laboratory-reared populations of Lymantria dispar, as well as to understand the dynamics of population

development in the natural environment.

Key-Words: Lymantria dispar, laboratory-reared population, development model, algorithm for experimental

estimation.

Received: April 21, 2022. Revised: October 13, 2022. Accepted: November 22, 2022. Published: December 15, 2022.

1 Introduction

Modeling the development of laboratory-reared

populations requires a rigorous mathematical

multifactorial process in sufficient detail even under

conditions of long-term observation of the

population. Therefore, their clarification and

addition is an important and urgent task in studying

the development of populations. This clarification

can take various forms.

regarding the temperature threshold from which the

sum of effective temperatures should be calculated

when hatching caterpillars from eggs, when

others. However, there are more complex ideas

about the threshold values, for example, that they

vary depending on the period of eggs stay at low

temperatures, [5], or some other factors, [6], [7]. In

with a new parameter and developing an algorithm

for its experimental evaluation. It will increase the

adequacy and correctness of the development

model.

It is known that under natural conditions the

formation and development of Lymantria dispar

caterpillars in the egg occurs in autumn, [7]. They,

as a rule, go into diapause after full formation. In the

literature, cases of caterpillars' non-diapause

development are known both in nature, [16], and

under laboratory conditions, [1]. The introduced

parameter will not make sense for a non-diapause

population since during the development of such a

population there is no effect of low temperatures on

caterpillars in eggs and the normal course of

diapause, a sufficient amount of heat in autumn and

moderate cold at the beginning of winter are

necessary, [7]. It is possible to fix one of the

parameters in laboratories. Thus, the sum of

effective positive summer-autumn temperatures was

recorded for all generations at the level of +580 ± 10

was experimentally established that with such a

distribution in nature compared to laboratory

conditions does not make it possible to obtain a

relatively simple mathematical model.

population is placed in a refrigerator at a

constructing a development model is the duration of

the period of exposure to low temperatures, during

which normal development of caterpillars will be

observed. It is obvious that this duration should

caterpillars will stop hatching altogether. The

condition for the hatching of at least a third of viable

eggs will be fulfilled in a certain range of D values

since hatchability is a continuous function of D. Of

gradual disappearance. It means either a reduction in

the habitat or the adaptability of the population to

new conditions. The first scenario is the most

probable with the Dneed min value not changing

significantly. If, on the contrary, its value tends to

decrease, then this indicates a gradual adaptability

and development towards a non-diapause

population. Global warming can lead to the

formation of a stable natural non-diapause

population, especially since such laboratory-reared

Based on the problem being solved, two approaches

to estimation are possible: according to the required

accuracy and according to the available source

material. The first approach assumes the presence of

satisfy the required estimation accuracy. We choose

approach. Therefore, we will have to use previous

experience, if available, and simple considerations.

For example, it hardly makes sense to use a step size

of less than one day. In this case, it will be difficult

to calculate the effective temperature, which can

lead to a decrease in the estimate accuracy.

Otherwise, the algorithm for estimating the

conditional threshold for the duration of exposure to

low temperatures will coincide with the first

approach.

exposure to low temperatures, but also the error

estimation. There are two types of errors to

consider. The first of them is a statistical error

associated with the limited sample N0. The second

error, as mentioned above, is related to the

approximation error. Then the total error will be the

sum of these two errors. For the number of hatched

caterpillars, the statistical error will be determined

by inequation (3). Table 1 provides some data on the

estimation accuracy and the sample size required to

dependence. For this purpose, we need to calculate

the regression residuals

indicator is reasonable and is associated with the

main parameters describing the development of the

laboratory population.

fertilized eggs were used in the experiments.

account errors (3) and (6), we obtain:

Thus, it was found that for the duration of

exposure to low temperatures

the condition

development of the laboratory-reared population of

Lymantria dispar, which is a conditional threshold

for the duration of exposure to low temperatures. An

algorithm for estimating this parameter using

experimental data is given. The calculation of the

estimation error is presented. This parameter can be

used to study the applicability of the Eigen quasi-

species model for the correct description of the

development of the laboratory-reared population of

Lymantria dispar.

References:

[1] Meshkova V.L., Seasonal development of

[2] Furuta K., Developmental zero temperature and

[4] Hihashiura Y., A method to forecast the dates

[5] Rubtsov I.A., Influence of constant and

[16] Kozhanchikov I.V., Peculiarities of wintering

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Sources of Funding for Research Presented in a

There is no funding provided to prepare the