ESTIMATION OF THE AVERAGE NUMBER OF EGGS IN LAYING OF LYMANTRIA DISPAR IN SAMARA REGION

Седельников А.В.

Кандидат физико-математических наук, Самарский государственный аэрокосмический университет имени академика С.П. Королёва

ОЦЕНКА СРЕДНЕГО ЗНАЧЕНИЯ КОЛИЧЕСТВА ЯИЦ В КЛАДКЕ LYMANTRIA DISPAR, ОБИТАЮЩЕГО В САМАРСКОЙ ОБЛАСТИ

Аннотация

В статье получены данные о среднем значении количества яиц в кладках Lymantria Dispar популяции, обитающей на территории Самарской области. Обсуждены статистические методы и погрешности полученных результатов. Проведён сравнительный анализ с данными других авторов.

Ключевые слова: Lymantria Dispar, вредители леса, кладка яиц.

 

Sedelnikov A.V.

PhD in Physics and Mathematics, Samara State Aerospace University named after S.P. Korolyev

ESTIMATION OF THE AVERAGE NUMBER OF EGGS IN LAYING OF LYMANTRIA DISPAR IN SAMARA REGION

Abstract

The article introduces the data about average number of eggs on layings of Lymantria Dispar population which inhabits the lands of Samara Region. There are discussed the statistic methods and result errors in the article.  Confirmation with the data of other authors is carried out.

Keywords: Lymantria Dispar, forest pests, egg laying.

Insects-phyllophages significantly hurt forestries. It determines the importance of research connected with vital functions of the insects. Accurate and contemporary determination of physical and biological parameters of populations makes it possible to predict the mass outbreaks in reproduction and to apply preventive measures. It provides minimization of the damage by insects-phyllophages’ activity.

Caterpillar Lymantria Dispar is a representative of insects-phyllophages. The caterpillars feed on more than 300 species of different plants which include conifers [1, p. 263].  Outbreaks in reproduction of Lymantria Dispar lead to mass defoliation in sizeable forestries and even in dachas, because one caterpillar can eat about 200-300 grams of live green weight during 35-50 days.

Nevertheless of the large amount of conducted researches about Lymantria Dispar, which are regularly financially supported, outbreaks in reproduction of Lymantria Dispar are regular and claim the great attention since it was extended in the North America [2, p. 49]. On the other hand increasing artificial influence on the nature as a whole and on the Lymantria Dispar in particular (mainly chemical and biological influence) leads to changes in physical and biological parameters of populations and to mutations of the specie. That is why monitoring of these parameters in different regions of Lymantria Dispar’ natural habitats with the aim of comparison with conducted researches for more accurate prediction of outbreaks in reproduction is of great urgency.

This paper deals with population of Lymantria Dispar in Krasnoglinskiy forest of Samara Region. The forest includes deciduous species, mainly oak, aspen, linden, birch and maple [3, p. 2]. he last outbreak in reproduction of Lymantria Dispar in Samara Region was marked in Shigonsk district in 2015. Around 70% of oak wood was damaged there [4]. The previous survived egg layings were studied. The 64 layings were fond out.

The volume of egg laying was estimated on the basis of its square. For the purpose the typical sizes of egg for 64 eggs from different layings were determined by statistical treatment of sizes. Maximum size is equal to 1,267±0,0091mm and minimum size is equal to 0,548±0,0034mm. These data absolutely agree with research results which are shown in [5, p. 8]. Then the typical middle square of egg as square of ellipse with axes related to typical egg sizes was determined. It was 0,5453±2,5·10-5 mm². Thus, an amount of eggs in laying can be supposed on the basis of estimated square of the laying. If total sum of squares of eggs was considered to be equal to square of the laying the estimation of eggs amount would be significantly overstated. So egg laying with square equal to 3 sm² includes 550 eggs.  However, even if eggs were closely packed in the laying one ellipse would touch with four neighboring ones.  That is why estimation on the basis of square of rectangle with sides related to axes of ellipse is more reliable. Then egg laying with square equal to 3sm² would include 430 eggs. It differs in 22% from results of previous estimation. Estimated values of egg laying volumes oscillated from 100 to 1350 eggs in one laying while the middle value was equal to 389 eggs. It conforms to research data in neighboring to Samara Orenburg Region which are shown in paper [6, p. 69]. Sampling of statistical material conforms to accuracy shown below:

,                                                           (1)

where  – root-mean-square deviation;  [7, p. 66];  – Laplace function. Confidence probability is suggested to be , then   and error of estimator according to (1):

.

Increase in amount of egg laying for determination of middle value of eggs can help to raise accuracy of estimate. However it is necessary to take into account factors mentioned below:

– measuring error in determination of typical sizes of egg layings;

– miscalculation in square of layings connected with differences between the shapes of the layings and the geometrical figures;

– error of estimate by the area method connected with hollow space between eggs which are not accounting for estimation;

– error connected with difference between real size sizes of eggs in certain laying and the middle value.

That is why real raise of accuracy is possible only in 10-15%. It should be accounted for treatment of statistical data by well-known mathematic programs such as Statistica and SPSS. Increasing in amount of analyzed biomaterial can’t influence four types of errors mentioned above. However it can cause illusion of significant improvement of estimation accuracy. It is necessary to apply more accurate valuation methods of basic physical and biological parameters of prototype system for real improvement of the accuracy [8].

To conclude it is necessary to pay attention to the one of the significant factors. In some of literature the estimation of middle value by maximum-likelihood method considered to be undoubted:

.                                                        (2)

Formula (2) is included in each mentioned programs of treatment of statistical material. However, this estimation is not exactly undoubted according to the practice. For example, the second simple value of Dixon [9, p. 100 ] allows escaping from possible samplings in statistical material. This estimation doesn’t account two extreme values from series ranked according to the growth. The estimation is mentioned below:

.                                                 (3)

In concerned statistical material the middle value gotten by (3) is equal to 379. The main problem of estimation by maximum-likelihood method (especially with small samplings) is instability to deviation of partition law of concerned value from normal. It is efficiently to apply Kenuai rapid assessment for five quantiles to smooth out these disadvantages [9, с. 102]:

.                                          (4)

Accounts for 64 layings by (4) are listed below:

.

These estimation is a powerful instrument if effectiveness equals 0,93 and absolute insensitivity to deviation from normal partition law is available. At last, in case of lack of statistic material Hodges–Lehmann estimator is absolutely indispensable. It is one of the best accurate estimators of middle value. The estimator consists in determination of median of Walsh middle row [9, с. 103].  There is  for Walsh middle row which consist  of n points. Thus, concerned sampling of 64 layings can be widened by Walsh middle row to 2016. In that way the middle value is equal to 352.

References

1. Vorontsov А. I. Lesnaja jentomologija. М.: Vysshaja shkola, 1982. 384 p.
2. Forbush E. H. The Gypsy Moth. – Boston: Wright&Potter Printing Co., 1896. 544 p.
3. Lesnoj plan Samarskoj oblasti [Electronic resource] URL: http://www.priroda.samregion.ru/forestry_sector/forest_plan/ (Accessed 07.11.2015).
4. Prognoz razvitija lesopatologicheskoj situatsii v nasazhdenijah Orenburgskoj i Samarskoj oblastej na vtoroe pjlugodie 2015 goda [Electronic resource] URL: http://orenburg.rcfh.ru/news/3147.html (Accessed 07.11.2015).
5. Turova G. I. Neparnyj shelkoprjad (Lymantria Dispar L.) v lesah Dal’nego Vostoka (rasprostranenie, biologija, hozjajstvennoe znachenie, osobennosti nadzora): Avtoref. dis. kand. biol. nauk. – Krasnojarsk, 1992. – 23 p.
6. Simonenkova V. А. Jekologicheskie osobennosti nasekomyh-fillofagov v lesnyh jekosistemah Yuzhnogo Predural’ja: dis. dokt. biol. nauk. – Orenburg, 2014. – 433 p.
7. Hruscheva I. V., Tsherbakov V. I., Levanova D. S. Osnovy matematicheskoj statistiki i teorii sluchajnyh prozessov. – SPb.: Lan’, 2009. – 336 p.
8. Sedel’nikov А. V. Osnovnye pokazateli dlja sravnitelnogo analiza vyzhivaemosti gusenits Lymantria Dispar v laboratornyh i estestvennyh uslovijah: sb. st. Mezhdun. nauch.-prakt. konf., Sterlitamak, 2015. 193 p.
9. Kobzar’ А. I. Prikladnaja matematicheskaja statistika. – М.: Fizmatlit, 2006. – 816 p.