RU2010515C1 - Method for determining development of pentatomid larvae - Google Patents

Abstract

FIELD: agriculture. SUBSTANCE: method involves determining dates of development of pentatomid larvae as a sum of earlier determined dates of emergence of first egg layings and time of egg development. Time of development is calculated mathematically from submitted relation. EFFECT: higher efficiency. 1 dwg, 1 tbl

Description

 The invention relates to agriculture, namely to protect plants from pests, and can be used to develop forecasts for the timing of the appearance of harmful turtle larvae in winter wheat fields.

 Larvae of a harmful turtle damage mainly wheat grain, which is especially dangerous for the crop, since it is almost impossible to compensate for its losses at this time. Therefore, for agricultural production, it is important to have accurate information about the possible timing of the appearance of pest larvae in winter wheat fields, so that using various methods of pest control, to prevent them from causing significant losses to the wheat crop - this main grain crop.

 There are several methods for predicting the timing of the appearance of various phases (stages) of crop pests, including by determining the duration or inverse of it — the rate of development of individual phases of the pest.

exp

- a(T-t²)

dt, (1) где Y_o - максимальная скорость развития;
Т - температура, соответствующая значение Y_o, в ^оС;
а - постоянный коэффициент, характеризующий скорость изменения Y относительно t.So, for example, a method is known for determining the rate of development of insects at variable temperatures (t _min <t <t _max ), based on the use of an integral form of an equation of the type:
Y (t _max -t _min ) = Y _o

exp

- a (Tt ² )

dt, (1) where Y _o is the maximum development rate;
T is the temperature corresponding to the value of Y _o , in ^o With;
a is a constant coefficient characterizing the rate of change of Y with respect to t.

To solve this integral, it is proposed to divide the temperature range from t _min to t _max into n equal parts and use the rather cumbersome Simpson formula to obtain the result using the parabola method.

 This method for practical calculations is very complicated, cumbersome and difficult to access for plant protection service workers.

 The closest technical solution is a method for determining the duration of development of a harmful bug larva by the method of summing effective temperatures, which is a prototype.

, (2) где m - длительность развития, в сутках;
СЭТ - сумма эффективных температур за данный период развития, ^оС;
Т - средняя температура за период, в ^оС;
t_o - нижний термический порог развития данной фазы вредителя, ^оС.In this case, the duration of development of a particular phase or period of activity of a harmful turtle is found as
m =

, (2) where m is the duration of development, in days;
SET - the sum of the effective temperatures for a given period of development, ^о С;
T - average temperature in the period in ^C;
t _o - lower thermal threshold for the development of this phase of the pest, ^about C.

This method is much simpler, more accessible and more convenient for practical calculations and it is widely used for forecasting at present. However, it has one, but a significant drawback - the method does not have high accuracy, which is due to the following reasons:
Firstly, in various climatic zones, for example, in all regions of Ukraine, where the pest is of economic importance, the sum of the effective temperatures necessary for the development of the same phase of the development of the pest will be different. For example, for the egg stage Eurygaster it may vary by 5-15 ^{° C,} for larval stage - 50-70 ^o C, etc...

 Secondly, the accuracy of determining the lower thermal thresholds for the development of various stages of a harmful bug does not exceed tenths of a degree, which also introduces a corresponding error in the calculation of their developmental duration.

 Thirdly, and this is very significant, the sum of the effective temperatures necessary for the development of an egg of a harmful bug, as a rule, also includes the temperatures recorded from the moment of arrival of the first adults (bugs) of the overwintered generation of the pest, and not from the moment of the first laying of eggs, which also leads to an increase in the calculation error.

 Finally, insect development durations calculated from the sums of effective temperatures are close to reality only in a relatively narrow range of average temperatures approaching optimal for an insect species.

 The aim of the proposed method is to increase its accuracy.

 The positive effect consists both in increasing the accuracy of determining the timing of the appearance of harmful turtle larvae in winter wheat fields, and in obtaining this information at least two decades before their actual appearance in winter wheat fields, and therefore the necessary and timely effective pest control measures, which will help to reduce wheat crop losses and environmental pollution, that is, the economic and environmental efficiency of the proposed method is also provided.

The method is based on taking into account the temperature characteristics of the environment, characterized in that, in order to increase its accuracy, determine in the field the timing of the first oviposition of a harmful turtle in the fields of winter wheat, and the timing of the appearance of larvae is determined as the sum of the period of occurrence of the first oviposition and the duration of development of the egg stage pest, while the duration of development of the egg is determined by the formula
N = (0.2569 + 0.0358T _cf. - 0.0009T _cf. ² ) ^-1 (3) where N is the duration of egg development, in days;
T _cf. - the average air temperature according to the weather service two decades ahead, ^about C.

 A comparative analysis of the claimed solution with the prototype shows that the claimed method differs from the known one in that: firstly, a new operation appears in it — the determination in the field of the period of occurrence of the first oviposites of a harmful turtle and secondly, the number of temperature characteristics is reduced (with three to one), which not only did not worsen the quality parameters of the method, but, on the contrary, significantly improved them, sharply increasing the accuracy of the method.

, (4) где

;

;

- частные производные функции f по переменным "а", "b" и "с".The following is a mathematical analysis of the basic calculation formulas used in the prototype and in the claimed method for the maximum absolute error, defined as the boundaries of the confidence interval of the function from the expression:
Δf =

, (4) where

;

;

- partial derivatives of the function f with respect to the variables "a", "b" and "c".

=

-

(5)
Тогда, используя выражение (4), получаем:
ΔV=

(6)
Определяя частные производные функции (5), будем иметь:

=

, (7)

= -

, (8)

= _ (T-t_o)·

(9)
Подставляя полученные значения частных производных (7,8 и 9) в выражение (6), получаем:
ΔV =

. (10)
Задавшись реальными значениями абсолютных погрешностей ΔТ, Δ t₀ и Δ CЭТ и практическими результатами Т, t₀ и СЭТ для случая развития яйца вредной черепашки как Δ T = Δ t₀ = 0,1^oC, ΔСЭТ = 10^оС, Т = 18^оС, t₀ = 10^оС и СЭТ = 90^оС, будем иметь:
ΔV =

= 0,01
(11) или в процентах Δv' = 1% .In the case of the prototype, when determining the rate of development (v) (v is the reciprocal of the duration of development), we will have
V =

=

-

(5)
Then, using expression (4), we obtain:
ΔV =

(6)
Defining the partial derivatives of the function (5), we will have:

=

, (7)

= -

, (8)

= _ (Tt _o )

(9)
Substituting the obtained values of the partial derivatives (7.8 and 9) into expression (6), we obtain:
ΔV =

. (10)
Given the real values of the absolute errors ΔТ, Δ t ₀ and Δ CET and the practical results of T, t ₀ and CET for the case of development of a harmful tortoise egg as Δ T = Δ t ₀ = 0.1 ^o C, Δ СET = 10 ^o C, T = 18 ^о С, t ₀ = 10 ^о С and СЭТ = 90 ^о С, we will have:
ΔV =

= 0.01
(11) or in percent Δv '= 1%.

= W = 0.2569 + 0.0358 T_ср - 0.0009 T $\genfrac{}{}{0ex}{}{\text{2}}{\text{с}}$ _р , (12) получаем значение ΔW, как
ΔW =

⁼

^ΔTcp (13)

= 0.0358 - 2 × 0.0009× T_ср= 0.0358 -0.0018 T_ср (14)
Подставляя значение (14) в выражение (13), будем иметь:
Δ W = (0,0358-0,0018 х Т_ср./ ΔТ_ср. (15)
Задавшись реальными значениями ΔТ_ср. = 1^оС и Т_ср. = 18^оС, получаем: ΔW = = (0,0358-0,0018 х 18/х1 = 0,0034 или в процентах ΔW' = 0,34% .Mathematically analyzing the formula (3) used in the proposed method for the maximum absolute error for the development speed of the harmful turtle egg, from the expression:

= W = 0.2569 + 0.0358 T _avg - 0.0009 T $\genfrac{}{}{0ex}{}{\text{2}}{\text{with}}$ _p , (12) we obtain the value ΔW, as
ΔW =

⁼

^ΔT cp (13)

= 0.0358 - 2 × 0.0009 × T _avg = 0.0358 -0.0018 T _avg (14)
Substituting the value (14) into the expression (13), we will have:
Δ W = (0.0358-0.0018 x T _cf. / ΔT _cf. (15)
Given the real values of ΔT _cf. = 1 ^about C and T _cf. = 18 ^{° C.,} we obtain: ΔW = = (0,0358-0,0018 x 18 / 0.0034 = x1 or percentage ΔW '= 0,34%.

=

= 3,2 (16) т. е. имеем повышение точности в предложенном способе в 3,2 раза.Comparing the obtained errors for the prototype case and the proposed method, we obtain:

=

= 3.2 (16), i.e., we have a 3.2-fold increase in accuracy in the proposed method.

 Thus, using only the operation of determining the average predicted temperature for a period of two decades after the laying of eggs by a harmful turtle, and not of three values (SET, average temperature and lower thermal threshold of egg development), as is done in the prototype, in the proposed method we obtain a new positive effect - a significant increase in the accuracy of determining the timing of the appearance of the larval stage of the pest.

 The two-decade period is justified by the fact that the maximum period of development of harmful tortoise eggs under natural conditions, as a rule, does not exceed 20 days.

 The use of the operation of preliminary determination of the time of occurrence of ovipositor eggs of a harmful turtle in winter wheat fields also helps to increase the accuracy of determining the time of occurrence of pest larvae, since this reduces the time for which forecasting applies.

The drawing shows the dependence of the duration of the egg stage Eurygaster (N) in days on the average temperature of eggs dvuhdekadny development period (T) in ^{° C,} obtained for long-term (17-20 years) and the time interval averaged according to the areas of Ukraine where the harmful bug has economic value as a pest of winter wheat.

 This dependence has a nonlinear character, passes through its extreme minimum, and allows one to determine, by any known temperature value, the strictly determined value of the duration of development of an unhealthy bug egg.

The invention is as follows:
In the field, the dates (dates) for the appearance of the first ovipositions of the bug in the fields of winter wheat are determined. Then, according to the forecasts presented by the weather service for a given area of air temperatures, their average value for a two-decade period after the period of occurrence of the first oviposition of a harmful turtle is determined. Using the formula (3) or a graph for this average air temperature (T), determine the duration of the development of the pest egg (N). Adding to the period (date) of the appearance of oviposition of a harmful turtle the duration of egg development, found by formula (3) or schedule (1), one obtains the date (date) of appearance of the harmful turtle larvae.

 The table shows the calculation results obtained by comparing the actual data for 20 years (1966-1985) and predicted by the proposed method for the conditions of the Poltava region (Poltava signaling and forecasting point).

=

= 0,947
(17) будет весьма высоким, достигая величины, равной η= 94,7%
Проведенные аналогичные расчеты для других областей Украины, где вредная черепашка имеет экономическое значение, как опасный вредитель озимой пшеницы, показывают, что между прогнозируемыми по разработанному способу и фактическими многолетними данными зависимости длительности развития яйца вредной черепашки от средней температуры воздуха за период развития, существуют очень тесные корреляционные связи со средним значением коэффициента корреляционного отношения η= 0,84.As follows from the calculations, the correlation coefficient between the actual and predicted by this method, the duration of the development of the eggs of harmful turtles, determined by the formula
η =

=

= 0.947
(17) will be very high, reaching a value equal to η = 94.7%
Similar calculations for other regions of Ukraine, where the harmful turtle is of economic importance as a dangerous pest of winter wheat, show that between the predicted by the developed method and the actual long-term data, there are very close dependences of the duration of development of the harmful turtle egg on the average air temperature over the development period correlation with the average value of the coefficient of the correlation ratio η = 0.84.

 Thus, as follows from the data obtained, the proposed method can be successfully used in all areas where the harmful bug has economic value, for example, in all 12 regions of Ukraine, i.e., the utilization rate of the method is very wide and the results of the reliability of the forecasts obtained according to the developed method, an average of 84% (from 74.2 to 94.7%).

Using the proposed method for determining the timing of the appearance of harmful bug larvae provides the following advantages compared to existing methods:
1. The accuracy of determining the timing of the appearance of harmful turtle larvae in winter wheat fields is increased, since the accuracy of determining the duration of development of the harmful turtle egg stage is more than three times higher, which is done by eliminating the dependence of the duration on three temperature characteristics and introducing this dependence on only one average temperature.

 2. The developed method allows to increase its utilization for large regions of the country, for example, for all regions of Ukraine, where a harmful bug has economic significance, while ensuring the reliability of the forecasted dates by an average of 84%.

 3. Due to the increased accuracy in determining the timing of occurrence of harmful bug larvae and obtaining this information at least two decades before their actual appearance in winter wheat fields, in practice, the necessary and effective pest control measures can be taken in a timely manner, which will help reduce losses wheat harvest and environmental pollution, i.e., corresponding economic and environmental effects will be ensured. (56) Makarov L.A., Doronina G.M. Methods for predicting the phases of the dynamics of harmful turtle populations, planning the volumes of protective treatments, signaling, and the timing of their implementation. L.: VNIIZR, 1985, p. twenty.

Claims (1)

METHOD FOR DETERMINING THE PERIODS OF APPEARANCE OF HARMFUL TURTLE LARVAS, including taking into account the temperature characteristics of the environment, characterized in that in the field the timing of the appearance of the first ovipositions of the harmful tortoise in winter wheat fields and the duration of the development of the pest egg stage are determined, and the timing of the appearance of the larvae is determined as the sum of the appearance time of the first oviposition and the duration of the development of the stidia of the egg of the pest, while the duration of the development of the egg stage is determined by the formula
N = (0.2569 + 0.0358T _cp -0.0009T _cp ² ),
where N is the duration of the development of the egg stage, days;
T _cf - the average air temperature according to the weather service for two decades ahead, ^o C.

Images