Selection of Scots pine seedling growth stimulants in extreme conditions of the Northern Kazakhstan steppe zone

The aim of this research is to determine optimal methods of using stimulants in a pre-sowing treatment of common pine seeds to increase their germination and obtain high-quality planting material. A study has been performed in forest nurseries of the State Forest Natural Reserve (SFNR) “Ertis Ormany” (Pavlodar region) and the Arykbalyk Branch of the State National Natural Park (SNNP) “Kokshetau” (Akmola region). The research is done with one-and two-year-old seedlings of ordinary pine sowing of 2017. A presowing seed preparation is carried out according to six options by using various types of stimulants. A method of mathematical processing of the thus obtained measurements of the seedlings with an insufficient number of measured plants is proposed by using a bootstrap analysis with and without quantile information. It allows one to estimate the influence of stimulants on the average growth of one-and two-year-old seedlings at a reliable level. As a result of these studies, it has been revealed that the pre-sowing treatment of pine seeds with ordinary stimulants increases the average height of annual seedlings. However, the results obtained in this experiment depend on the region of nursery location, but the use of soil irrigation with an “EridGrow” activator has increased the average height in both nurseries: by 13.9% in the “Kokshetau” SNNP for one-year-old seedlings, by 37.2% for two-year-old seedlings compared with the average height of the control seedlings. For pine seedlings in the “Ertis Ormany” SFNR nursery the influence of the stimulants is insignificant, but the positive effect on the average growth with the “EridGrow” soil irrigation is a 7.3% increase in the first year and a 24.7% one in the second year.


Introduction
The effectiveness of forestry operations largely depends on the quality of planting material, which can only be grown in optimal environmental conditions [1]. If agricultural technology does not ensure the modeling of optimal conditions and acquisition of well-developed seedlings throughout the entire period of planting material growth, such planting material will take longer and harder to grow in forest crops in the first years. Since in Kazakhstan the cultivation of seedlings in forest nurseries is carried out according to extensive technology, the planting material is rarely standard and its output per unit area does not meet the GOST. Furthermore, the existing recommendations are outdated with the emergence of new means of mechanization, various bio-based additives and methods of growing seedlings. There are numerous works in the scientific literature dedicated to innovative methods of growing planting material, including the use of various stimulants, but they are scattered in nature, and the research results vary depending on the type of stimulants used, research regions, and tree species. Therefore, there is a need for careful development of regional recommendations. Plant growth stimulants are actively used in agriculture, and there are many methods for plant growth escalation [2][3][4]. In the near-abroad and far-abroad countries, new methods are being developed for pre-sowing treatment of woody plant seeds using stimulants [7][8][9], fungicides [10], unconventional preparations [11], various radiation treatments, and others [12]. The researchers have found that soaking seeds in accounting segment was selected on each line in two replicates, on which at least 100 seedlings were measured. The plant height was measured from the soil surface to the apical bud with an accuracy of 0.1 cm. The control was seeds and seedlings of Scots pine grown without the use of stimulants. Tables 1-4 and Figures 1-2 show the initial indicators of the considered samples for the nurseries of the SNNP "Kokshetau" and SFNR "Ertis Ormany" for 2016 and 2017.

The results and discussion
Note that in the nursery of the SNNP "Kokshetau" all stimulants led to an increase in the tree growth compared to the control group of seeds which was not exposed to any treatment, while the improvement in the average growth was more significant after the second year of plant life (Tables 1,  2). The best results for both years were obtained by the use of the "Humate + 7 trace elements" stimulator and the "EridGrow" irrigation. A year after treatment "EridGrow" irrigation showed an increase in height by 14.1%, after two years by 37.2%, while the stimulator "Humate + 7 trace elements" showed an increase by 20.2% and 30.4% compared to the tree height of the control group. For the nursery in the SFNR "Ertis Ormany", the influence of stimulants was not so apparent (Tables  3, 4). A stable, albeit insignificant positive effect for two years was achieved by irrigation with the "EridGrow" stimulator with an increase by 7% in the first year and 24.7% in the second year.
It can be seen from the figures that in the different nurseries the height of the plants is significantly different; however, the effect of stimulants on the average growth shows some similarities. Note that the sizes of the samples vary widely depending on the year of life of the seedlings and the nursery location. Moreover, the measurement results were rounded or not accurate enough (the accuracy was 5 mm), which ultimately led to the lack of data normality and, consequently, to the inability to use standardized statistical procedures to show the presence of differences in the samples. As a result, to identify the influence of stimulants on the average plant growth, the bootstrap sample propagation method was used [22], which allows one to find true values of the average plant growth as if all the trees in the study were measured, and not just those that were in the sample size. The bootstrap simulation parameter is M=10 5 .
The bootstrap method has shown that, regardless of the stimulator, the average growth of one-and two-year-old pines is normally distributed (see Figs. 3 and 4), but the distribution parameters (the mean and standard deviation (SD)) are different. From Tables 5-8 one can see that the most effective treatment involves irrigation of the soil with the "Extrasol" stimulant with different concentrations (Ex 0.05 and 0.1 spray) and the "EridGrow" activator (ErGrw irrigation), spraying with HDD spray, presowing treatment of seeds with the stimulants HDD (HDD 5 min), "Humate + 7 trace elements" (Hum + 7 18 h and Hum + 7 24 h), and "Extrasol" (Ex 0.1 5 min).              It is interesting to note that according to the SFNR "Ertis Ormany" some stimulants have led to a decrease in the average height of plants compared to the control group both in the first and second years of plant life, which is explained by inaccuracy in the measurements (rounding) and small sample size, especially for the plant height of the second year of life, where the sample size of the control group N = 40. To correct this inaccuracy, additional expert information was used for the control group, according to which two-year-old pines in only 1% of cases have a height below 3 cm, i.e., in fact, we know the quantile q x = 3 cm of the cumulative distribution function (cdf) Xthe height of two-year-old pines and its level q = 0.01: This allows us to find a more accurate estimate of the average height of biennial pines in the control group using the formula [23]: (2) where observations N X X X ..., , , 2 1 are independent, equally distributed rv with cdf the indicator function. It is well-known that the estimate (2) is asymptotically unbiased, normally distributed with the variance [24]: is the variance of the usual mean estimate that is for large enough N , 2 2    q hence, due to the asymptotic objective the new estimate is more accurate than the classical one. Figure 5 shows a graph of dependence of 2 q  on q and  a uniform in (0,1) cdf [25]. Also note that the accuracy of the estimate q X was investigated using simulation modeling. Figure 4 shows values of the standardized for N mean squared  is the standard normal cdf, q x = 0, q = 0.5, obtained by simulation modeling with the number of iterations R=10 5 . Here . EX a  Figure 6 shows that taking into account the additional information (1) has made it possible to significantly increase the accuracy of estimating the average, since for all considered values of N > 5 the error Using formula (2) to calculate a more accurate value of the average height of two-year-old plants of the control group of the nursery SFNR "Ertis Ormany", we have found that q X = 10.226 cm, while X =11.587 cm, which is actually 1.361 cm less. This implies that the use of additional information showed that all stimulants had a beneficial effect on the height of the plants. Figure 7 shows the graphs of distribution densities p q (x) for q X and p(x) for X obtained by using bootstrap modeling with a modeling parameter М=10 5 .

Conclusions
As a result of the research performed above it has been revealed that the presowing treatment of pine seeds with ordinary stimulants positively affects the annual seedlings by increasing their average height. However, the results thus obtained depend on the region of the nursery location. In the SNNP "Kokshetau" the average height of the annual seedlings in the experiment with irrigation of the soil with an "EridGrow" activator increased by 13.9%, the two-year-old seedlings increased by 37.2% compared to the control seedlings. For pine seedlings in the SFNR "Ertis Ormany" nursery, the influence of stimulants turned out to be insignificant, but the positive effect on the growth with the "EridGrow" soil irrigation is 7% in the first year and 24.7% in the second year. Therefore, for the conditions of the SFNR "Ertis Ormany" nursery, in order to increase the height of the common pine seedlings it is recommended to irrigate the soil with the "EridGrow" activator with a dose of 1 liter per 10 liters of water for 1 m 2 ; for the SNNP "Kokshetau" nursery, in addition to watering the soil with the "EridGrow" activator, soaking the seeds in "Humate + 7 trace elements" with a dose of 0.5 g per 1 liter of water for 18 hours is recommended. For the first time in forestry research, a method of mathematical processing of the thus obtained measurements of seedlings with an insufficient number of measured plants was proposed by using a bootstrap analysis with and without additional quantile information that allows one to estimate the effect of stimulants on the growth of one-and two-yearold seedlings at a reliable level. x, cm p(x) pq(x)