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Density-Invariant Dispersion Indices and Fixed Precision Sequential EUROPEAN JOURNAL OF ENTOMOLOGYENTOMOLOGY ISSN (online): 1802-8829 Eur. J. Entomol. 115: 642–649, 2018 http://www.eje.cz doi: 10.14411/eje.2018.063 ORIGINAL ARTICLE Density-invariant dispersion indices and fi xed precision sequential sampling plans for the peach twig borer Anarsia lineatella (Lepidoptera: Gelechiidae) PETROS DAMOS 1, 2 1 Pharmacy Department, University General Infectious Diseases Hospital of Thessaloniki AHEPA, Thessaloniki, Greece; e-mail: [email protected] 2 Laboratory of Applied Zoology and Parasitology, Department of Crop Production (Field Crops and Ecology, Horticulture and Viticulture and Plant Protection), Faculty of Agriculture, Forestry and Natural Environment, Aristotle University of Thessaloniki, University Campus, Thessaloniki, Greece; e-mail: [email protected] Key words. Lepidoptera, Gelechiidae, Anarsia lineatella, sampling, spatial dispersion, integrated pest management, moth, peach production Abstract. Estimating the spatial dispersion of pest arthropods is crucial for the development of reliable sampling programs and one of the main components of integrated pest management. The natural spatial distribution of a population of a species may be random, uniform, or aggregated and can be so classifi ed based on calculation of variance to mean relations and related dispersion indices. In this work some classical density-invariant dispersion indices and related regression models are used for the fi rst time to quantify the spatial dispersion of an important peach pest Anarsia lineatella Zeller (Lepidoptera: Gelechiidae) and construct fi xed precision sequential sampling schemes. Taylor’s power law, Iwao’s patchiness regression and Nachman’s model were used to analyse the damage to peaches caused by A. lineatella. All three regression models fi t the data well, although the results indicate that Iwao’s patchiness model provides a better description of the relationship between variance and mean density. Taylor’s b and Iwao’s b regression indices were both signifi cantly smaller than 1, indicating that the distribution of individuals was uniform rather than random or aggregated. According to Green’s and Kuno’s models, the minimum sample size at the precision level of 0.2 varies from 3 samples, when total population density is more than 3 larvae/sample, to 10 samples, when population density is between 1 and 2 larvae/sample. Kuno’s fi xed sampling plan indicates that a small number of samples (i.e., 3–10 branches with fruit) is suffi cient to estimate the mean population density of A. lineatella larvae with a precision of 0.2. The Resampling for validation of sampling plans (RVSP) method confi rmed that the average level of precision of the fi xed sequential plans matched the desired precision in most cases. The sampling plan presented here provides a level understanding of A. lineatella spatial ecology suitable for pest management decisions. INTRODUCTION trients or moisture may maximize the distance between Insect sampling is a basic component in the decision individuals and result in a uniform distribution. Random making process in integrated pest management (IPM) and distribution generally occurs when resources and environ- the development of cost-effi cient sampling plans has the mental conditions are homogenous and not limited within potential to increase the adoption of IPM systems by grow- a habitat. Patchy resources, fi nally, may underlie an aggre- ers and minimize insecticide use. Nevertheless, a prereq- gated distribution, which is most common in natural envi- uisite for developing a sound sampling plan is understand- ronments (Heard & Remer, 1997), and some agrosystems ing the spatial distribution of insect populations on crops (Ifoulis & Savopoulou-Soultani, 2006; Hahn et al., 2017). (Binns & Nyrop, 1992). Southwood (1978) summarised the common methods The spatial distribution of a population refl ects its de- and related estimates used to describe the spatial arrange- mographic and behavioural responses to environmen- ment of arthropod pests. Most widespread methods include tal drivers including, food conditions, predation risk and those based on mean-variance relationships of insect num- other habitat factors (Tscharntke et al., 2002; Vinatier et ber per sampling unit through time, which provide a fi xed al., 2011). Three basic types of spatial distribution of indi- year to year relationship based on the observed sampling viduals are recognized: uniform (or regular), random and mean (Taylor, 1961, 1984; Iwao, 1968, 1975; Kuno, 1969, aggregated (or clumped) (Young & Young, 1998). Intense 1991). Other common estimates are based on the correla- competition among individuals for resources such as nu- tion between the sample mean and the variance of sam- Final formatted article © Institute of Entomology, Biology Centre, Czech Academy of Sciences, České Budějovice. An Open Access article distributed under the Creative Commons (CC-BY) license (http://creativecommons.org/licenses/by/4.0/). 642 Damos, Eur. J. Entomol. 115: 642–649, 2018 doi: 10.14411/eje.2018.063 pling units not infested by a pest population (Nachman, and all the fruit inspected (range: 10 ± 2 fruit). All the fruit on 1981, 1984). In this case, the presence or absence of in- each branch were inspected for the presence of larvae regardless sects serves as a basis for estimating the mean population of instar. The total number of peaches and of damaged peaches that signifi cantly reduces sampling cost (Bisseleua et al., was recorded for each of the branches sampled. Four branches per block per day were examined for 12 successive days (2 weeks). 2011). Sequential sampling with a fi xed precision has the Thus, for each block there were 48 datasets that were used to advantage of considerably reducing the time and cost of estimate the mean and variance for each block, yielding a total estimating insect density in contrast to conventional sam- of 12 replicates. pling, where the sample size is fi xed in advance (Hutch- Accumulated degree-days were used as a criterion to ensure that ison, 1994). Thus, in some cases only half the number of the counts made in successive years were done at the same time observations is required compared to classical sampling in terms of the development of the pest. Temperature data were (Mace, 1974). collected using a HOBO data-logging unit (Onset Computer Cor- The peach twig borer, Anarsia lineatella Zeller (Lepi- poration®). Degree-days (DD) were accumulated from March 1st doptera: Gelechiidae), causes serious problems in more and calculated assuming a linear response and a minimum base threshold for A. lineatella of 11.4°C. Data were collected daily than 44 countries that cultivate peaches (Sorenson & Gun- for ca. 2 weeks, as previously described, before harvest and after nell, 1955; EPPO Global Database, 2018) and is one of the accumulation of 850–950 DD, a period which is 1 to 2 weeks the major economic pests of stone fruits worldwide (Bala- after the peak of the second fl ight of adults (Damos & Savopou- chowsky, 1966; Damos & Savopoulou-Soultani, 2010). lou-Soultani, 2010). In this particular period, fruit changes col- Moreover, among the species that attack stone fruits, A. our, damage is easily visible and larvae have not yet left the fruit lineatella is the most serious pest and is therefore consid- in order to pupate. In addition, there was no sampling during the ered a key pest requiring the establishment and usage of period of the fi rst fl ight (overwintering generation) because the a an effective control strategy in terms of integrated pest fruit is then immature, hard and very small and larvae prefer to management (IPM). A sound IPM strategy requires the feed on the terminal shoots (indicated by shoot fl agging). development of decision tools such as sampling programs 2.3 Statistical analyses of density-invariant dispersion for determining the action to be taken (i.e., pesticide treat- indices ments). Such decision tools are, however, not defi ned for Density-invariant indices of dispersion usually overcome the most peach pests including A. lineatella. limitation of sampling scale since in most cases the size of the The purpose of this work is fi rst to develop density-in- sample unit usually has little effect on the exponent of Taylor variant dispersion indices in order to provide information Power law, which is scale invariant (Taylor, 1984; Jørgensen, 1997). Three different models and related parameter indices were on the spatial distribution of A. lineatella larvae in a fruit chosen in order to obtain a consensus on the spatial dispersion of orchard. Then, based on the information derived from the the larvae: (i) Taylor’s power law, (ii) Iwao’s patchiness regres- density-invariant dispersion indices, this paper develops sion and (iii) Nachman’s model. All indices were estimated for and validates sequential sampling plans at fi xed levels of block sizes with a constant sample size as previously described. precision to provide peach growers, plant protection advi- (i) Taylor’s power law sors and researchers a cost-effective sampling method for the peach twig borer. Compared with fi xed-sample size Taylor’s power law states that the variance in larval population size (S 2) relates to its mean density (m) as: sampling, the motivation for developing fi xed-precision 2 b sequential sampling plans for different levels of precision, S = αm (1a), is that it can result in a 35 to 50% reduction in sampling which translates into a linear relationship on a log-log scale: effort (Binns, 1994). log S 2 = log α + b log m (1b), in which the index of aggregation b is species specifi c and α is 2. MATERIAL AND METHODS considered as a sampling factor (Taylor et al., 1978). Index of ag- 2.1 Fruit orchards gregation indicates a uniform, random, or aggregated dispersion Fieldwork was conducted during three successive growth sea- if b < 1, b = 1, and b > 1, respectively. sons (2005–2007) in four nearby organic fruit orchards of the (ii) Iwao’s patchiness regression al.m.me® cooperative (Kouloura Imathias) located in Northern Iwao’s patchiness regression is defi ned as: Greece (40.539904°N, 22.310345°E).
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