By using the semivariogram, it is possible to describe, both qualitatively and quantitatively, the spatial variation and to obtain the parameters that determine kriging. In this way,the values of the nugget , plateau and range effects and determination coefficient and Spatial Dependency Index were obtained. The nugget effect ranged from 4.01 to 17.00; while the plateau from 8.978to 60.48. The spatial dependence analyzed by FDI increased over the years, presenting an initial value of 0.553 in 2003,reaching 0.719 in 2010; being always classified as moderate.For the Avros material, the range was always considered high, ranging from 2428 to 3165 m and an average valueof 2939 m. If there was interest in executing new oil palm plantations using Avros material on or near the farm, the distance between the old orchards  and the new plantations should be respected, so that old diseased plants do not interfere with the sanity of new planting.Geostatistics have been widely used to study the spatial distribution of both pests and plant diseases, and the rangeis one of the most relevant results for the studies. Dionisio et al. evaluated the spatial distribution pattern and aggregation radius of Metamasius hemipterus in an oil palm and have observed patches of 78 to 199 m. Oliveira et al. When evaluating the spatial distribution of citrus leprosis in two orchards in the citrus region of Northeast of Para, obtained a range between 9 and 30 m.The coefficient of determination  presented excellent values, always greater than 0.90, which shows a good correlation between the empirical model of the semivariogram and the calculated one . The cross-validation proved the reliability of the data due to the excellent values obtained,especilly for coefficient  that always has been above 0.85and close to one.Based on the semivariogram, Kriging maps were generated for the years 2003, 2006, 2008 and 2010.It is observed that a concentration of cases of the disease has been occurring since 2003 in the central part of the area and a less incidence in the North and South. This distribution remained similar until 2010, however with the increase in the cases of disease in the whole area, but mainly in the central region.

It was not possible to observe correlation between the occurrence of the disease and proximity to the rivers of the farm.The Deli  Lame variety was originally developed in Ivory Coast and introduced in Costa Rica in 1980. The bunches of these varieties are considered small, weighing less than18 kg and oil content less than 26%, led grow lights but with a high toleranceto periods of droughts. The parental generation of the Lamevarieties was developed between 1955 and 1973 and originated from 21 plants of the Tenera variety. The commercial varieties of Deli Lame progenies have elongated fruits, with thin skins, high bunches production, long leaf plants and short stems. The Deli  Lame variety is considered the standard variety of almost all oil palm plantations in the world.This material is characterized by being a little older with plots planted predominantly in 1989 and 1990, some in 1996and one in 2000. It is the most extensive material in the study.In total, there were 56 plots of average size equal to 29.13 ha,which totaled an area of 1631 ha and 233 289 plants .Ten Deli  Lame varieties were used in the experiment:C1001F, C2001, C7701, C2023, C2501, C3701, C1101F, C2001,C2310 and C2528.It is observed that until 2008, the disease maintained a relatively low and constant infection growth, with an increase from 8 to 22 new infected plants per year. Since 2010, this rate has dramatically increased up to 10 106 plants in 2014, representing an average of 6.2 plants per ha or 181 diseased plants per plot. In the same year, the crop reached its maximum infection, 4.33%. Out of this total, 6288 plants had been infected in the last two years which shows the severity of the disease .In this material, the spatial distribution of the FY in oil palm was adjusted to the Gaussian, Spherical and Exponential models, with a slight predominance of the first model. The first year of the study was characterized as purenugget effect, due to the low incidence of the disease. The range showed a strong variation over the years, with a minimum value of 653, maximum of 4320 and average of2169 m. The nugget  effect ranged from 0.067 to 24 000,while the plateau ranged from 0.64 to 137 600. Spatial dependence was predominantly characterized as strong with only two years of moderate dependence. The coefficient of determination obtained excellent adjustments with predominance of values greater than 0.9.The cross-validation was satisfactory for most of the years, but in 2011, 2012, 2013 and 2014, the coefficient a showed positive value and greater than 1. The coefficient b was predominantly close to 1 except in 2010. According to Vieira et al., this implies that the high values of diseased plants were overestimated, and the low values of diseased plants were under estimating .By analyzing the Kriging maps, it was observed that in the beginning, the disease had small foci of occurrence, but in a reasonable amount, distributed more randomly by the area and little aggregate. In 2009, this aggregation increased, and a higher incidence of the disease was observed in the south part of the area, which represented the Center-West region of the farm.

In 2012 and 2014, the complete southern part of the area was highly infected by the disease, presenting alarming values .Some of the plots of higher occurrence of the disease in this material were close to one of the branches of the river,towards the south of the area, similar to plot F16, which presented infection of 43% and was cut by a branch of the river.The greater humidity of the place may have contributed to the increase of the infection of the disease. These results are consistent with Laranjeira et al. who reported a higher occurrence of oil palm diseased by FY at sites near rivers and streams, and also to those of Torres et al. who suggest that the causal agent of Fatal Yellowing would be the fungus Phy-tophthora palmivora, whose dissemination occurs through water draining.eli  Lame  is a material developed in Brazil from Deli  Lame, by the genetic improvement program of Embrapa Ocidental. This material is characterized by having agronomic attributes superior to its source material.The Deli  Lame  material was planted predominantly in 2000 and 2001 and some plots in 1996, therefore it is a younger material than the others in the study. Thus, the area of Deli  Lame  material consisted of area A1, consisting of 28 medium-sized plots of 30.45 ha, totaling 853 ha of area and 121 925plants, contained by the C2301 and C2501, and area A2, consisting of three plots of the variety C2501 with a total size of85.11 ha and 12,170 plants planted in 1996 . Because there were few plots in Area A2  and distant from the others, they were not considered in the statistical and geostatistical calculations of the Deli  Lame  and were discarded.By analyzing the annual data of diseased plants of Deli  Lame  material, a very slow growth of the disease is observed in the first 10 years of the study, ranging from 1 to 5 new infected plants per year . Since2011, the number of diseased plants has increased consider-ably, culminating in 2651 infected plants in 2014, which represented an infection rate of 2.17%, or 3.1 diseased plants perha.When examining the semivariograms models that were the best fitted, a predominance of the Gaussian distribution was observed, except for the last two years, 2013 and 2014,where the best fit was obtained with the Spherical model. The Gaussian model demonstrates that the evolution of the disease presented a sense of dispersion, guided by some factor that is usually environmental, for example wind direction or even the rain. In the last two years, the best fit model was the spherical one, precisely because of the high infestation of the disease in the area, since it began to have dispersion in several directions.The nugget effect  varied from 0.008 3 to 2300, while the plateau  from 0.092 8 to 27 430. The spatial dependence ranged from 0.734 to 1.0 with a predominance of values above 0.9, vertical grow system characterized as a strong dependency for all years,except for 2003 where it was classified as moderate.

The range varied from 710 to 1323 m with an average value of1162 m. The coefficient of determination  presented values close to 1 in most years, which shows a good adjustment of the models.The cross-validation was satisfactory mainly in the years when the coefficient of determination was not so high, as2012, 2013. In these years, the coefficient of values presented values close to 1 . However, in 2014, the coefficient a showed negative value and greater than 1. This implies that the high values of diseased plants were under estimating and the low values of diseased plants were overestimated .Despite the correlation coefficient of cross-validation having presented low values, semivariograms were validated due to the other coefficients, as linear, angular and determination.Pelissari et al.and Roveda et al. also obtained low values of coefficient of cross-validation, however high values of coefficient of determination, thus validating the semivariogram.Few cases of the disease and a more random distribution were observed in the area in 2003 as it was found in the color scale on the right where the numbers ranged from 0 to 1.4.Nevertheless, in 2009, the disease spread more aggregately,presenting two points of greater concentration in the North of the area. In 2012, the disease continued to expand and the small points of high concentration reached several plots,in addition to increasing the number of diseased plants perplot, as it can be observed by the increment in the values in the scale. Finally, in 2014, the entire Northwest part of the area was highly infected by the disease. It was not possible to observe an expressive correlation between the occurrence of the disease and the proximity to the rivers on the farm.By analyzing the semivariograms models of the genetic mate-rials, it is observed the occurrence of the Gaussian, Exponential and Spherical models, with predominance of the first model. These models describe the dispersion of pests and dis-ease of biotic factors and match the models used by Shim-wela et al.who studied the spatial temporal distribution of huanglongbing , in citrus in florida; Pinho et al.that analyzed the spatial distribution of Rhynchophorus pal-marum in oil palm plantations in eastern Amazonia and Guoet al., when studying the spatial distribution of rice blastin China caused by the fungus Magnaporthe oryzae. These results reinforce the idea that FY has a biotic cause.FY developed in an aggregate manner for all genetic mate-rials. Silva et al. studying the Spatial distribution of FY on organic oil palm plantation also noted an aggregated distribution and existence of disease forming foci, suggesting that FY probably has biotic origin. The materials Deli  Lame and Avros presented Pure Nugget Effect in the first and in the first two years of the study, respectively, which characterized the onset of infestation and distribution randomization. By com-paring the Spatial Dependence Index among the genetic materials, we observed a predominantly strong FDI for the Deli  Lame and Deli  Lame  materials, and moderate for the Avros material; that is, the disease dispersed in a much more aggregated way in the materials Deli  Lame and Deli  Lame , than in Avros material.The range of spatial dependence  is an important parameter in the geostatistical studies, since it indicates the radius of aggregation, that is, the distance at which spatial dependence occurs between the samples in the field. It is observed that among the three materials, Avros material presented the highest values , followed byDeli  Lame material  and Deli  Lame with a range of 853 m. This means that a diseased plant or a diseased portion of the Avros material would be influencing the health of another plant further from the other materials, that is, the radius of influence of the Avros material would be greater. In practice this would interfere whether new oil palm plantations were to be carried out, or even if a seedling nursery were implanted on the farm, for example.