1. Introduction
Beet army worm, Spodoptera exiguae Hübner (Lep., Noctuidae), is one of the important pests of corn in Iran (Mardani-Talaee et al., Reference Mardani-Talaee, Nouri-Ganbalani, Naseri, Hassanpour, Mottaghinia and Mansouri2016) which is native to the south Asian region (Wilson, Reference Wilson1932). The pest's larvae feed on the parenchyma tissues of leaves during first instars and consume the entire leaf, leaving the midrib and other large veins of the leaf during fourth and fifth instars (East et al., Reference East, Edelson and Cartwright1989). Sesamia cretica Led. (Lep., Noctuidae) is another important pest of corn in Iran (Cordero et al., Reference Cordero, Malvar, Butrón, Revilla, Velasco and Ordás1998; Yaghubi et al., Reference Yaghubi, Askarianzadeh and Abbasipour2015). Larvae feeding causes dead-heart and longitudinal tunnels in young and older plants, respectively. The plants are broken below or above ear level (Ezzeldin et al., Reference Ezzeldin, Sallam, Helal and Fouad2009).
Information about biological aspects of pests, e.g., seasonal population dynamics and spatial distribution, is critical for developing integrated pest management (IPM) program (Pedigo, Reference Pedigo2002; Rajabpour & Yarahmadi, Reference Rajabpour and Yarahmadi2012; Yarahmadi & Rajabpour, Reference Yarahmadi and Rajabpour2013). Appropriate sampling plan, i.e., easy to implement and suitable for the rapid decision-making process, is needed to establish successful IPM program (Namvar et al., Reference Namvar, Safaralizadeh, Baniameri, Pourmirza and Karimzadeh2012; Shahbi & Rajabpour, Reference Shahbi and Rajabpour2017; Kafeshani et al., Reference Kafeshani, Rajabpour, Aghajanzadeh, Gholamian and Farkhari2018). In comparison with conventional sampling plan, where a fixed number of samples are used for population estimation, sequential sampling plan can result in a 35–50% reduction in sampling effort (Binns, Reference Binns, Pedigo and Buntin1994). Also, the sampling procedure is faster and more reliable because the required sample number depends on the size of the population under survey (Fernandez et al., Reference Fernandez, Spesspoto, Degrande and Rodrigues2011; Kogan & Herzog, Reference Kogan and Herzog2012).
Weeds in the field cause more bio-diversity in agro-ecosystem. Therefore, they may affect the insect pests and their natural enemies (NEs) (Andow, Reference Andow1991; Schellhorn & Sork, Reference Schellhorn and Sork1997). Weeds may influence the pest population by providing a source of shelter and alternative prey/host to NEs, used as a physical barrier, alternation of colonization condition, chemical interaction, etc. (Altieri et al., Reference Altieri, Van Schoonhoven and Doll1977). Weedy culture, allowing selected weeds to grow intermingled with crops, is a special method for vegetational diversification within agricultural fields (Andow, Reference Andow1991). The effect of weedy culture, which is known by many names including nursery crops, living-mulches, cover cropping, etc., was documented for some pests including Pseudaletia unipuncta Haworth (Lep., Noctuidae) on corn (Laub & Luna, Reference Laub and Luna1991), Bemisia aggentifolii Bellows & Perring (Hom., Aleyrodidae) and Aphis gossypii Glover (Hom., Aphididae) on buckwheat (Fagopyrum esculentum Moench) and yellow mustard (Sinapis alba L.) (Hooks et al., Reference Hooks, Valenzuela and Defrank1998), Myzus persicae Sulzer (Hom., Aphididae) on broccoli (Banks, Reference Banks2000), Diabrotica virgifera virgifera LeConte (Col., Chrysomelidae) on maize (Lundgren & Fergen, Reference Lundgren and Fergen2010), and S. litura F. (Lep., Noctuidae) on sesbania (Sesbanin roxburghii Merr.), sunn hemp (Crotalaria juncea L.), and rapeseed (Brassicae campestris L. variety chinensis) (Tuan et al., Reference Tuan, Li, Yeh, Tang and Chi2014).
However, there has been no effort to develop a fixed-precision sequential sampling plan of S. exigua and S. cretica in the case of the corn field. Also, no previous study was performed on the effect of the weedy culture on the pests’ damage and their population densities, spatial distributions, and fixed-precision sequential sampling plans. Therefore, the objective of this study was to estimate and compare damage, population densities, spatial distributions, and fixed-precision sequential sampling plans of the noctuid pests in the weedy and weed-free corn fields.
2. Material and methods
2.1 Description of experimental area
This study was carried out in experimental corn fields, 10,000 m2, in Shush, Khuzestan province, southwest of Iran (32°14′32.0″N 48°13′46.2″E) (fig. 1). Seeds of a commercial corn cultivar, BC678®, were cultivated (≈75,000–85,000 plants per hectare) in the experimental field. The fields were divided into ten plots (900 m2) and wide ridges (2 m) were made between them. Cultural practices were carried out according to practical advisements of Khuzestan Agricultural Organization and no pesticides were applied during the study period.
Fig. 1. Aerial image of geographical position of the experimental field.
In five plots, randomly chosen, weeds were completely eradicated by applications of Nicosulfuron® 4% SC (0.5 liter h−1) and 2–4-D + MCPA® 67.5 SL (0.5 liter h−1) (Giah Company, Iran). In other plots, a weedy band (1 m wide) was maintained surrounding each plot and weeds of other parts of the field were controlled by the herbicides. By this method, 10% of the total field area had a weedy condition.
2.2 Sampling
Experiments were done during two growing seasons (2016/2017). Samplings were usually carried out at weekly intervals from June to September 2016 and June to October 2017 during the first and second growing seasons, respectively. This period synchronized with phenological steps of the emergence of one shoot to flowering. At each sampling date, ten plants were randomly selected by traveling in an X-shaped pattern through each plot. From each selected plant, three leaves from the top, middle, and bottom of the plant were chosen and numbers of live larvae and egg masses on them were separately recorded.
Cumulative insect days (CIDs) of S. exigua and S. cretica larvae in each plot of the weedy and non-weedy cultures were calculated by equation 1 (Ruppel, Reference Ruppel1983):
$${\rm CID} = \mathop \sum \limits_{i = 1} \left( {\displaystyle{{x_{i-1} + x_i} \over 2}} \right) \times \Delta t,$$where x is the mean number of the larvae on sample day i, x i−1 is the mean number of the larvae on the previous sample day, and t is the number of days between samples i−1 and i.
Harvesting was done during December 2016 and 2017 in the first and second growing seasons, respectively. After harvesting, the total yield of each experimental treatment was separately weighted by an economical mechanical bench scale (Model D500 M, Ohaus Company, China).
2.3 Spatial distribution
Taylor's power law (TPL) and Iwao's patchiness (IP) were used to evaluate the spatial distribution of S. exigua and S. cretica larvae on corn. TPL describes the regression between logarithm(10) of population variance and logarithm(10) of population mean according to equation 2:
$${\rm Log}(s^2) = a + b{\rm Log}(\bar{X}),$$where S 2 is the larval population variance, 
$\overline X $ is the larval population mean, a is the Y-intercept, and b is the slope of the regression line. The regression slope ‘b’ is an index of species spatial pattern. When b < 1, b = 1, and b > 1, the spatial distribution pattern of the larvae is uniform, random, and aggregated, respectively (Southwood, Reference Southwood1978; Shahbi & Rajabpour, Reference Shahbi and Rajabpour2017; Kafeshani et al., Reference Kafeshani, Rajabpour, Aghajanzadeh, Gholamian and Farkhari2018). Also, the regression coefficient (r 2) was calculated to obtain goodness of fit of TPL. Two-tailed t-test at n − 2 degrees of freedom was performed to determine if slope and regression coefficient values of the regression relation are significantly different from 1 and 0, respectively (Snedecor & Cochran, Reference Snedecor1980).
IP regression was used to quantify the relationship between mean crowding index (X*) and mean 
$\overline X $ by using equation 3:
$$X^{^\ast} = {\rm \alpha} + {\rm \beta} \bar{X}$$Where,
$$X^{^\ast} = \bar{X} + \left( {\displaystyle{{S^2} \over {\bar{X}}}} \right)-1.$$Different linear regressions were tested for heterogeneity of slopes (Sokal & Rohlf, Reference Sokal and Rohlf1995) by analysis of covariance of data collected from different growing years using SPSS software (Version 16.0).
Student's t-test can be used to determine if the colonies are randomly dispersed (equations 5 and 6):
$$In{\rm}\; Taylor^{\prime}s \; {\rm} power{\rm} \; law:b = {\rm} 1t = {\rm} \lpar {b-1} \rpar /SE_b$$
$$In{\rm}\; Iwao^{\prime}s\;{\rm} patchiness:{\rm \beta} = {\rm} 1t = {\rm} \lpar {{\rm \beta} -1} \rpar /SE_{\rm \beta}, $$where SE b and SE β are the standard errors of the slope for TPL and IP regression models, respectively. The calculated value of t is compared with the tabulated value of t with n − 2 degrees of freedom. If the calculated t (t c) < t-table (t t), the null hypothesis (b = 1) would be accepted and the spatial distribution would be random. If t c > t t, the null hypothesis would be rejected and if b > 1 or b < 1, the spatial distribution would be aggregated or uniform, respectively (Sedaratian et al., Reference Sedaratian, Fathipour, Talebi and Farahani2010; Kafeshani et al., Reference Kafeshani, Rajabpour, Aghajanzadeh, Gholamian and Farkhari2018).
2.4 Fixed-precision sequential sampling plan
The optimum sample size (n) needed to estimate each noctuid pest species density at two levels of fixed precision, 0.25 and 0.1, was calculated using equation 7:
$$n = \displaystyle{{a{\bar{X}}^{b-2}} \over {D^2}},$$where D is a fixed precision level, and a and b are the coefficients obtained from the regression of TPL (Buntin, Reference Buntin, Pedigo and Buntin1994). Precision levels of 0.25 and 0.1 are generally acceptable for sampling in IPM and research purposes, respectively (Southwood, Reference Southwood1978).
Due to fit data with Taylor's mean-variance model, the Green's method was used and stop lines of fixed-precision sequential sampling were calculated (Naranjo & Hutchison, Reference Naranjo and Hutchison1997). The stop lines of S. exigua and S. cretica in the non-weedy and weedy corn cultures were estimated by equation 8:
$$T_n \ge ((an^{1-b}/D^2)^{(1/(2-b))}),$$where T n is the larval cumulative number in n samples, and a and b are the Taylor coefficients, D is the desired precision level.
2.5 Validation of sampling plan
The sequential sampling plan was validated by Resampling for Validation of Sampling Plans (RVSP) software based on Naranjo & Hutchison's (Reference Naranjo and Hutchison1997) method. The software requires independent data sets to serve as validation data sets (Shhabi & Rajabpour, Reference Shahbi and Rajabpour2017; Kafeshani et al., Reference Kafeshani, Rajabpour, Aghajanzadeh, Gholamian and Farkhari2018). Hence, ten independent data sets with a range of low-, medium-, and high-density levels of each pest larvae were randomly selected from a total of 38 data sets, which were collected from two growing seasons in the non-weedy and weedy corn cultures. The mean densities of these data sets for S. exigua and S. cretica ranged from 0.002 to 0.12 and 0.001 to 0.082 larvae per plant on the non-weedy corn culture and 0.001 to 0.115 and 0.002 to 0.77 larvae per plant on the weedy corn culture, respectively. The sample size of each data set consisted of 50 plants. Simulations were carried out using 500 resamplings without replacement.
2.6 Data analyses
Experiments were performed in a completely randomized plot design with five replications. Data of CID and total yield were compared by analysis of variance using SAS software. When data were not normally distributed, the data were log (x + 1) transformed to meet the assumptions of normality.
3. Results
3.1 Population density and total yield
Population densities of S. exigua and S. cretica per plant (according to CID) in the weedy and non-weedy cultures are presented in table 1.
Table 1. Comparisons between mean ± SE of Spodoptera exigua and Sesamia cretica cumulative insect days (CIDs) in the weedy and non-weedy fields (by independent t-test).
Population densities of both noctuid pests in the weedy culture were significantly lower than the non-weedy culture. In the first growing season, CID values of S. exigua and S. cretica in the non-weedy culture were 2.4- and 3.1-fold the weedy culture, respectively. Similar results were observed during the second growing season.
In both growing seasons, there was no significant difference between total yields of corn in the weedy and non-weedy cultures (table 2).
Table 2. Comparisons between mean ± SE (kg plot−1) of total yield in the weedy and non-weedy fields (by independent t-test).
3.2 Spatial distribution
Spatial distribution patterns and parameters of S. exigua and S. cretica according to TPL and IP on corn in the weedy and non-weedy cultures are shown in tables 3 and 4, respectively.
Table 3. Spatial distribution statistics of Spodoptera exigua and Sesamia cretica on corn using Taylor's power law regression analysis.
Table 4. Spatial distribution statistics of Spodoptera exigua and Sesamia cretica on corn using Iwao's patchiness regression analysis.
TPL provided a significant relationship between variance and mean density for both noctuid pests on the weedy and non-weedy cultures. Although, for both species on the cultures, no significant relationship was observed between mean crowding and mean density in IP regression. For all cases, the aggregation incidence (b) of TPL was significantly more than 1 which indicates aggregative dispersions of S. exigua and S. cretica larvae on corn in both treatments.
3.3 Fixed-precision sequential sampling plan
The optimum sample size of S. exigua and S. cretica at the fixed precision levels of 0.25 and 0.1 on the weedy and non-weedy corn cultures is presented in figs 2 and 3, respectively. With increasing larval densities, the optimum sample size dramatically decreased. Also, at the precision level of 0.25, the optimum sample size was always lower than the level of 0.1. To estimate S. exigua population densities on the non-weedy and weedy corn cultures at the precision level of 0.25 or 0.1, the sample size ranged from 532 to 895 and 428 to 597 plants or 3327 to 5370 and 2679 to 5296 plants, respectively. For S. cretica, the optimum sample size for the non-weedy and weedy corn cultures ranged from 43 to 297 and 29 to 326 plants at the precision level of 0. 25 as well as 274 to 1862 and 186 to 2040 plants at the precision level of 0.1, respectively. Therefore, the study implicated that the optimum sample sizes were different based on the weed condition of the corn field. Moreover, there were differences between the optimum sample sizes of the noctuid pests on corn.
Fig. 2. Optimum sample size of Spodoptera exigua on corn in the weedy and non-weedy cultures at the precision levels of 0.25 and 0.1.
Fig. 3. Optimum sample size of Sesamia cretica on corn in the weedy and non-weedy cultures at the precision levels of 0.25 and 0.1.
Estimated stop lines using Green's model for S. exigua and S. cretica on the weedy and non-weedy corn cultures are shown in figs 4 and 5, respectively. Based on the estimated stop lines, numbers of required sampled plants to cross the stop lines are significantly changed. The results indicated that the sampling of S. exigua must be continued until the cumulative number of larvae on the non-weedy corn culture reaches 0.000057 larvae per plant at the precision level of 0.25 or 52.59 larvae per plant at the precision level of 0.1. In the weedy corn culture, the sampling should be continued until the cumulative number of larvae reaches 0.00029 and 58.87 larvae per plant at the precision level of 0.25 and 0.1, respectively. For S. cretica, the sampling should be continued until the cumulative larval number in the non-weedy culture reaches 1.59 and 111.5 and in the weedy culture reaches 2.09 and 98.03 at the precision levels 0.25 and 0.1, respectively.
Fig. 4. Fixed precision sequential sampling stop lines for Spodoptera exigua on corn in the weedy and non-weedy cultures at the precision levels of 0.25 and 0.1.
Fig. 5. Fixed precision sequential sampling stop lines for Sesamia cretica on corn in the weedy and non-weedy cultures at the precision levels of 0.25 and 0.1.
3.4 Validation of developed sampling plan
Estimated sample size of S. exigua and S. cretica on the non-weedy and weedy corn cultures according to resampling analysis using RVSP software is shown in figs 6 and 7, respectively. The mean of sample sizes for S. exigua on the non-weedy and weedy corn cultures was 1199 and 1534 plants at the precision level of 0.25 and 7498 and 9593 plants at the precision level of 0.1, respectively. For S. cretica, the mean of sample sizes was 1521 and 2493 plants at the precision level of 0.25 as well as 9511 and 15,583 plants at the precision level of 0.1.
Fig. 6. Summary of re-sampling validation analysis using ten independent data sets of Spodoptera exigua on the non-weedy and weedy corn cultures showing the calculated sample size means (±SE) for Green's sequential sampling plan at the precision levels of 0.25 and 0.1.
Fig. 7. Summary of re-sampling validation analysis using ten independent data sets of Sesamia cretica on the non-weedy and weedy corn cultures showing the calculated sample size means (±SE) for Green's sequential sampling plan at the precision levels of 0.25 and 0.1.
For the ten independent data sets covering different densities, the average precision levels for S. exigua and S. cretica on the non-weedy corn culture were 0.265 and 0.263 at the precision level of 0.25 as well as 0.112 and 0.11 at the precision level of 0.1, respectively (figs 8 and 9). In the weedy corn culture, the average precision levels for S. exigua and S. cretica were 0.26 and 0.261 at the precision level of 0.25 as well as 0.115 and 0.112 at the precision level of 0.1, respectively (figs 7 and 8). All averages of observed precision levels are close to the desired precision.
Fig. 8. Summary of re-sampling validation analysis using ten independent data sets of Spodoptera exigua on the non-weedy and weedy corn cultures showing the calculated precision level means (±SE) for Green's sequential sampling plan at the precision levels of 0.25 and 0.1.
Fig. 9. Summary of re-sampling validation analysis using ten independent data sets of Sesamia cretica on the non-weedy and weedy corn cultures showing the calculated precision level means (±SE) for Green's sequential sampling plan at the precision levels of 0.25 and 0.1.
4. Discussion
Our data indicated that the weedy culture causes significant reduction in the larval densities of S. exigua and S. cretica in comparison with the non-weedy culture in the corn field. The reduction may be due to enhancement in NE activities by providing a source of shelter and alternative prey/host. Moreover, the weeds can affect the pest population by applying physical barrier, alternation of pest colonization condition, chemical interaction with the main host plant, and confusing the pest for the main host plant selection (Altieri et al., Reference Altieri, Van Schoonhoven and Doll1977). Abate (Reference Abate1991) demonstrated that the population density of Heliothis armigera Hubner (Lep., Noctuidae) larvae and their important NEs, Tiphia sp. (Dip., Tachinidae), in the weedy corn culture were significantly lower and higher than weed-free maize culture, respectively. Also, it was reported that when weeds were removed from corn fields, population density of Agrotis ipsilon Hufnagel (Lep., Noctuidae) larvae and its damage were enhanced compared to the weedy corn culture. Delaying weed removal until four-leaf stage corn resulted in significant grain yield reductions from both weed competition and A. ipsilon damage and only from weed competition (Engelken et al., Reference Engelken, Showers and Taylor1990). In a rotation of corn, soybean, and forage crops, it is documented that weed bands, as living mulches, cause a significant increase in ground beetle population (Col, Carabidae) and, therefore, significant reduction in population density of the plant important pest including Osterinia nubilalis Hübner (Lep., Crambidae) (Prasifka et al., Reference Prasifka, Schmidt, Kohler, O'neal, Hellmich and Singer2006). Totally, the data suggest that population densities of S. exigua and S. creticae can be reduced on corn when about 10% of total field area had a weedy condition.
Spatial distributions of both noctuid pests were clumped on corn. However, the spatial distribution parameters were different between the pests. Moreover, no significant differences were observed between spatial distribution parameters of the pests in weedy and non-weedy cultures. Spatial distribution of an herbivore insect is influenced by many factors such as insect behavior, environment, the host–plant characteristics, sampling methods, NEs, and so on (Southwood, Reference Southwood1978). The obtained data agree with Mitchell & Fuxa (Reference Mitchell and Fuxa1987) and Serra & Trumper (Reference Serra and Trumper2006) who showed that spatial distribution of Spodoptera frugiperda Smith (Lep., Noctuidae) is aggregative and TPL fitted the spatial distribution data well. Similarly, it is documented that the spatial distribution of S. cretica Led. (Moyal et al., Reference Moyal, El-Said and Mosad2002) and Sesamia calamistis Hampson (Kouame, Reference Kouame1995; Gounou & Schulthess, Reference Gounou and Schulthess2004) on maize is clumped.
Desired precision level and larval density have a critical role to determine the optimum sample sizes of the lepidopteran pests. The relationship between the mean and the variance of the pest densities as expressed by the slope of Taylor's regression leading to the number of samples required to attain the desired precision level is a strong function of density. In this case, a higher sample size is required at the lower pest density (Kapatos et al., Reference Kapatos, Stratopoulou, Sahinoglu, Tsitsipis and Lycouresis1996; Kafeshani et al., Reference Kafeshani, Rajabpour, Aghajanzadeh, Gholamian and Farkhari2018). The sample sizes of S. exigua and S. cretica were different according to the pest species. The differences might be attributed to different pest aggregation incidences of each lepidopteran pest. Moreover, the optimum sample size of each pest in the non-weedy corn culture was relatively lower than the weedy corn culture. Minor differences were observed in slope and intercept values of TPL regression between the non-weedy and weedy cultures which may be the main reasons for the difference. If the end user needs a plan with an acceptable trade-off between time invested in sampling and the precision of the resulting estimation in the whole range of possible densities found in the field, we would recommend using the developed stop-lines of Green's sequential sampling plan for S. exigua or S. cretica based on the field weedy conditions. No previous study has been performed to develop a fixed-precision sequential sampling plan of S. exigua and S. cerica. Hence, our result cannot be compared with other studies. Optimum sample sizes of S. frugiperda on maize varied 1–12 sample units according to the sample universe (Serra & Trumper, Reference Serra and Trumper2006). The sample size was significantly different from our result. The differences may be due to different pest species or sample universe. For Helicoverpa zea Boddie (Lep., Noctuidae) on corn, the sample size was 38 and 227 plants at the precision levels 0.25 and 0.1 which is close to our result, respectively (O'Rourke & Hutchison, Reference O'Rourke and Hutchison2003). Also, our results in line with Moyal et al. (Reference Moyal, El-Said and Mosad2002) showed that the optimum sample size of S. cretica on maize is about 200–300 plants at the precision level 0.2.
5. Conclusion
Population densities of S. exigua and S. cretica in the weedy corn culture were significantly lower than the non-weedy culture. There was no significance between total yield in the weedy and non-weedy corn cultures. Also, the spatial distribution parameters of both lepidopteran pests were not significantly affected by the weed condition of the corn field. Also, optimum sample size and fixed-precision sequential sampling stop lines were different according to the lepidopteran pest species and weed status of the corn field. Results of the study can be used in the IPM program of corn fields.
Acknowledgements
The research was financially supported by the Agriculture and Natural Resources University of Khuzestan (grant no. 9428407). Also, the authors declare that they have no conflict of interest.
