Key words : aphids, spatial distribution, Green's plan, Taylor's Power Law, Iwao's mean crowding, intercropping, polyculture, bootstrap

M. M. Rashid^*, S. T. S. Hassan^*, R. A. Bakar^* and M. Y. Hussein^**

Author's full names: Mansor Mohd Rashid, Syed Tajuddin Syed Hassan, Rohani Abu Bakar and Mohd Yusof Hussein

 Running title : Spatial distribution and Green's plan for A. gossypii in intercropping

Dalam usaha mengurangkan kehilangan hasil cili akibat virus rintik urat daun cili yang dibawa oleh Aphis gossypii, sistem polikultur telah diketahui dapat mengawal populasi perosak melalui pemangsaan oleh Menochilus sexmaculatus. Namun, maklumat yang ada tentang taburan spatial perosak dan pemanga utama dalam sistem polikultur adalah sangat sedikit. Maklumat sedemikian penting bagi membentuk pelan pensampelan untuk pengurusan perosak. Taburan spatial dua spesies perosak, A. gossypii pada pokok cili dan terung serta Heteropsylla cubana pada pokok leucaena (petai belalang); dan satu spesies predator, M. sexmaculatus telah dianalisis berdasarkan kaedah penanaman dan peringkat hidup yang berbeza, dengan menggunakan Hukum Kuasa Taylor (pekali b) dan indeks min kesesakan Iwao (pekali b ). Seterusnya, pekali-pekali Taylor digunakan bagi membentuk pelan berjujukan Green untuk A. gossypii bagi setiap kaedah kultur. Kajian ini menunjukkan bahawa kesemua kategori artropod bertaburan secara berkelompok, dengan nilai b dan b melebihi 1 secara ketara. Apabila varians diregresi pada min densiti, Hukum Kuasa Taylor menunjukkan kepadanan tertinggi dengan nilai r² yang lebih tinggi dan ralat piawai yang lebih rendah dibandingkan dengan pengiraan secara min kesesakan Iwao. Ketidakupayaan terbang bagi nimfa afid dan afid tanpa sayap menghasilkan tahap perkelompokan yang tinggi. Dalam membentuk suatu pelan pensampelan, monokultur memerlukan saiz sampel yang kecil dibandingkan dengan dikultur dan trikultur. Densiti populasi spesies serangga dalam monokultur adalah lebih tinggi berbanding dengan dikultur dan trikultur. Pelan Green memerlukan saiz sampel yang lebih kecil berbanding dengan pelan saiz-sampel-tetap. Saiz sampel juga berkurangan dengan penurunan tahap kepersisan daripada 0.20 kepada 0.30; pengurangan daripada 44 kepada 12 dalam monokultur, daripada 41 kepada 14 dalam dikultur, dan daripada 51 kepada 17 dalam trikultur. Setiap jenis kultur juga menghasilkan peratusan yang tinggi bagi nilai kepersisan sebenar kurang daripada kepersisan optimal. Hasil yang diperoleh menunjukkan bahawa pelan Green dapat diamalkan dan digunakan dalam program pengurusan perosak bagi A. gossypii, dengan tahap kepersisan 0.30.

 In preventing crop losses due to chilli veinal mottle virus (CVMV) transmitted by Aphis gossypii on chilli plants, a polyculture system is known in many cases to suppress pests by predation by Menochilus sexmaculatus. However, information on spatial distribution of major pests and predators in polyculture crop system is little known. Yet such information is essential in developing sampling plan for pest management. The spatial distributions of two pest species, A. gossypii on chilli and brinjal plants and Heteropsylla cubana on leucaena plants; and one predator species, M. sexmaculatus, were analyzed with respect to different culture methods and life stages using Taylor's Power Law (b coefficient) and Iwao's mean crowding index (b coefficient). Subsequently, Taylor's coefficients were used in developing the Green's sequential plan for A. gossypii for each culture method. This study indicates that all arthropod categories were clumped, with b and b values significantly larger than 1. On regressing the variance on the mean density, Taylor's Power Law indicates the best fit with higher r² and lower standard errors compared to Iwao's mean crowding. The immobility of aphid nymphs and wingless aphid tends to result in high aggregations, whereas decreasing aggregations in winged aphid are due to the flight ability. In developing a sampling plan, monoculture requires smaller sample size than that required by diculture and triculture. Population density of insect species in monoculture is higher than those in diculture and in triculture. The Green's plan required smaller sample size than fixed-sample-size plan. As the precision level is decreased from 0.20 to 0.30, the sample size decreases, from 44 to 12 in monoculture, from 41 to 14 in diculture, and from 51 to 17 in triculture. Each type of culture yielded a high percentage of actual precision level lower than the optimal precision level. The result obtained indicates that the Green's plan is feasible and applicable in pest management program for A. gossypii with a precision level of 0.30.

 Introduction

In Malaysia, Aphis gossypii Glov. (Homoptera: Aphididae) has been recognized as a major pest of chilli (Capsicum annuum L.) that transmits the chilli veinal mottle virus (Abdul Samad 1984). This aphid vector extremely polyphagous and transmits over 50 plant viruses (Blackman and Eastop 1984). The various sources of infection would limit the effectiveness of chemical control on vectors (Maelzer 1986). Hussein and Abdul Samad (1993) studied the effectiveness of the cultural methods in controlling A. gossypii and the viruses through intercropping or polyculture and found that the vectors were abundant in monocropping (chilli only) than the dicrop combinations of either chilli-brinjal (Solanum melongena L.) or chilli-maize (Zea mays L.).

Knowledge of dispersion patterns aids in understanding of the dynamics of the distribution of an arthropod in its ecosystem (Sevacherian and Stern 1972) because of the interactions between the insect and its habitat which may reflect behavioural characteristics of the species (Taylor 1961). The distribution of any arthropod can be described by a theoretical probability distribution models such as Poisson, negative binomial, positive binomial, or by empirical relationships between parameters fitted by linear regressions. The empirical relationships for direct-counts are determined by regressing Lloyd's mean crowding ( Lloyd 1967) against the corresponding sample mean parameters (Iwao 1968) and the logarithmic linear regression of the variances and means (Taylor 1961, 1984). On the other hand, the empirical relationships of presence-absence counts are determined by the logarithm regression of mean density on the proportion of empty sampling units (Kono and Sugino 1958), the proportion of infestation [P(I)] calculated based on four distribution models against the actual P(I) (Wilson and Room 1983, Hassan 1996), and the numerical density functions of optimum sample size curves (Hassan and Rashid 1997). Distribution information is essential in developing sampling plan either for density estimation or for classification to aid decision making in integrated pest management (IPM).

The objective of this paper is to describe the spatial distribution of major arthropods in an experimental polyculture system. Subsequently, a set of fixed-precision sequential sampling plans based on the empirical model of Taylor's Power Law as proposed by Green (1970), is developed for A. gossypii and presented here.

 Results and discussion

Distribution parameters using Iwao's mean crowding and Taylor's Power Law regression models on two pests, A. gossypii (on chilli and brinjal plants) and H. cubana (on leucaena plants) with respect to the different categories are shown in Table 1. However, the predator, M. sexmaculatus, data were pooled by all categories including life stages, culture methods and crops for regression analysis because of low population densities (Table 1). Taylor's Power Law coefficients provided the best fit (r²) to all stages of arthropod categories and cultural methods (Table 1). The coefficients of determination (r²) of Taylor's regression ranged from 84.96 to 98.65 while for the Iwao's regression model the values ranged from 62.04 to 92.29. The standard errors of the regression coefficients were smaller in Taylor's regression model (0.01-0.08), compared with Iwao's regression model (0.03-0.27), similarly showing that the Taylor's Power Law approach yielded the better fit to the distribution of the data. Aggregation coefficients ( and ) by both models were significantly larger than 1 (p <0.01), indicating that each species conformed well to the aggregative pattern of distribution. However, it should be noted that for each species, for different populations and in different agroecosystems, arthropods could exhibit different patterns of spatial distribution (Hassan 1996), because of different behavioural characteristics resulting from interactions between the arthropod and its habitat (Taylor 1961).

Taylor's coefficients of aphid nymphs and wingless adults are slightly larger than those for winged aphid, with aphid nymphs showing higher aggregation level in all types of culture method and for both chilli and brinjal plants (Table 1). The higher aggregation of wingless (apterous) adults is due to their immobility, whereas that of the nymphs is due to higher concentration in the same area (Reilly and Sterling 1983). In contrast, the flight ability of the winged (alate) adults leads to dispersal, hence decreasing the aggregation. The leucaena pest, H. cubana, also showed similar patterns of aggregation with respect to eggs and nymphs (higher degree of aggregation), in comparison with the psyllid adults.

Taylor's parameters estimates of the combined all-stages (winged, wingless and nymphs) data of A. gossypii (Figure 3) at different cultural methods, were used in subsequent simulation runs to evaluate and develop the sampling plan using Green's (1970) algorithm. In a sampling plan using the stop line, samples are to be taken sequentially until the cumulative number of aphids exceeds the stop line values for a given number of samples taken. The required sample size (n) increases as the desired level of precision increases from D₀ = 0.3 to 0.2. Figure 4 shows the Green's sequential stop lines for A. gossypii at different densities and culture methods used in this study. It can be seen that at a certain precision for a similar population density and comparing the three cropping cultures, the monoculture demands the least sample size while the triculture requires the largest. These results were probably affected by the use of different Taylor's coefficients during constructing the plans.

Data sets with the mean number of aphids < 1 per plant were excluded from the simulation in order to attain a 20% precision level. Only the earlier sampling dates in each sampling month (from July to November 1991) were selected for simulation analysis to ensure that the pest management program for A. gossypii is carried out monthly and during the first week of each month. Therefore, 5 samples (sampling dates) out of 16 samples (sampling dates) with n = 60 and 90 samples for each date were simulated and their summary statistics for each cultural method are shown in Table 2 to Table 4. The monoculture (chilli) crop showed aphid population densities ranging from 9.17 to 51.48 per plant (Table 2). The aphid population densities ranged from 7.54 to 44.27 per plant (Table 3) for diculture plots (chilli and brinjal) and from 7.93 to 34.82 aphids per plant in the triculture (chilli, brinjal and Leucaena) (Table 4). These results showed that the density of aphids were higher in the monoculture than in diculture and triculture plots. Hussein and Abdul Samad (1993) reported a similar finding in numbers of A. gossypii in monoculture relative to those in diculture planting.

On each sampling date and at each precision level, the Green's sequential plan requires less sample size than fixed-sample-size sampling (FSS). The number of samples decreased as precision level decreases, but the standard error of the estimated mean increased in proportion with the decreasing precision level (Table 2 to Table 4). Numbers of samples required by the Green's plan to stop sampling reduced from 44 to 12 in monoculture, from 41 to 14 in diculture and from 51 to 17 in triculture, as the precision levels decreased from 0.2 to 0.3.

The simulated populations mean densities based on Green's algorithm were within 95% range of actual population mean densities (original data sets using FSS plan) even though precision levels differ (Table 2 to Table 4). However, the standard errors of the mean estimates are mostly larger than those of fixed-sample-size plan especially at higher mean densities, probably due to the small sample size required by Green's sequential plan (Table 2 to Table 4). Therefore, the values of the actual precision levels (D) yielded from the higher mean densities plots are larger than the desired precision levels (D₀) as shown for the first sampling date (11 July 1991) in all culture methods (Table 2 to Table 4). For the first sampling date, D is lower than D₀ by less than 20% at almost all precision levels and for all culture methods. Nonetheless, as the precision level decreased, the percentages of D lower than D₀ increased as shown by the second sampling date of monoculture, from 27.2 to 51.0 (Table 2) and from 28.6 to 50.0 for the third sampling date of diculture plots (Table 3). For other sampling dates, this sampling plan is applicable since a higher percentage of D lower than D₀ is indicated even at a high precision level (D = 0.2). In monoculture, the actual precision level ranged from 55.8% to 100%, from 64.6% to 100% in diculture and from 82.2% to 100% in triculture. The highly aggregated distribution pattern shown by aphids was probably the cause of high variability in the data sets. At high densities, as the variances of the density estimates increased, the cumulative number of aphids (T_n) rapidly increased, thus making possible a quick stop in the sequential sampling operation. Consequently, smaller sample sizes were obtained through the sequential sampling plan. Therefore, the high standard errors would lead to lower precision since the precision level is defined as standard error divided by the mean. However, sample size should be minimized at higher densities to reduce sampling cost and sampling time for counting the large numbers of aphids. Hence, it becomes obvious that some management actions (e.g. spray the crops with insecticide) may be necessary even if the estimates of high population density is made at lower precision levels (Cuperus et al. 1982, Shelton et al. 1994).

Generally, the number of samples required by the Green's plan was less than that of fixed-sample-size plan. At a higher population density, the plan required less number of samples compared with populations at lower densities, which led to a smaller probability of achieving the required precision level. It is clearly shown that decreasing the precision level from 0.2 to 0.3 reduces the sample size and increases the percentage of precision level, even at a high population density (Table 2 to Table 4). Therefore, the precision level at 0.3 is recommended for management applications for A. gossypii at different culture methods, especially when cost and time are limiting.

We are most grateful to the staff of Farm Division of Universiti Putra Malaysia for their various assistance and cooperation. Research grants were provided by the Malaysian National Scientific Research and Development Council (IRPA Grants 1-07-05-024, 1-07-05-064 and 01-02-04-0082).

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