SPATIAL DISTRIBUTION OF PLANT-PARASITIC NEMATODES IN SUGARCANE FIELDS

Nematodes are important parasites of sugarcane in Brazil. Because of this, several studies have been conducted in recent years to evaluate the effectiveness of control methods. However, no studies have been reported on the spatial distribution of nematodes in sugarcane fields, and such studies are indispensable for the development of sampling plans, aimed at their application in integrated management programs. The spatial distribution of Meloidogyne javanica, Pratylenchus zeae, and mixed populations of P. zeae and P. brachyurus was studied in six commercial fields, with areas ranging from 0.26 to 0.50 ha; samples were obtained during the rainy season. The samples, represented by about 50 g roots, were collected within a rectangular grid measuring 7 × 12 m, 7 × 10 m or 5 × 13 m. Among the ten calculated semivariograms (four for M. javanica populations and six for P. zeae populations or the mixture between P. zeae + P. brachyurus), four could not be fitted to any model and presented a pure nugget effect; the spherical model showed the best fit to the semivariograms of data observed in the other six conditions. In those cases, values of range in semivariogram varied from 18 to 35 m, allowing the nematode aggregation area to be estimated at 2,110 m, on average, suggesting that at least five sampling points per hectare would be necessary, on average to obtain a reliable estimate for the population of these plant parasites in a given area.

The spatial distribution of nematodes in the field is frequently described as aggregate (Ferris & Wilson, 1987), which means that there is spatial dependence between the populations in the sampled points.In view of this, geostatistics is the most adequate tool for the study of these populations, since it quantifies the spatial dependence between field-collected samples to be quantified and used to construct maps (Leibhold et al., 1993;Roberts et al., 1993;Ellsbeury et al., 1998).
The present study aimed to characterize the spatial distribution of M. javanica, P. zeae or mixed populations of P. zeae and P. brachyurus (Godfrey) Filipjev & Schuurmans Stekhoven in sugarcane, using geostatistical analysis, so as to provide guidance for sampling procedures in the field.

MATERIAL AND METHODS
The spatial distribution of M. javanica, P. zeae, and mixed populations of P. zeae and P. brachyurus was studied in six commercial fields, whose characteristics are presented in Table 1.Areas ranging from 0.26 to 0.50 ha were selected in each field.Samplings were obtained in these areas during the rainy season, when populations usually peak due to favorable moisture and temperature conditions, as well as to abundant root growth.Samples were collected within rectangular grids measuring 7 × 12 m (areas 1 to 4), 7 × 10 m (area 5), or 5 × 13 m (area 6), (Table 1).Each sample was represented by about 50 g sugarcane roots, from which the nematodes were extracted by a combination of sifting and centrifugal flotation methods, in sucrose solution, according to Coolen & D´Herde (1972).
Data were initially analyzed by descriptive statistics and mean, standard deviation, coefficient of variation, maximum value, minimum value, skewness and kurtosis were obtained using the Statistical Analysis System (SAS Institute, 1995).In order to obtain lower coefficients of variation, data were transformed to log(x+1), and basic statistics were recalculated.
To verify the hypothesis of normality of the data, the Shapiro & Wilk (1965) test was carried out using the Statistical Analysis System (SAS Institute, 1995).After this, geostatistical analyses of the transformed data were run using semivariograms and kriging interpolation to construct maps, as described by Vieira et al. (1983).The semivariogram analyses were conducted using the GEOSTAT software (Vieira et al., 1983).Based on the models fitted to the semivariograms, the jackknifing test was used to verify whether the estimates of semivariogram parameters were adequate and to estimate the number of neighbors that should be used in kriging (Vieira, 2000).Once the parameters for the model were confirmed and the adequate numbers of neighbors were estimated, values were interpolated for the locations where they were not measured, by the kriging method, using the GEOSTAT software (Vieira et al., 1983).The kriging-estimated values were used in the Surfer software (Golden Software, 1999)

RESULTS AND DISCUSSION
Among the important nematode species for sugarcane, M. javanica and the mixed population of P. zeae and P. brachyurus were found in area 1, P. zeae was found in area 2, M. javanica and the mixed population of P. zeae and P. brachyurus were found in area 3, M. javanica and P. zeae were found in area 4, M. javanica and P. zeae were found in area 5, and P. zeae was found in area 6.In all areas, great differences were observed between the maximum and minimum populations, both for M. javanica and P. zeae or for the P. zeae + P. brachyurus mixture, considering original data (Table 2) or transformed to log(x+1) data (Table 3).
Considering original data (Table 2) and the criteria proposed by Pimentel Gomes ( 2000), all populations presented very high coefficients of variation (CV > 30%).Analyzing transformed data, the variability was lower, and only M. javanica population in area 3, in area 4 and in area 5 still presented very high coefficients of variation (Table 3).For M. javanica population in area 1, the coefficient of variation was high and for Pratylenchus species the coefficients of variation were considered low or medium, with values between 5 and 12.3%.
For M. javanica the coefficients of variation were higher than the values obtained for Pratylenchus species, indicating that the variability of populations of that species was higher than the variability of Pratylenchus populations (Tables 2 and 3).The reasons for greater variability in Meloidogyne populations are related to its biology.Because Meloidogyne is a sedentary endoparasite, the females lay all their eggs at the same place, in masses, resulting in a highly-aggregated spatial pattern (Ferris et al., 1990).On the other hand, nematodes in the genus Pratylenchus are migratory and therefore move through the plant and the soil, laying their eggs individually, resulting in a more uniform distribution in the area.All variables original data did not follow normal distribution according to the Shapiro-Wilk test and to the skewness and kurtosis values (near zero) (Table 2).When transformed data were analyzed, two populations showed normal distribution (P.zeae in area 5 and area 6), with skewness and kurtosis values near zero (Table 3).However, for all Pratylenchus populations and for M. javanica populations in area 1, the mean values were very similar to the median values (Table 3), suggesting that the data presented a near to normal distribution in these cases.
Since using transformed data, the coefficients of variation, skewness and kurtosis were lower and most of then showed similar normal distributions, it was decided to use the transformed data to run the geostatistical analysis.However, according to Cressie (1991), it is not necessary that data present normal distribution to use geostatistical analysis; it is just convenient that the distribution curve does not show a long tail, endangering the results.So, considering the previous analysis of these data, it is possible to admit that the studied variables had appropriate distributions for geostatistical analysis.
Among the ten calculated semivariograms (four for M. javanica populations and six for P. zeae populations or the P. zeae + P. brachyurus mixture), those corresponding to M. javanica populations in areas 1, 3, and 5, and the semivariogram corresponding to the P. zeae population in area 4 exhibited a pure nugget effect (Table 4).This means that the spatial distribution of nematodes in the above-mentioned cases occurred simply at random, within the sampling distance used in the study, that is, the distance between sampling points was too large to allow the detection of a spatial dependence between them.
Regarding to studies involving insects, Liebhold et al. (1993) stated that the occurrence of a pure nugget effect is quite common and is mainly attributed to the fact that the spatial dependence occurs at a smaller spatial scale than the sampling scale that is often adopted.The same can be said of studies involving nematodes.
Mathematical models were fitted for the M. javanica populations in area 5, mixed P. zeae and P. brachyurus populations in areas 1 and 3, and P. zeae populations in areas 2, 5, and 6, and the spherical model was best fitted to the semivariograms of data of these six conditions (Figure 1, Table 4).Although the observed r 2 values were low, the parameters estimated for the spherical model (C 0 , C 1 , a) were endorsed by the jackknifing test, since the mean values for the reduced errors were near zero and the values for the variance of reduced errors were near 1 (Table 4).
The jackknifing test also revealed the ideal number of neighbors to be used in kriging.As a result, kriging was performed using 20 neighbors for the mixed population of P. zeae and P. brachyurus in area 1, 16 neighbors for the mixed population of P. zeae and P. brachyurus in area 3, 12 neighbors for P. zeae in area 2 and M. javanica in area 4, and 8 neighbors for P. zeae in areas 5 and 6.The constructed maps based on the data are presented in Figure 2.
The portion of variability attributed to spatial dependence, given by the C 0 /(C 0 + C 1 ) ratio, ranged from 0.29 to 0.68 (Table 4).These values indicate a moderate spatial dependence between samples (Cambardella et al., 1994).The range (a), representing the distance at which there is spatial dependence between samples, varied from 18 m for P. zeae in area  javanica, respectively, would not be statistically independent.These data allowed us to estimate that the nematode aggregation area (A = Π 2 , in which r = a), in the various fields, varied from 1.018 m 2 to 3.848 m 2 , with an average value of 2.106 m 2 , suggesting that five sampling points per hectare would be necessary, on average, to obtain a reliable estimate for the nematode population in a given area.The samples would be collected at distances of 25 m.This value is higher than the value currently recommended for sampling in commercial areas (2 points/ha; Dinardo-Miranda, 2006), suggesting that changes should be made in the sampling plans in order to improve nematode population estimates.
Other authors have also revealed that the spherical model of the semivariogram best describes the spatial distribution of plant-parasite nematodes, with similar range values as those herein determined.Caswell & Chellemi (1986), studied the spatial dis- tribution of Rotylenchulus reniformis for pineapple in Hawaii and found a 10 m range value, and by.Farias et al. (2002) worked with the same species in cotton in Brazil and determined a mean range value of 15 m.Webster & Boag (1992) worked with Heterodera avenae and Globodera rostochiensis and also verified that the spherical model best fitted to the obtained data, with an approximate range of 60m.In the same way, Wallace & Hawkins (1994) worked with a forage grass and fitted the spherical model to a semivariogram for Tylenchorhynchus spp.population data, with a range value around 40 m.The data herein presented reveal that the use of geostatistics is viable to evaluate the spatial distribution of plant-parasite nematodes in sugarcane and to define sampling plans aimed to implement an integrated management program.However, further studies are required, especially those involving areas infested with Meloidogyne, since in the present work it was not possible to prepare maps for three of the four sampled areas, in which this species was present, because a larger sampling scale was adopted than the scale at which spatial dependence occurs between the points.In addition, the commercial cultivation of sugarcane in Brazil involves a large number of varieties, grown at the most diverse production environments, which are factors that interfere with the spatial distribution of nematodes.Therefore, our data suggest that in order to obtain a reliable estimate of nematode populations in a given area, at least five samples per hectare must be collected, on average; however, more studies are required due to the great variations in sugarcane-cultivation conditions that exist in the country.

Table 1 -
Characteristics of the studied fields.

Table 2 -
Statistical parameters of the original data of plant-parasitic nematode populations in sugarcane.

Table 3 -
Statistical parameters of transformed data by log(x+1) of plant-parasitic nematodes populations in sugarcane.