Introduction

Avocado (Persea americana Mill) is one of Mexico's most important agri-food export products. The production of this fruit shows an upward trend, with Mexico being the main producer and exporter worldwide. In 2020, the national production of avocado increased 5.6 % with respect to that obtained in 2019, where Michoacán stood out as the national leader in production and export (^{Servicio de Información Agroalimentaria y Pesquera [SIAP], 2020}).

Avocado production for export is affected by pests such as seed and branch borers, thrips, mites, and several species of scales. Thrips and scales, which develop mainly on the fruit (^{Rugman-Jones et al., 2009}), cause aesthetic damage and reduce the quality of the fruit to be sold in the market. In addition, these pests increase production costs by approximately 3 %, because they are very small insects that are difficult to remove on the packing line (^{Olivares, 2017}; ^{Ripa et al., 2007a}; ^{Stocks & Evans, 2017}).

In recent years, Hemiberlesia lataniae (Signoret), known as armored scale, has become an economically important pest due to poor control (^{Evans et al., 2009}; ^{Navea & Vargas, 2012}). H. lataniae is present in several economically important hosts such as fruit trees, ornamentals, and forest hosts (^{Apostolos et al., 2010}). This pest infests branches, twigs, leaves and fruit, mainly in low and internal areas of the tree, where there is greater humidity and lower solar radiation. In high infestations, this species can weaken and even kill the attacked structures. In the case of fruits, these change slightly in color, develop depressions on their surface and may even fall from the tree (^{Lemus-Soriano, 2018}).

Infestation in orchards has been more recurrent due to climate change and over-reliance on chemical control, which is used excessively and indiscriminately. This has led to pest resistance, higher production costs (^{Park et al., 2007}), insecticide residues in consumer products, environmental pollution, loss of biodiversity and damage to health (^{Carbajal & Martos, 2019}).

In response to the growing demand for safe food and the demand for greater production (quality and quantity), at low cost and with less environmental impact, it is necessary to implement sustainable pest management strategies and methods. Furthermore, tools and techniques are required to know the distribution and behavior of phytosanitary problems; that is, to identify infestation areas. This will allow the grower to direct the different control measures more precisely, avoiding their spread to other production orchards or other crops. In this sense, geostatistics includes a set of tools used to analyze, prevent, and predict the spatial distribution patterns and behavior of a pest by means of infestation maps and semivariograms (^{Ramírez-Dávila, & Figueroa-Figueroa, 2013}).

Understanding the distribution of the armored scale is essential to develop integrated management programs; therefore, the objective of this study was to determine the spatial distribution of H. lataniae populations in the ‘Hass’ avocado crop in Estado de Mexico.

Materials and methods

The study was carried out in three ‘Hass’ avocado growing areas in Estado de Mexico: Coatepec Harinas (18° 55’ 25’’ N and 99° 43’ 7’’ W, at 2 260 m a. s. l., mean annual temperature of 24 °C and relative humidity of 62 %), Donato Guerra (19° 24’ N and 100° 18’ W, at 2 200 m a. s. l., mean annual temperature of 21 °C and relative humidity of 60 %), and Ixtapan del Oro (19° 16’ 18’’ north latitude and 100° 16’ 5’’ west longitude, at 1 640 m a. s. l., mean annual temperature of 21 °C and relative humidity of 60 %), mean annual temperature of 21 °C and relative humidity of 60 %) and Ixtapan del Oro (19° 16’ 18” N and 100° 16’ 5” W, at 1 640 m a. s. l., mean annual temperature of 18 °C and relative humidity of 65 %).

The experiment was established in one plot (4 ha) of 8 to 10 years old ‘Hass’ avocado per municipality with presence of H. lataniae. Sampling was carried out according to the quadrat methodology, which consists of dividing the plot into 100 quadrats of 20 x 20 m, 40 quadrats were taken at random per plot and 10 trees were selected, giving a total of 400 trees. Each tree was marked with a plastic band and georeferenced with a differential global positioning system (DGPS; Nomad^™ 1050 Lc, Trimble®).

The sampling methodology used to estimate armed scale infection was that described by ^{Urías-López et al. (2010)}, which consists of dividing the tree into three strata (high, medium, and low). From each stratum, a terminal branch oriented to each cardinal point (north, south, east and west) was marked and 20 cm were sampled. Samplings were performed twice a month from August 2019 to July 2020. The number of scales was quantified using a 20x magnifying glass. The insect was identified at the Colegio de Postgraduados, Campus Montecillo. To determine the normality of the data, a statistical exploration of the original data of the armored scale populations in each sample was carried out. The skewness coefficient and the kurtosis test were used for this purpose.

The most used methods to determine the type of spatial distribution of populations of biological organisms are: 1) classical statistics (dispersion index, Green's index, among others) and 2) spatial statistics (geostatistics and SADIE). The methodology of classical statistics does not consider the spatial location of the sample; consequently, it is not possible to observe the distribution of the population in the plot. On the contrary, geostatistics allows identifying the areas where infestations are present in crops, which facilitates the management and control of these problems in a timely and relevant manner. In fact, with the data obtained it is possible to elaborate spatial distribution maps and use traditional statistical indexes (^{Ramírez-Dávila & Porcayo-Camargo, 2009}); therefore, the spatial statistical method was used in this study.

Results and discussion

An aggregate spatial behavior of the insect was observed in the 24 samples. It should be noted that the concepts of isotropy and omnidirectionality were considered in each semivariogram, because the insect studied does not prefer any specific direction or area within the study plots (^{Ramírez-Dávila & Porcayo-Camargo, 2009}).

With respect to Coatepec Harinas, most of the samples were adjusted to the spherical model (Table 1). In this type of model, infestation centers are located at specific points and randomly with respect to the rest of the points sampled in the plot (^{Ramírez-Dávila & Figueroa-Figueroa, 2013}). The spherical model allows us to assume the existence of microclimates that benefit the development of the armored scale within the plot. On the other hand, the exponential model was only present in six samples. This model refers to an aggregate distribution of irregular boundaries within the plot, which presents an accelerated growth that then stabilizes.

Table 1 shows the values of the parameters analyzed. In Coatepec Harinas, sill values were obtained from 1520 to 3780, and from 14.76 to 30.34 m in range, this value was the maximum distance at which there is a relationship between the data of each sample. The nugget effect values were, in all cases, zero; this means the sampling error is minimal and the sampling scale is correct (^{Rosii et al., 1992}).

The level of spatial dependence was high in all samples, which suggests that the populations of this pest are dependent on each other and have a high level of aggregation. A variable is considered to have a strong spatial dependence if the value is lower than 25 %, moderate if the value is between 25 and 75 %, and weak if it is greater than 75 %. Such results are similar to those observed by ^{Acosta-Guadarrama et al. (2017)} and ^{Rivera-Martínez et al. (2017)}, who point out that thrips populations have a high level of spatial dependence with strong aggregates, which were observed in the incidence maps of both studies.

Having strong aggregates in one sample indicates that the distribution pattern will continue to be present in subsequent samples (Figure 1). Strong aggregates are high densities of H. lataniae populations in specific areas within plots, and where the data is closely related.

Figure 1 Density maps of armored scale populations in Coatepec Harinas. 

The semivariograms obtained with the Donato Guerra data were adjusted to Spherical, exponential and Gaussian models, although sample 11, corresponding to the first sample in January and it was the only one that was adjusted to the Gaussian model. In this model, the aggregation centers are continuously present in the plot, which allows us to assume the existence of various environmental factors that favor their dispersion and development in the plot. The values of sill, in this municipality, were found between 6.07 and 477.4, while the values of range varied between 8.84 and 19.76 m. As already mentioned, a nugget effect of zero and a high level of spatial dependence were present in all samples. These values coincide with those reported by ^{Ramírez-Dávila et al. (2013)} and ^{Maldonado-Zamora et al. (2017)}, who found that thrips populations in avocado are distributed in an aggregated manner at specific points in the plot.

In the case of Ixtapan del Oro, the theoretical semivariograms were mostly adjusted to the spherical model; only 10 samples were adjusted to the exponential model (Table 1). The range values were between 8.2 and 24.8 m. Similarly, the nugget effect was zero and a high level of spatial dependence was obtained (Figure 3). These results agree with those reported by ^{Lara-Vázquez et al. (2018)}, whose study presented a high degree of spatial dependence in red spider mite sampling in avocado crop.

Figure 2 Density maps of the armored scale populations in Donato Guerra. 

Figure 3 Density maps of armored scale populations in Ixtapan del Oro. 

In the three municipalities studied, it was determined that the ranges of the semivariograms are sufficiently high. The above indicates that the adjusted models obtained represent, mathematically, the spatial behavior of the scale throughout the study area (^{Maldonado-Zamora et al., 2017}). The cross-validation geostatistical parameters (Table 2) allowed validation of the experimental semivariograms of the three study areas at the different sampling dates.

In Coatepec Harinas, the highest densities of armed scale were found from September to May, where the first sample in January had a sample mean of 122.90 insects per tree. The months with the lowest densities were August, September, June, and July. The second sample in July had the lowest density (39.46) (Table 1 and Figure 1). It should be noted that the highest percentage of infestation was 99 % in sample five, corresponding to the first sample in October, and the lowest percentage was the second sample in August (77 %) (Table 1).

Density maps (Figure 1, 2 and 3) show the different aggregation centers. Each map shows geographic coordinates; at the bottom are the east coordinates and on the left side are the north coordinates. Figure 1 shows the largest infestation centers in the central and northern parts of the country. The months with the lowest density are distributed in the northern part, with a slight tendency towards the west side of the map, except for sample 22, which has an aggregation center in the southern part. An infestation percentage higher than 90 % was observed in most of the samples, which coincides with that reported by ^{Lara-Vázquez et al. (2018)} in the study on spider mites.

Donato Guerra reported the highest densities from November to April, with a mean of 55.88 insects per tree in sample 14. The months with the lowest density recorded a mean of 1.93 insects per tree, corresponding to the second sample in July. The highest percentage of infested area was recorded in sample 6 (96 %), and the lowest in sample 24 (77 %) (Table 1). Aggregation foci in August are located in the northwestern part of the map, and in September the foci tend to the central and southern part of the map. Aggregation foci in the months with higher density are scattered over almost the entire plot; however, aggregation centers tend to be in the center, west, and south of the map. Sample 22 has only two aggregation centers, one located on the west side and the other on the east side of the map. In the last two samples, only one aggregation center is observed on the east side of the map (Figure 2).

In Ixtapan del Oro, the sample mean was 3.41 insects per tree for sample 2, and 23.73 insects per tree for sample 14 (Table 1). The highest densities were found from December to February, where the centers of aggregation were located in the southeastern and northwestern part of the map (Figure 3). In the months from March to July, the aggregation centers were also located in the southeastern part of the map, but with lower intensity. The highest percentage of infested area was obtained in samples 9, 12 and 21 (94 %), and the lowest percentage in the first sample in August (75 %).

^{McClure (1990)} indicates that humidity and temperature play an important role in scales populations; because, at low temperatures, birth, distribution, and establishment of migratory nymphs decreases. On the contrary, with high temperatures and no rainfall, populations tend to be more abundant in their hosts (^{Balderas-Palacios et al., 2017}). ^{Ponsonby and Copland (2000)} reported that temperatures of 20 to 28 °C, and relative humidity of 55 to 65 %, are favorable for the development of Abgrallaspis cyanophylli. This suggests that climate plays an important role in the development of pests. Furthermore, climate can act as a natural mortality agent by regulating these populations.

Mean annual temperature and relative humidity records obtained from each study area were different. Coatepec Harinas reports rainfall from June to October, July was the month with highest rainfall (221 mm). Mean annual temperature was 24 °C, with mean relative humidity of 62 %. However, in the data collected, the lowest incidences were obtained from June to August, with distribution on the north side of the map.

In Donato Guerra, the mean annual temperature was 21 °C and relative humidity was 60 %. In this municipality, the highest rainfall was observed in July (140 mm), a month that had only one infestation center on the east side of the plot. In this case, the months with higher density had infestation in almost the entire plot, possibly due to favorable climatic conditions to develop. Records of Ixtapan del Oro show rainfall of 231 mm in July, mean annual temperature of 18 °C and relative humidity of 65 %. The maps show that in January and February the infestation centers go from south to north, possibly due to the winds that go in this direction. However, infestation centers in the samples from March to July are stable, which could indicate that in this area scale found favorable microclimatic conditions to develop.

In the three study areas, the armored scale had an aggregate behavior, results were verified by cross-validation of the semivariograms (Table 2). Density maps (Figures 1, 2 and 3) show the different aggregation centers, and it was evident that the armored scale infests specific points of the plots. The above coincides with that reported by ^{Duarte et al. (2015)}, who indicate that insect and mite populations are heterogeneously distributed in the zones, and generally have infestation centers in areas with high and low density. ^{Larral et al. (2018)} and ^{Sánchez-Castro et al. (2016)} determined an aggregate pattern of thrips in avocado and Empoasca spp. in beans. Also, several studies on spatial distribution have been carried out, such as the one reported by ^{Valencia-Arias et al. (2019)} of Melolonthidae in avocado crop, they had similar results to those obtained in this study.

In the present study, the insect was present on branches, leaves and fruits, which complicates its control. However, only distribution and behavior of the scales on twigs was determined because they are permanently present on branches, and on fruits and leaves the pest appears as progressive and differentiated infestations during the year (^{Faber & Phillips, 2003}).

The presence of H. lataniae on branches and fruit induces the accumulation of phenolic compounds. These compounds increase the rigidity of the cell walls of the affected part, and even decrease fruit quality and increase production costs by eliminating damage manually in the packing line (^{Hernández-Rivero et al., 2013}; ^{Sepúlveda-Jiménez et al., 2004}; ^{Ripa et al., 2007a}).

Pest management should be based on a correct identification of the pest and natural enemies, as well as on the choice of measures that cause the least disturbance to the environment and the area. In the case of the armored scale, the crucial moment for its management is the stage of migrant production, the only mobile stage of the pest and of greater susceptibility to insecticides. At this stage, scales look for a suitable place on the tree to feed and can even disperse to other hosts with the help of the wind (^{Vargas & Rodríguez, 2008}). Therefore, their movement towards the fruit should be avoided to preserve its quality.

Integrated pest management is an economically viable method, and a sustainable alternative that combines several control methods to reduce and avoid phytosanitary problems, thus reducing adverse effects on human health and the environment. This method considers the use of agrochemicals as a last resort, and aims to protect biodiversity and the environment, while increasing crop yields. This helps to minimize economic losses due to pests and to maintain crop profitability (^{Ripa et al., 2007b}). In this context, some preventive measures, such as pruning, should be considered when developing and establishing an integrated management of scale. This is done, together with weeding (hosts), with the aim of creating unfavorable conditions for the development of the pest and favorable conditions for the development of the crop. In the case of scales (whose infestation occurs in the lower part of the tree, in hidden twigs and near the ground [^{Olivares, 2017}; ^{Vargas & Rodríguez, 2008}]), this strategy benefits the entry of light and air circulation to the interior of the tree; consequently, it increases the mortality of pest stages, which limits their dispersal to other trees in the plot or crops near them.

Subsequently, monthly monitoring of twigs, leaves and fruits is recommended to estimate abundance, distribution, phenology, presence and efficiency of natural enemies of the armored scale (^{Vargas & Rodríguez, 2008}). Monitoring allows growers to obtain information that will help them make decisions and apply management and control methods in a timely and targeted manner.

Biological control is a strategy to keep orchards in balance by introducing natural enemies (parasitoids, predators) of a pest. However, in avocado-growing areas, these control agents are scarce due to excessive application of insecticides. It has been observed that the armored scale, being a cosmopolitan species, is regulated by its natural enemies (^{Peña, 2008}). In some avocado-growing areas, parasitoids and predators have been found that regulate scale populations in both the nymphal and adult stages. In Mexico, the parasitoids Encarsia citrina and Aphytus sp. and the predator Chilocorus cacti have been found (^{Lázaro-Castellanos et al., 2012}). The parasitoid Aphytis diaspidis was observed in adult populations of armored scales (^{Navea & Vargas, 2012}); however, as they do not find food, they cause mortality, since they feed on their hosts in immature stages (^{Collier, 1995}; ^{Navea & Vargas, 2012}).

^{Heraty et al. (2008)} noted that E. citrina has great adaptability, so it has been introduced in several countries for biological control purposes (^{Carbajal & Martos, 2019}; ^{Myartseva & González-Hernández, 2008}). The predators Rhizobius lophanthae and Coccidophilus citricola are efficient because they pierce the protective cover of the scale to feed on its hemolymph (^{Ripa et al., 2007b}; ^{Vargas & Rodríguez, 2008}). Many of these natural enemies have been manipulated and are currently used as ready-to-apply formulations, as is the case of R. lophanthae (^{Gómez-Vives, 2002}).

Therefore, knowing the spatial distribution of the armored scale in municipalities with high avocado production in Estado de Mexico, and the elaboration of density maps, can help to direct control measures, whether chemical, biological or cultural. To implement strategies in areas with high pest densities will help producers reduce economic losses. Moreover, to target these control measures will prevent the pest from moving to other areas within the field.

Strategies should be proposed that change the paradigm of the current management of armed scale and the rest of the phytosanitary problems that avocado have. This will reduce natural and cross-resistance in avocado pest management. Furthermore, it could raise awareness among producers and technicians about respect for the environment, since agricultural activity generates a very important percentage of environmental pollution. The results of this study can contribute to the restructuring and improvement of the control of the armed scale based on the use of geotechnologies that allow us to make the work in the field more efficient.

Conclusions

Geostatistics is an effective tool to determine the behavior and spatial distribution of armed scale in avocado crop in the municipalities of Coatepec Harinas, Donato Guerra and Ixtapan del Oro. Population density maps allow us to know the fluctuations, as well as the position of the pests within the plot. This is of great help in proposing and implementing integrated management strategies to reduce the presence of insecticides in the fruit, and ecological and environmental damage due to their indiscriminate use.