ANTONIO DE SOUZA SILVA¹, THIAGO ALEXANDRE MOTA¹, MARCOS GINO FERNANDES¹and SAMIR OLIVEIRA KASSAB¹

¹ M. Sc. in Entomology and Biodiversity Conservation, Universidade Federal da Grande Dourados, CEP 79.804-970, Dourados, Brasil. antoniobios@yahoo. com.br. Corresponding author.
² Ph. D. Professor and researcher of Universidade Federal da Grande Dourados, CEP 79.804-970, Dourados, Brasil.

The Cassava (Manihot esculenta Crantz) is one of the most important crops with respect to socioeconomics and human consumption (FAO 2008). The plant is considered the main carbohydrate source for more than 925 million people in 105 countries across tropical and subtropical regions (FAO 2010, 2011). Not only is a food source, cassava is also a raw material for the chemical, paper and biofuels industries (Felipe et al. 2010). Cultivated in all Brazilian states, national cassava production in 2011 was estimated at 27.1 million tons, an increase of 9.1% compared to 2010 (IBGE 2011).

Brazilian cassava crops are subject to pest attacks, which are generally cyclical and may not occur each year (Farias et al. 2000; Espinel et al. 2009; Bellon et al. 2012). These attacks reduce the production and commercialization of cassava and its derivatives (Silva et al. 2007). Among the main pests, the whitefly, Bemisia tuberculata Bondar, 1923 (Hemiptera: Aleyrodidae), is a vector of virus known as frogskin disease (Angel et al. 1990). Damage caused by B. tuberculata can result in losses between 5% to 80% (Schimitt 2002; Bel-lotti et al. 2007; Sagrilo et al. 2010).

Direct injuries are caused by sucking of sap, potentially causing decreased plant vigor, defoliation, wilting, chlorotic spots and premature leaf fall. Indirect damage is also caused by the growth of sooty mold on the honeydew, which acts to reduce photosynthesis (Pietrowski et al. 2010).

Studies on the distribution frequency of different insect species in different cultures are important for acquiring knowledge on spatial distribution of these individuals, adopting appropriate sampling criteria to estimate population parameters and facilitate the control of the pest (Barbosa 1992).

Utilization of a sampling model for assessing pest population is fast, reliable and less costly according to the philosophy of Integrated Pest Management (IPM), and is very important for sustainable food production (Hodgson et al. 2004). Therefore, to establish a reliable sampling plan it is necessary to know the spatial distribution of pest species in the crop (Giles et al. 2000).

Spatial dispersion of a population usually follows one of three in accordance with one of the tree models: aggregated (or contagious), random (or by chance) or uniform (or regular) (Barbosa 1992; Young and Young 1998). To determine the spatial distribution pattern of a given species it is necessary to obtain data on the count of individuals in the ecosystem to be considered. It is fundamental that the ecosystem in question allows for sampling (Fernandes et al. 2003).

These samples, according to Young and Young (1998), can be used to infer the form of distribution of the population sampled or the characteristics of the distribution. For the description of population distribution forms, the aggregation indices and frequency distributions were used.

Initially the area under study should be divided into study several units or quadrants (grids) of the same size and subsequently describe the area occupation model for individuals in the population as a distribution of frequencies of individuals observed in each quadrant (Kuno 1991).

Based on these facts, the objective of this study was to evaluate the spatial distribution of adults of B. tuberculata in the cassava crop, seeking to devise a sampling plan that may be adopted by farmers.

Description of the sampling area. The experiment was conducted during the first crop cycle of 20l2 in a commercial production area, located in the municipality of Ivinhema, Mato Grosso do Sul, Brazil. The sampled area consisted of 2,500 m², located at 22°20'57"S 53°54'37"W and elevation of 423 m.

Spacing of the plants was 0.90 m between rows and 0.45 m between plants of the "fécula-branca" variety. This variety is included in the group of those most tolerant to B. tubercula (Sagrilo et al. 2010). The cuttings were planted on August 28^th, 2011; fertilizer was applied at a rate of 290 kg ha^-1 (N-P₂O₅-K₂O; 00-30-10 formulation) and in the area used there was no trace of chemical treatment for pest control.

Sampling. The sampling was organized as follows: one area was demarcated in the sampling area. It was divided into 100 plots of 25 m² (5 m x 5 m). In each plot, there were evaluated five randomly chosen plants, totaling 500 plants in field. For sampling of whitefly adults, visual observations were made in the morning by slightly turning the leaves to the side (Tonhasca Jr et al. 1994).

The complete sampling period lasted from January 7^th, 2012 to April 14^th, 2012; totaling 15 samples according to occurrence of the whitefly in the crop. This period ranges from the beginning of colonization of the pest until completion of the its first cycle in the crop.

Statistical analysis. The statistical analyses used for determining the spatial distribution pattern of the insect consider the mean of B. tuberculata adults found in the quadrants of the area under study. For this purpose the following parameters were used:

Dispersion indexes

Variance/Mean ratio: this ratio (I) is an index that measures the deviation of a random data arrangement. For this index values equal to one indicate random or by chance spatial distribution, whereas smaller values indicate that the unit presents regular or uniform spatial distribution and values significantly greater than 1 indicate aggregated or contagious distribution (Rabinovich 1980).

Morisita index: the Morisita index (I5) is relatively independent on the mean and number of samples. Thus, when I5 = 1 the distribution is random; when I5 > 1 the distribution is contagious and when I5 < 1 the distribution is regular (Sil-veira Neto et al. 1976).

Exponent k of the negative binomial distribution: the exponent k is a suitable dispersion index when the size and numbers of sample units are the same in each sample, since this is frequently influenced by the size of the sampling units. This parameter is an inverse measure of the degree of aggregation, where in this case negative values indicate a normal or uniform distribution, positive values near zero indicate an aggregated dispersion and values greater than eight indicated a random dispersion (Elliot 1977; Southwood 1978). Regarding this aspect, Poole (1974) used another interpretation when 0 < k < 8, the aggregated distribution index and 0 > k > 8 indicated random distribution.

Poisson distribution: also known as random distribution, characterized by presenting a variance equal to the mean (S₂= m).

Negative Binomial Distribution: presents a variance greater than the mean, thereby indicating an aggregated distribution and it also has two parameters: the mean (m) and the parameter k (k > 0).

Chi-square adherence test: The chi-square adherence test was used to compare the total frequency observed in the sampling area with the expected frequencies, according to Young and Young (1998), where these frequencies are defined by the product of the probabilities for each class and the total number of sample units utilized. For this test, it was opted to fix an expected frequency equal to one.

The presence of B. tuberculata adults was observed in all samples collected, since sampling dates coincided with the occurrence period of the pest in cassava (Gomez et al. 2005). The population peak of B. tuberculata occurred on January 21^st, 2012 and the average number of adults observed per plot was 24.39 (Table 1).

Results of the aggregation indices indicated variance/ mean and Morisita values significantly greater than one. For these indexes the pest dispersion presented an aggregated pattern. In the Morisita index it was observed that in all evaluations of this study the values were higher than one with significance level of 1% probability and values resulting from the exponent k ranged from 0.372 to 4.638. i.e., positive values less than eight (Table 1).

The aggregation indexes showed that all evaluations performed for the B. tuberculata adults presented aggregated dispersion of individuals in the population studied. However, in studies with the whitefly, considering the presence and absence of the pest rather than the population, was found that the spatial distribution of Bemisia tabaci Gennadius in bean plants presented a regular dispersion (Pereira et al. 2004). Considering the whitefly population in cotton (Naranjo and Flint 1995; Rodrigues et al. 2010) and melon (Tonhasca Jr et al. 1994; Gould and Naranjo 1999) it found that B. tabaci showed an aggregated distribution in the field.

With respect to test results for removal of randomness from the Poisson chi-square, these were significant at 1% probability level for 14 samples, adjusting the randomness only on January 21^st, 2012, i.e., adjusting to aggregation (Table 2).

Moreover, of all the 15 sampling events performed, ten samples adjusted to the negative binomial distribution model with non-significant chi-square value. The values were significant at 1% probability in only five samples (Jan 21^st, 2012; Feb 18^th, 2012; Feb 25^th, 2012; Mar 3^rd, 2012; Apr 14^th, 2012).

Therefore, according to the results of the aggregation index and the frequency index, the aggregated distribution best defined B. tuberculata in cassava because the negative binomial model was that which best fit to the data obtained in the field.

According to the advanced strategies of IPM, control of this pest in cassava should not rely solely on chemical insecticides, but adopt systems that emphasize the ecological management of populations of this arthropod. Thus, understanding the distribution of B. tuberculata in the crop may promote alterations in the sampling and pest control strategies, which may then contribute to phytosanitary management of this species in the culture.

B. tuberculata adults presented an aggregated spatial distribution throughout the occurrence period. This spatial distribution model requires a large number of units per area so that the data obtained during sampling does not underestimate or overestimate the number of insect pests in the area. Furthermore, it is suggested that insecticides and/or biopesticides be applied locally in order to reach the clusters of B. tuberculata.

To the "Coordenacäo de Pessoal de Nivel Superior (CAPES)" and "Universidade Federal da Grande Dourados (UFGD)" for the Master's scholarship granted to the first author. To the undergraduate Gabriela Piñeyro for translating the abstract to Spanish.

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