Introduction

The occurrence of forest pests, which is known as “the no-smoke forest fire” are likely to cause tree die-out, ecological destruction, and subsequently reduce forest carbon sequestration (Xu 2015). Dendrolimus superans (Butler) is the main leaf-eating insect found in the northeastern forests of China, which turns tree branches bleak when its larvae gnaw the leaves (Dang et al. 2018). D. superans can also be found in other regions under similar latitude and climatic conditions (Kang 2005; Tomin et al. 2011; Myong et al. 2012). The pests can outbreak depending on the environment and climatic conditions, and the degree of damage, spreading direction, and duration of different stages can be forecast by studying the growth ratio of larvae (Natalia et al. 2009).

The occurrence of forest pests is a result of many factors, including biological characteristics, natural enemies, meteorological conditions, site conditions, and stand structure (Chen et al. 2017). The relationship between meteorological factors and the occurrence of forest pests is a system consisting of many mathematical inputs. These inputs have an interactive effect with one another, including evaporation capacity, precipitation, average temperature, and accumulated temperature (Tang and Niu 2010). However, it is difficult to formulate the relationship between a designated meteorological factor and the occurrence of forest pests (Feng et al. 2013). Most of the existing research has obtained an approximate relationship between these two factors through data integration, analysis, and exploration, and most of these results were non-linear (Zhang et al. 2012; Abdul et al. 2014).

Previous studies on the relationship between the occurrence of forest pests and meteorological factors in Northern China have revealed that temperature and precipitation during the spring and summer were the most critical factors influencing pest population (Tang and Niu 2010; Chen and Zhang 2011). This influence was greater at the larval stage, while the annual accumulated temperature (The sum, counted in degrees, by which the actual air temperature rises above or falls below a datum level over a year), annual precipitation, and dryness had the greatest Pearson correlation coefficients with pest area (Yang et al. 2014; Nie et al. 2017). A similar study concluded that extreme heat or cold had little effect on annual catches of Ips typographus, while growth rate had a linear relationship with temperatures between 15 and 25°C (Bakke 1992; Wermelinger and Seifert 1998). In a separate study, Diprion hercyniae outbreak was induced by the hot and dry climate and severe low moisture (Marchisio et al. 1994). Moreover, a stepwise regression analysis revealed that the daily average temperature during the winter and precipitation during the breeding season was a key factor influencing population fluctuations of D. superans, while the larval stage and breeding season were the most critical periods (Yu et al. 2016).

More and more novel algorithms are being used for pest control and forecasting by utilizing big data and information on climate globalization (Kumar et al. 2015). The artificial neural network, multilayer feedforward neural network (MLFN), generalized regression neural network (GRNN), support vector machine (SVM), and other algorithms have been used to forecast the occurrence of pest, and these machine learning measures have been more accurate than multiple linear regression predictions (Chon et al. 2000; Zhang et al. 2017; Rathee and Kashyap 2018). However, like other systemic analysis methods in machine learning measures, regression analyses require mass data and expect much of the data to take on a typical probability distribution (e.g., linear, exponential, logarithmic, and so on). Multiplication, division, and power operations are often involved in the computational process, but small errors can result in serious errors, which lead to discrepancies between the quantitative results and qualitative analysis. This may also lead to a relationship between systems that cannot be objectively expressed (Cao 2007; Liu and Xie 2013). Additionally, due to the complexity of computational models, they are not widely used by forest workers or researchers. Therefore, when the grey correlation analysis is used to study the relationship between meteorological variation and pest occurrence, the vector set was easy to divided and call for no more others variables, the model needs to possess less calculative complexity and easy to operate.

In this study, the selected meteorological index was easy to calculate and the system did not affect the simplicity or functioning of the model. Thus, this analytical method and the findings of this study can serve as a theoretical reference for pest forecasting and early warning. For example, this analytical method and the findings can be widely used for forest workers, when precipitation during the first 10 days of July (the Breeding season of D. superans) was less than others year, more attention should be paid the D. superans outbreak next year.

Materials and Methods

Location and status of the studied habitats

This study was conducted in the southeast of Xiaoxinganling Mountains located in Tieli of Yichun City, Heilongjiang Province, China. Regional vegetation mainly includes Pinus koraiensis, Larix gmelinii, and Picea jezoensis. As for the climate, the winters are long and the summer is short. The maximum air temperature may exceed 35°C, while the minimum air temperature can drop below -41°C. Meteorological data were collected from the Tieli weather station (128°01′E and 46°59′N). The altitude of the observation site was 210.5 m, and the altitude of the senor of the barometer was 213.4 m. The height of the wind speed sensor to the platform was 9.36 m, while the height of the observation platform to the ground was 11.76 m.

Statistics and data compilation

A grey correlation analysis was used to study the relationship between meteorological variation and pest occurrence. The selection of characteristic data is key for the foundation of this analysis. D. superans occurrence from 1997 to 2017 was used as the main time period response sequence: X₀ andX₀= x₀(k) (k = 1, 2,… n), then X_i= x_i(k) (i = 1, 2,… m, k = 1, 2,… n) (n = 21), where x_iwas the ith influencing factor of the system and X_i(i = 1, 2,… n) was the characteristic time response data sequence. The analysis in same sample plot did not consider the soil composition, stand structure, or human disturbance, which made D. superans occurrence of Tieli the main data sequence, while the temperature, precipitation, average wind speed, and other time node meteorological data were used as the characteristic data sequences. The grey correlation degree was acquired by the grey correlation analysis, and the degree revealed that precipitation during the spring and summer had the greatest effect on D. superans’ occurrence (Li et al. 2019).

The influence of different precipitation parameters on D. superans occurrence was investigated further. In this analysis, D. superans occurrence from 1997 to 2017 was the main time response sequence: X₀, andX_i= x_i(k) (i = 1, 2… m, k = 1, 2,… n) (m = 18, n = 21), where X_iwas the different precipitation periods from March to August. Each month was divided into 3 parts, x₁, x₂, and x₃, which represented the first, sec, and third 10 days of March, while x₄, x₅, and x₆represented the first, sec, and third 10 days of April; this pattern spanned through August until x₁₈ (Table 1). Then, the correlative relationship between precipitation and D. superans occurrence was investigated.

Data processing and analysis

The goal of the grey correlation analysis was to explore the similarity between data sequence trends, where higher similarity indicates a higher degree of correlation in the system. While comparing the similarity between these two data sequences, both the numerical values and the dimensions were considered. If the data sequence was incomparable, data transformation was conducted in order to eliminate dimensions.

Feature data processing

When Xi = (x_i(1), x_i (2),…, x_i (n)) was the characteristic time response data sequence of the system, D₁ was the operator of the sequence, such that:

(Eq. 1),

(Eq. 2),

Where D₁ represents the average operator of the sequence and X_iD₁ represents the average image. Then, the characteristic average image sequence data table was acquired (Table 2).

Grey relational degree calculation

The calculation for the grey relational degree was conducted as follows: after data transformation, the characteristic average image sequence was obtained, then the grey degree was calculated. In addition to the general relation degree, the mathematical model according to the characteristics of this system was explored, including “B,” “C,” and “T” types of grey relation degrees, as well as the degree of grey slope-correlation (Liu and Xie 2013). The grey slope-correlation expresses the average change over time response sequence, system factors, and the main sequence (Wekan et al. 2011). If the change tended closer, then the grey slope-correlation was larger (Zhang et al. 2019). When investigating the influence of different precipitation periods on D. superans occurrence, these periods during different months exhibited a time response; this grey slope-correlation was selected for further analysis. When ξ (k) was the correlation coefficient:

(i = 1, 2,… m; k = 1, 2,… n) (Eq. 3).

When calculating the last year, “k + 1”was empty. Therefore, it was decided to stop at the “k - 1” year. This did not affect the trend of data changes. In this calculation, i = 1, 2,… 18 and k = 1, 2,… 21. Then, the correlation coefficient sequence data was obtained (Table 3).

The grey slope-correlation relation degree of X₀ and X_i were donated as γ(X₀_, X_i), which was calculated as follows:

(i = 1, 2,… m; k = 1, 2,… n) (Eq. 4).

Simplified grey slope-correlation model

The grey slope-correlation was used to compare the correlational degree of factors over time. However, the calculating process of Eq. 3 (ξ (k)) required many calculative steps. Therefore, the computational model was simplified as follows:

(i = 1, 2,… m, k = 1, 2,… n) (Eq. 5),

Where the simplified correlation coefficient, ξ (k), was affected by the denominator coefficient. When the numerical values of and were similar, the data sequence curves were parallel and the variation tendencies of X₀ and X_i were closer, thereby simplifying the calculation of the correlation coefficient data (Table 4).

Then, the simplified grey slope-correlation relation degree of X₀ and X_i were marked as γ`(X₀_, X_i), where

(i = 1, 2,… m; k = 1, 2,… n) (Eq. 6),

Results

The grey slope-correlation relation degree of X₀ and X_i

It could be derived from Eq. 4 that the results of the grey slope-correlation relation degree were γ₀₁= 0.54, γ₀₂= 0.50, γ₀₃= 0.63, γ₀₄= 0.50, γ₀₅= 0.54, γ₀₆= 0.47, γ₀₇= 0.57, γ₀₈= 0.58, γ₀₉= 0.59, γ₀₁₀= 0.53, γ₀₁₁= 0.51, γ₀₁₂= 0.51, γ₀₁₃= 0.67, γ₀₁₄= 0.59, γ₀₁₅= 0.48, γ₀₁₆= 0.62, γ₀₁₇= 0.53, and γ₀₁₈= 0.58, which represented the time responses of precipitation during different months and D. superans occurrence. The results revealed that precipitation during different seasons had different degrees of correlation with D. superans occurrence, when the value of γ (X₀, X_i) was higher, the correlation degree of X₀and X_iwas greater. Specifically, as it turns out, precipitation during the first 10 days of July had the largest correlation (γ₀₁₃= 0.67), and the third 10 days of March (γ₀₃= 0.63) and first 10 days of August (γ₀₁₆= 0.62) had better correlation with D. superans occurrence. Meanwhile, the precipitation during the third 10 days of April (γ₀₆= 0.47) and the third 10 days of July (γ₀₁₅= 0.48) correlated less with D. superans occurrence (Table 3).

The simplified grey slope-correlation relation degree of X₀ and X_i

From Eq. 6, the following results could be obtained: γ`₀₁= 0.47, γ`₀₂= 0.49, γ`₀₃= 0.56, γ`₀₄= 0.50, γ`₀₅= 0.56, γ`₀₆= 0.48, γ`₀₇= 0.57, γ`₀₈= 0.60, γ`₀₉= 0.62, γ`₁₀= 0.58, γ`₁₁= 0.48, γ`₁₂= 0.51, γ`₁₃= 0.69, γ`₁₄= 0.58, γ`₁₅= 0.52, γ`₁₆= 0.61, γ`₁₇= 0.55, and γ`₁₈= 0.60.

Table 1: The characteristic sequence data table

Area and precipitation	1997	1998	1999	2000	2001	2002	2003	2004	2005	2006	2007	2008	2009	2010	2011	2012	2013	2014	2015	2016	2017
X0/×10⁵hm²)	4.07	7.73	5.05	3.25	3.07	2.75	4.13	2.87	1.67	1.24	1.31	0.95	0.9	0.98	0.8	0.75	0.35	0.35	0.28	0.34	0.48
X1/(0.1mm)	5	0	6	25	73	0	28	0	32	99	21	147	62	0	18	41	7	37	122	40	63
X2/(0.1mm)	22	204	51	68	36	0	1	67	51	30	4	63	44	193	75	3	0	30	127	10	38
X3/(0.1mm)	67	61	88	16	79	0	120	46	64	113	144	220	94	85	0	91	95	0	73	0	0
X4/(0.1mm)	0	51	71	31	89	164	0	50	99	11	125	89	3	163	7	0	9	4	122	115	20
X5/(0.1mm)	76	38	85	48	11	305	216	123	103	1	85	0	161	91	2	77	33	18	11	53	71
X6/(0.1mm)	77	90	150	225	64	175	92	58	306	84	1	281	5	79	30	252	3	110	32	10	40
X7/(0.1mm)	13	75	37	127	145	71	0	385	144	32	124	393	54	459	302	72	249	266	247	368	201
X8/(0.1mm)	183	263	1	183	195	286	175	189	163	0	329	129	9	354	56	67	206	391	467	364	205
X9/(0.1mm)	436	365	134	161	26	139	444	212	111	34	520	309	133	151	367	244	156	545	146	228	166
X10/(0.1mm)	616	571	51	91	50	504	215	3	600	284	222	336	180	156	536	1504	432	115	368	456	126
X11/(0.1mm)	175	699	275	62	223	421	137	352	211	863	15	233	760	80	197	340	401	145	320	275	785
X12/(0.1mm)	106	732	568	316	33	320	342	349	58	861	395	192	1278	126	15	115	391	1535	1313	826	398
X13/(0.1mm)	447	1646	969	253	426	230	688	477	441	343	280	608	668	351	586	1388	970	943	923	1021	100
X14/(0.1mm)	88	12	54	1217	347	351	565	75	342	371	222	170	447	561	346	297	209	749	32	67	960
X15/(0.1mm)	961	97	505	992	514	39	521	180	1468	794	378	2	304	312	62	157	786	1518	892	670	88
X16/(0.1mm)	1119	631	449	741	393	300	625	372	173	355	226	273	479	1066	790	528	1562	110	787	353	1669
X17/(0.1mm)	194	550	193	327	533	218	494	33	137	161	148	58	804	245	528	110	393	1108	203	262	0
X18/(0.1mm)	621	327	273	533	221	424	1206	443	41	121	669	591	289	812	110	790	292	188	187	238	247

Table 2: The characteristic average image sequence data table

Average image	1997	1998	1999	2000	2001	2002	2003	2004	2005	2006	2007	2008	2009	2010	2011	2012	2013	2014	2015	2016	2017
X0D₁	1.98	3.75	2.45	1.58	1.49	1.33	2	1.39	0.81	0.6	0.64	0.46	0.44	0.48	0.39	0.36	0.17	0.17	0.14	0.17	0.23
X1D₁	0.13	0	0.15	0.64	1.86	0	0.71	0	0.81	2.52	0.53	3.74	1.58	0	0.46	1.04	0.18	0.94	3.1	1.02	1.6
X2D₁	0.41	3.84	0.96	1.28	0.68	0	0.02	1.26	0.96	0.56	0.08	1.18	0.83	3.63	1.41	0.06	0	0.56	2.39	0.19	0.71
X3D₁	0.97	0.88	1.27	0.23	1.14	0	1.73	0.66	0.92	1.63	2.08	3.17	1.36	1.23	0	1.31	1.37	0	1.05	0	0
X4D₁	0	0.88	1.22	0.53	1.53	2.82	0	0.86	1.7	0.19	2.15	1.53	0.05	2.8	0.12	0	0.15	0.07	2.09	1.97	0.34
X5D₁	0.99	0.5	1.11	0.63	0.14	3.98	2.82	1.61	1.35	0.01	1.11	0	2.1	1.19	0.03	1	0.43	0.24	0.14	0.69	0.93
X6D₁	0.75	0.87	1.45	2.18	0.62	1.7	0.89	0.56	2.97	0.81	0	2.73	0.05	0.74	0.29	2.44	0.03	1.07	0.31	0.1	0.39
X7D₁	0.07	0.42	0.21	0.71	0.81	0.4	0	2.15	0.8	0.18	0.69	2.2	0.3	2.56	1.69	0.4	1.39	1.49	1.38	2.06	1.12
X8D₁	0.91	1.31	0	0.91	0.97	1.42	0.87	0.94	0.81	0	1.64	0.64	0.04	1.76	0.28	0.33	1.02	1.95	2.32	1.81	1.02
X9D₁	1.82	1.53	0.56	0.67	0.11	0.58	1.86	0.89	0.46	0.14	2.18	1.29	0.56	0.63	1.54	1.02	0.65	2.28	0.61	0.95	0.69
X10D₁	1.75	1.62	0.14	0.26	0.14	1.43	0.61	0	1.7	0.8	0.63	0.95	0.51	0.44	1.52	4.26	1.22	0.33	1.04	1.29	0.36
X11D₁	0.53	2.11	0.83	0.19	0.67	1.27	0.41	1.06	0.64	2.6	0.05	0.7	2.29	0.24	0.59	1.02	1.21	0.44	0.96	0.83	2.36
X12D₁	0.22	1.5	1.16	0.65	0.07	0.65	0.7	0.71	0.12	1.76	0.81	0.39	2.61	0.26	0.03	0.24	0.8	3.14	2.69	1.69	0.81
X13D₁	0.68	2.51	1.48	0.39	0.65	0.35	1.05	0.73	0.67	0.52	4.23	0.93	1.02	0.54	0.89	2.12	1.48	1.44	1.41	1.56	0.15
X14D₁	0.24	0.03	0.15	3.33	0.95	0.96	1.54	0.2	0.93	1.01	0.61	0.46	1.22	1.53	0.95	0.81	0.57	2.05	0.09	0.18	2.62
X15D₁	1.8	0.18	0.94	1.85	0.96	0.07	0.97	0.34	2.74	1.48	0.71	0	0.57	0.58	0.12	0.29	1.47	2.84	1.67	1.25	0.16
X16D₁	1.81	1.02	0.73	1.2	0.63	0.48	1	0.6	0.28	0.57	0.37	0.44	0.77	1.72	1.28	0.85	2.52	0.18	1.27	0.57	2.7
X17D₁	0.61	1.72	0.61	1.03	1.67	0.68	1.55	0.1	0.43	0.5	0.46	0.18	2.52	0.77	1.66	0.34	1.23	3.47	0.64	0.82	0
X18D₁	1.51	0.8	0.66	1.3	0.54	0.69	2.93	0.72	0.1	0.29	1.63	1.44	0.7	1.98	0.27	1.92	0.71	0.46	0.45	0.58	0.6

The simplified grey slope-correlation of X₀ and X_i revealed that the precipitation during the first 10 days of July had the best correlation (γ`₁₃= 0.69), which reflected the results of the classical model. In the simplified model, the top 5 groups of precipitation that had better associations with D. superans occurrence included the precipitation during the first 10 days of July (γ`₁₃= 0.69), the third 10 days of May (γ`₀₉= 0.62), the first 10 days of August (γ`₁₆= 0.61), the sec 10 days of May (γ`₀₈= 0.60), and the third 10 days of August (γ`₁₈= 0.60). However, according to the classical model, the top 5 group included the first 10 days of July (γ₁₃= 0.67), the third 10 days of March (γ₀₃= 0.63), the first 10 days of August (γ₁₆= 0.62), the sec 10 days of May (γ₀₈= 0.58), and the third 10 days of August (γ₁₈= 0.58). The results showed that, the top 5 groups of precipitation that had better associations with D. superans occurrence between the two models was very similar. In the simplified model, the 5 groups of precipitation that were less associated with D. superans occurrence included the precipitation during the first 10 days of March (γ`₀₁= 0.47), the third 10 days of April (γ`₀₆= 0.48), the sec 10 days of June (γ`₁₁= 0.48), the sec 10 days of March (γ`₀₂= 0.49), and the third 10 days of June (γ`₁₂= 0.51). In the classical model, the 5 groups that were less associated with D. superans occurrence included the third 10 days of April (γ₀₆= 0.47), the third 10 days of July (γ₁₅= 0.48), the sec 10 days of March (γ₀₂= 0.50), the sec 10 days of June (γ₁₁= 0.51), and the third 10 days of June (γ₁₂= 0.51). The results also proved that the two models were very similar (concluded from Eq. 4 and Eq. 6).

Comparative and analysis

Considering that many complex computing models are not and cannot be widely used by forest workers or researchers, the simple grey slope-correlation model was developed to analyze the relationship between precipitation and D. superans occurrence. The grey slope-correlation model is able to express the average changes in many factors over a time response sequence.

Table 3: Correlation coefficient sequence data table

Correlation coefficient	1997	1998	1999	2000	2001	2002	2003	2004	2005	2006	2007	2008	2009	2010	2011	2012	2013	2014	2015	2016
ξ_0k	0.68	0.40	0.43	0.58	0.89	0.60	0.69	0.37	0.49	0.21	0.44	0.42	0.92	0.45	0.61	0.21	0.55	0.52	0.31	0.91
ξ_1k	0.70	0.29	0.56	0.55	0.89	0.60	0.41	0.71	0.73	0.14	0.43	0.70	0.59	0.43	0.04	0.47	0.50	0.51	0.08	0.68
ξ_2k	0.64	0.55	0.20	0.54	0.89	0.60	0.46	0.50	0.56	0.87	0.58	0.43	0.84	0.81	0.48	0.46	1.00	0.45	0.85	0.79
ξ_3k	0.65	0.56	0.57	0.58	0.63	0.75	0.41	0.45	0.12	0.54	0.98	0.03	0.53	0.04	0.93	0.32	0.47	0.46	0.81	0.17
ξ_4k	0.41	0.49	0.83	0.23	0.48	0.57	0.76	0.65	0.01	0.52	0.72	0.50	0.54	0.03	0.49	0.83	0.56	0.66	0.62	1.00
ξ_5k	0.75	0.53	0.53	0.29	0.57	0.45	0.87	0.40	0.30	0.94	0.42	0.02	0.54	0.43	0.51	0.01	0.51	0.31	0.31	0.67
ξ_6k	0.73	0.67	0.44	0.84	0.52	0.75	0.41	0.51	0.24	0.60	0.48	0.14	0.56	0.78	0.24	0.35	0.94	0.88	0.87	0.48
ξ_7k	0.86	0.67	0.39	0.89	0.70	0.51	0.66	0.64	0.74	0.52	0.46	0.06	0.53	0.17	0.81	0.36	0.68	0.73	0.69	0.49
ξ_8k	0.60	0.45	0.58	0.17	0.52	0.74	0.61	0.82	0.34	0.53	0.77	0.43	0.97	0.55	0.70	0.64	0.58	0.28	0.85	0.61
ξ_9k	0.65	0.09	0.50	0.56	0.49	0.37	0.69	0.37	0.56	0.75	0.58	0.54	0.81	0.52	0.58	0.42	0.27	0.53	0.98	0.26
ξ_10k	0.78	0.49	0.26	0.56	0.63	0.29	0.49	0.94	0.48	0.02	0.43	0.59	0.10	0.55	0.67	0.44	0.36	0.57	0.75	0.72
ξ_11k	0.72	0.83	0.81	0.11	0.50	0.79	0.69	0.19	0.44	0.45	0.59	0.54	0.10	0.12	0.51	0.35	0.57	0.96	0.57	0.43
ξ_12k	0.79	0.84	0.31	0.68	0.58	0.75	1.00	0.61	0.94	0.55	0.24	0.92	0.51	0.62	0.60	0.59	0.97	0.84	0.93	0.09
ξ_13k	0.12	0.43	0.40	0.29	0.88	0.96	0.14	0.40	0.70	0.58	0.94	0.62	0.89	0.72	0.92	0.59	0.58	0.04	0.76	0.60
ξ_14k	0.10	0.43	0.49	0.54	0.07	0.63	0.41	0.39	0.67	0.47	0.72	0.50	0.94	0.22	0.60	0.34	0.67	0.67	0.66	0.12
ξ_15k	0.45	0.91	0.52	0.54	0.84	0.84	0.82	0.70	0.54	0.62	0.65	0.70	0.68	0.90	0.70	0.36	0.07	0.48	0.42	0.65
ξ_16k	0.85	0.43	0.51	0.69	0.43	0.82	0.07	0.40	0.67	0.87	0.46	0.52	0.30	0.57	0.21	0.35	0.61	0.19	0.96	0.79
ξ_17k	0.42	0.78	0.49	0.43	0.75	0.70	0.28	0.15	0.50	0.57	0.79	0.49	0.64	0.14	0.52	0.63	0.65	0.84	0.95	0.81
ξ_18k	0.68	0.40	0.43	0.58	0.89	0.60	0.69	0.37	0.49	0.21	0.44	0.42	0.92	0.45	0.61	0.21	0.55	0.52	0.31	0.91

Table 4: The simplified correlation coefficient sequence data table

Simplified correlation coefficient	1997	1998	1999	2000	2001	2002	2003	2004	2005	2006	2007	2008	2009	2010	2011	2012	2013	2014	2015	2016
ξ`_1k	0.35	0.60	0.22	0.34	0.53	0.40	0.59	0.63	0.30	0.54	0.14	0.65	0.48	0.55	0.43	0.77	0.19	0.29	0.53	0.82
ξ`_2k	0.12	0.71	0.59	0.71	0.53	0.40	0.02	0.85	0.86	0.52	0.07	0.80	0.23	0.70	0.53	0.68	0.50	0.23	0.47	0.30
ξ`_3k	0.50	0.56	0.68	0.20	0.53	0.40	0.76	0.55	0.49	0.83	0.55	0.65	0.84	0.55	0.52	0.64	0.50	0.55	0.45	0.43
ξ`_4k	0.35	0.58	0.83	0.34	0.51	0.40	0.59	0.42	0.61	0.09	0.99	0.52	0.02	0.57	0.52	0.68	0.65	0.03	0.79	0.46
ξ`_5k	0.42	0.39	0.93	0.58	0.04	0.56	0.89	0.80	0.58	0.01	0.58	0.51	0.66	0.56	0.03	0.96	0.69	0.81	0.21	0.99
ξ`_6k	0.58	0.50	0.54	0.60	0.35	0.50	0.94	0.17	0.68	0.48	0.58	0.52	0.07	0.70	0.12	0.68	0.03	0.65	0.53	0.28
ξ`_7k	0.20	0.87	0.27	0.83	0.71	0.40	0.59	0.83	0.66	0.27	0.29	0.55	0.12	0.87	0.59	0.25	0.93	0.91	0.78	0.55
ξ`_8k	0.69	0.60	0.61	0.89	0.64	0.53	0.72	0.78	0.57	0.48	0.75	0.53	0.02	0.60	0.80	0.28	0.52	0.73	0.70	0.56
ξ`_9k	0.49	0.78	0.64	0.56	0.19	0.37	0.82	0.94	0.70	0.06	0.89	0.66	0.97	0.38	0.79	0.86	0.29	0.64	0.74	0.61
ξ`_10k	0.51	0.64	0.45	0.71	0.10	0.48	0.59	0.63	0.79	0.78	0.56	0.70	0.81	0.27	0.35	0.84	0.58	0.30	0.97	0.48
ξ`_11k	0.32	0.79	0.71	0.28	0.50	0.46	0.35	0.98	0.23	0.49	0.07	0.30	0.50	0.38	0.55	0.58	0.61	0.42	0.74	0.40
ξ`_12k	0.17	0.89	0.92	0.54	0.11	0.70	0.76	0.71	0.07	0.62	0.81	0.15	0.50	0.59	0.12	0.26	0.25	0.97	0.63	0.53
ξ`_13k	0.36	0.94	0.72	0.58	0.74	0.40	1.00	0.75	0.97	0.12	0.67	0.88	0.64	0.54	0.41	0.82	0.97	0.87	0.90	0.44
ξ`_14k	0.36	0.19	0.04	0.60	0.89	0.91	0.64	0.20	0.74	0.68	0.97	0.37	0.86	0.84	0.93	0.81	0.28	0.56	0.56	0.07
ξ`_15k	0.36	0.18	0.43	0.70	0.55	0.07	0.74	0.12	0.83	0.63	0.58	0.51	0.93	0.62	0.40	0.18	0.52	0.81	0.68	0.45
ξ`_16k	0.43	0.94	0.50	0.71	0.88	0.63	0.91	0.90	0.44	0.71	0.68	0.56	0.47	0.94	0.79	0.29	0.52	0.14	0.57	0.23
ξ`_17k	0.52	0.77	0.49	0.60	0.67	0.56	0.61	0.21	0.70	0.87	0.75	0.07	0.56	0.43	0.58	0.24	0.35	0.61	0.94	0.43
ξ`_18k	0.42	0.85	0.43	0.65	0.72	0.27	0.69	0.69	0.32	0.18	0.86	0.68	0.37	0.60	0.14	0.91	0.74	0.87	0.93	0.76

Table 5: The correlation coefficient accumulation table

Correlation coefficient accumulation	March	April	May	June	July	August
classical	γ₀₁+γ₀₂+γ₀₃	γ₀₄+γ₀₅+γ₀₆	γ₀₇+γ₀₈+γ₀₉	γ₁₀+γ₁₁+γ₁₂	γ₁₃+γ₁₄+γ₁₅	γ₁₆+γ₁₇+γ₁₈
classical	1.67	1.51	1.74	1.55	1.74	1.73
simplified	γ`₀₁+γ`₀₂+γ`₀₃	γ`₀₄+γ`₀₅+γ`₀₆	γ`₀₇+γ`₀₈+γ`₀₉	γ`₁₀+γ`₁₁+γ`₁₂	γ`₁₃+γ`₁₄+γ`₁₅	γ`₁₆+γ`₁₇+γ`₁₈
simplified	1.52	1.54	1.79	1.57	1.79	1.76

In this study, the grey slope-correlation model of precipitation and D. superans occurrence in the Xiaoxinganling Mountain Tieli forest region was constructed and the grey slope-correlation relation degree was calculated. According to the calculations and analysis of the grey slope-correlation classical model, the simplified grey slope-correlation model required fewer steps and was easier to operate. After incorporating the correlation coefficient of each month in the classical and simplified models, the correlation coefficient accumulation was obtained (Table 5).

The correlation coefficient accumulation during May and July had good measure in both models (Table 5). This indicated that the precipitation during May and July were the greatest contributing precipitation factors on D. superans occurrence compared to other periods. Although both models exhibited different correlation coefficient accumulations, both models indicated that the precipitation period that contributed the least was during the spring. Moreover, the results of the models were similar, where the precipitation during May and July had the greatest associations with D. superans occurrence, but the simplified model required fewer calculative steps.

Discussion

According to the results, precipitation during May (γ₀₇+ γ₀₈+ γ₀₉= 1.74, γ`₀₇+ γ`₀₈+ γ`₀₉= 1.79) and July (γ₁₃+ γ₁₄+ γ₁₅= 1.74, γ`₁₃+ γ`₁₄+ γ`₁₅= 1.79) had the greatest associations with D. superans occurrence. In previous studies, the larval stage and breeding season were found to be the critical periods for D. superans (Yang et al. 2014; Yu et al. 2016). The life cycle of D. superans can be divided into the larval, larger larval, pupa, eclosion, adult, and spawning stages. D. superans produces 1 generation a year and overwinters as larvae in the Tieli forest region. The larval stage lasts for 3 seasons in Northeast China. Larvae hatch in autumn, stay in the litter layer during the winter, and finally climb up the trees during the spring of the next year. Precipitation has a great effect on D. superans occurrence. Aside from precipitation, temperature is also a critical factor that affects the larvae’s ability to climb trees, while warm and dry climatic conditions benefit larval growth (Liu 1994; Tiit et al. 2010). Precipitation during the third 10 days of March (γ₀₃= 0.63, γ`₀₃= 0.56) was found to be the most important time period affecting D. superans occurrence compared to the other periods in March (Li et al. 2019). Because more precipitation tends to increase humidity, the additional humidity disturbs the water balance in insects, leading to epidemics of pathogenic microorganisms. Precipitation during the late spring promotes tree growth and provides food for larvae. When larvae experience high humidity for long periods of time, the body water loss balance can cause developmental delays or abnormalities (Chen and Zhang 2011; Abdul et al. 2014).

In the D. superans breeding season (July, August), precipitation during the first 10 days of July (γ₁₃= 0.67, γ`₁₃= 0.69) was found to be the most important factor affecting D. superans occurrence (Chen and Zhang 2011). This finding was similar to the results of a previous study on climate change and the occurrence of crop insects, where occurrence and precipitation exhibited a positive correlation (Zhang et al. 2012). When the average annual precipitation and heavy rainfall increased by 1 mm, pest occurrence rates increased by 0.004 and 0.008 and pest occurrence increased by 59.5 × 10⁴and 11.89 × 10⁴hm², respectively. Thus, precipitation clearly facilitated migratory pest decent and increased the base number of insects (Zhang et al. 2012). Moreover, precipitation influences pest food sources (i.e., trees and others plant), their natural enemies (e.g., Trichogramma), and other biotic factors (Vladimir et al. 2016)

The application of grey system theory requires less data input than the multiple linear regression analysis method, and the calculations are simple and easy to operate (Abdul et al. 2019; Zhang et al. 2019). Specifically, the selected meteorological index was easy to calculate and the system had no force requirement due to its simple capacity and regularity (Cao et al. 2007). Moreover, grey slope-correlation can reveal the correlational degree of factors over time (Wekan et al. 2011). The simplified correlation coefficient was affected by the denominator coefficient, while the simplified model was easy to calculate, required fewer steps, and the results was very similar with the classical model (concluded from Eq. 4, 6 and Table 5). These findings provide a theoretical reference for pest forecasting and early warning. This simple method was used to uncover the most critical periods of precipitation affecting pest occurrence, which was found to be the first 10 days of July. Thus, the grey system theory can be widely used by forest workers and researchers. Monitoring precipitation during the first 10 days in July should be a focus, and when the precipitation of the first 10 days in July increases while other factors are consistent, precautions should be implemented the next spring.

Different precipitation periods from March to August were measured by the weather service department. While D. superans was prone to sprawling, occurrence was the main time response sequence data that was difficult to calculate. In this study, occurrence data was obtained from actual measurements and empirical prediction, but its scientific foundation and precision needs to be improved. The period of precipitation with the greatest effect on pest occurrence was the first 10 days of July, which corresponds with the breeding season of D. superans. However, the life stages of this pest overlap in time and determining the specific pest stage (i.e., feathering, spawning, or hatching periods) was affected by which precipitation period was difficult to discern. Therefore, refinement of this scientific model requires further investigation.

Conclusion

Both grey slope-correlation and simplified models revealed that precipitation during the first 10 days of July had the greatest correlation (γ₁₃= 0.67, γ`₁₃= 0.69) with D. superans occurrence, while the first 10 days of August (γ₁₆= 0.62, γ`₁₆= 0.61), the sec 10 days of May (γ₀₈= 0.58, γ`₀₈= 0.60), and the third 10 days of August (γ₁₈=0.58, γ`₁₈=0.60) also had large correlations with D. superans occurrence. However, the least-correlated time periods of precipitation affecting D. superans occurrence were quite different between the two models. The classical model showed that third 10 days of April (γ₀₆= 0.47) were the least correlated, while the simplified model showed that the first 10 days of March (γ`₀₁= 0.47) were the least correlated with D. superans occurrence. When adding the correlation coefficients of each month in the classical and simplified models, the correlation coefficient in May and July had good measures in both models. Thus, precipitation during May and July was clearly the most important precipitation factor affecting D. superans’ occurrence, while precipitation during the spring was the least important precipitation factor.

Acknowledgments

This study was supported by the Fundamental Research Funds for the Central Non-Profit Research Institution of the Chinese Academy of Forestry (No. CAFYBB2018QA011).

Author Contributions

Zhiru Li and Zhenkun Miao conceived and designed the models; Xiaofeng Wu, Beihang Zhang and Quangang Li performed the experiments; Lizhi Han and Jun Wang contributed the insect data of forestry, and Zhiru Li wrote the paper.

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Abstract