Semivariogram models for estimating fig fly population density throughout the year

Abstract

-The objective of this work was to select semivariogram models to estimate the population density of fig fly (Zaprionus indianus; Diptera: Drosophilidae) throughout the year, using ordinary kriging. Nineteen monitoring sites were demarcated in an area of 8,200 m 2 , cropped with six fruit tree species: persimmon, citrus, fig, guava, apple, and peach. During a 24 month period, 106 weekly evaluations were done in these sites. The average number of adult fig flies captured weekly per trap, during each month, was subjected to the circular, spherical, pentaspherical, exponential, Gaussian, rational quadratic, hole effect, K-Bessel, J-Bessel, and stable semivariogram models, using ordinary kriging interpolation. The models with the best fit were selected by cross-validation. Each data set (months) has a particular spatial dependence structure, which makes it necessary to define specific models of semivariograms in order to enhance the adjustment to the experimental semivariogram. Therefore, it was not possible to determine a standard semivariogram model; instead, six theoretical models were selected: circular, Gaussian, hole effect, K-Bessel, J-Bessel, and stable.Index terms: Zaprionus indianus, geostatistics, integrated pest management, monitoring, regionalized variables, spatial dependence. Modelos de semivariogramas para estimar a densidade populacional da mosca-do-figo ao longo do anoResumo -O objetivo deste trabalho foi selecionar modelos de semivariogramas para estimar a densidade populacional da mosca-do-figo (Zaprionus indianus; Diptera: Drosophilidae) ao longo do ano, com uso da krigagem ordinária. Dezenove locais de monitoramento foram demarcados em área de 8.200 m 2 , cultivada com seis espécies de frutíferas: caquizeiro, citros, figueira, goiabeira, macieira e pessegueiro. Durante um período de 24 meses, foram realizadas 106 avaliações semanais nesses locais. O número médio de moscas-do-figo capturadas semanalmente por armadilha, por mês, foi submetido aos modelos de semivariogramas circular, esférico, pentaesférico, exponencial, gaussiano, quadrático racional, seno cardinal, K-Bessel, J-Bessel e estável, por meio de interpolação por krigagem ordinária. Os modelos com melhor ajuste foram selecionados a partir da validação cruzada. Cada conjunto de dados (meses) tem uma estrutura de dependência espacial específica, o que torna necessário definir modelos específicos de semivariogramas para melhorar o ajuste ao semivariograma experimental. Portanto, não foi possível definir um modelo padrão de semivariograma; ao invés disso, seis modelos teóricos foram selecionados: circular, gaussiano, seno cardinal, K-Bessel, J-Bessel e estável.Termos para indexação: Zaprionus indianus, geoestatística, manejo integrado de pragas, monitoramento, variáveis regionalizadas, dependência espacial.

Interpolators in predicting the estimated population density of Oebalus spp.

“…The asymmetry values reveal that the evaluations for species in crop data was positive ( Table 1). The difference between the farming in the average values of adults per m 2 (Table 1) reflects the dispersal ability of the species because a smaller crop area have a tendency to have higher population densities than most farming areas (Pasini et al, 2014). Such observation was possible since the cropped areas present similar host plants along their surroundings in their constitution.…”

“…In all evaluations, the presence of spatial dependence was confirmed in the tested models (Table 2). This result indicates that the spatial dependence greatly contributes to the variability of the data inferences by OK for theoretical models of semivariograms performed in evaluations and crops (Pasini et al, 2014;Pasini et al, 2015). In cross validation (Table 3 and 4), most models with the largest sum of scores did not achieve the highest score for all indicators, revealing a discrepancy among the estimated values.…”

“…in which the semivariance and N(h) are the number of pairs of the measured values Z(x i ) and Z(x i +h), separated by an h vector. From the experimental semivariograms, 11 theoretical models of semivariograms, Circular, Spherical, Tetraspherical, Pentaspherical, Exponential, Gaussian, Rational quadratic, Hole effect, K-Bessel, J-Bessel and Stable, were adjusted according to Johnson et al (2001) and Pasini et al (2014). By using the algorithm of weighted least squares, these models were adjusted to the experimental semivariogram, and the model parameters were defined: nugget effect (C 0 ), sill (C 0 +C 1 ), and range (a).…”

“…In order to verify the existence of spatial dependence, the spatial dependence index (SDI) was applied. This index is the ratio representing the percentage of data variability explained by spatial dependence (Pasini et al, 2014). After confirmation of spatial dependence, inferences were performed by ordinary kriging (OK) according to Johnson et al (2001).…”

“…Insect populations in croplands can be estimated with the use of interpolation procedures, which are able to generate continuous surfaces by single point sampling units (Soares et al, 2008). Among the kriging interpolation methods, the inverse of the weighted distance is more used (Coelho et al, 2009;Souza et al, 2010;Silva et al, 2010;Dinardo-Miranda et al, 2011;Pasini et al, 2014;Pasini et al, 2015;Pazini et al, 2015). The ordinary kriging (OK) method uses the spatial dependence among neighboring samples, expressed in the semivariogram to estimate values at any position in the field not using trend and with minimum variance (Mello et al, 2003).…”