).
Field surveys of population for constructing a life table usually involve intense sampling with a short interval between successive samples. If the duration between successive samples is shorter than the life stage of interest, then some individual insects will be counted more than once, but if the duration between successive samples is too long, then some individuals will be missed. Therefore, formula (3) is needed to make corrections.
Previous models (Pang et al. 1995) had relied on an average temperature determined over the entire sampling period of a survey to calculate the development time (Ti) of each life stage and subsequently the intermediate numbers (according to Equation 3) of individuals per life stage for each sampling date.
However, if the temperature change during the investigation is relatively large, the change in the developmental time of the insect will be relatively large. Use of only an average temperature to make the correction would result in a large error. For example, in Table 3, the duration of the 3rd instar larval at the average temperature on each of the following days was as follows: Nov 6, 2.30 d; Nov 21, 3.09 d; Dec 6, 4.37 d. Assuming that the survey data was corrected for 10 individuals /m2, then the corrected number of individuals on the above 3 days would be as follows: Nov 6, 13.04 /m2; Nov 21, 9.71 /m2 and Dec 6, 6.86 /m2. If the corrected density of the population had been calculated based only on one average temperature (presumably Nov 21), the survey data of Nov 6 would have underestimated the population density, whereas the survey data of Dec 6 would have overestimated the population density.
Zhou et al. (2011) recently modified this approach by using the actual temperatures measured on each sampling date to calculate the adjusted intermediate number (according to Equation 3) and initial number of individuals (according to Equation 4) of each life stage on the given sampling date. Although their approach lowered the estimated survival rates compared with the approach of Pang et al. (1995), life tables produced with data from different population surveys still showed unrealistic rates above 100% (Zhou et al. 2011). In this study, we further adjusted the models to calculate corrected initial numbers of individuals per life stage on each given sampling date by referring to the duration and intermediate numbers of individuals of the preceding life stage estimated for the associated preceding sampling date on which the preceding life stage was present (instead of the numbers of individuals of the preceding life stage estimated for the given sampling date).
If the temperature was relatively constant during the period of the survey, the calculation of the life table based on the average temperature over the entire sampling period (Pang et al.'s method) could produce realistic results. However, if the temperature varied significantly during the sampling period, the use of one average temperature for construction of the life table would produce inaccurate results because the development time of each life stage depends on the temperature: the higher the temperature, the shorter the duration of each life stage (Dan 1994). If the temperature was rising gradually, the duration of each stage would shorten gradually. Therefore, if population density was calculated by using the same average duration, the population density of early life stages would be partially overestimated and that of late stages would be underestimated. By introducing the temperatures measured on each sampling date into the model and using the average of the temperature between two consecutive sampling dates (Zhou et al.'s method), life table results were improved but still remained unrealistic in certain cases. In Zhou et al.'s method, the adjusted intermediate number of individuals (Nim) and the corrected initial number of individuals (Nib) per life stage on any given sampling date were calculated based on the survey data from the same sampling date. In our revised new method, these values were further corrected and calculated based on data from two associated sampling dates (the given date and the preceding date on which the preceding life stage was present). For example, the corrected initial number of 1st-2nd instars on 3 Nov was related to the duration (approximately 3 d) and adjusted intermediate number of eggs on 31 Oct (instead of the duration and adjusted intermediate number of eggs on 3 Nov). Similarly, the corrected initial number of 3rd instars on 9 Nov was related to the duration (approximately 6 d) and adjusted intermediate number of 1st-2nd instars on 3 Nov. With this approach, we were able to eliminate the previous shortcomings.
For all of the 9 re-analyzed life tables, the population growth trend index (I-value) calculated with the revised new method was smaller than that obtained with Pang et al.'s method (see Table 6). The main reason for this result was as follows. In each life table, the corrected initial total egg density calculated by the revised new method was higher whereas the corrected initial total number of pupae was lower than each initial total number calculated by Pang et al.'s method. Consequently, with the egg density increased and pupa density decreased, the population growth trend index (I-value) was reduced compared with that calculated by Pang et al.'s method.
A successful biological control rests on reliable survey methods for monitoring and interpreting the population dynamics of the target pest in response to treatments. As shown in this study, analysis of sampling data by different methods would lead to different conclusions. By estimating the population density in each of 9 different fields infested with P. xylostella (with realistic survival rates below 100% for each life stage), the I-value calculated by the revised new method was a precise and useful parameter for the evaluation of diamondback moth control efforts.
Changying Zheng and Fangmeng Duan contributed equally to the work and share first authorship. This research was supported by National Natural Science Foundation of China (31272044), Agro-scientific Research in the Public Interest of China (201103021), National Science and Technology Support Plan of China (2008BADA5B02), High-level Personnel Startup Funds of Qingdao Agricultural University (630737), Innovation Program of Chinese Academy of Sciences (KSCX2-YW-NF-02), Tai-Shan Scholar Construction Foundation of Shandong Province, and The Ecological View of Hong Kong. We thank X. Pang, G. Liang, S. Huang, M. Zhang, Y. He, M. Mo, Y. Zhuang, and the Shenzhen Ecological Farm for help during the field survey. Prof. X. F. Pang was a member of Chinese Academy of Sciences, but he died some years ago.
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