Entomological Research
Volume 54, Issue 7 e12753
Research Paper
Full Access

Larval occurrence prediction of Dendrolimus punctatus based on fuzzy integrated evaluation method

Guo-Qing Wang, 

Guo-Qing Wang

School of Forestry and Landscape Architecture, Anhui Agricultural University, Hefei, Anhui, China

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Yue Xu, 

Yue Xu

School of Science, Anhui Agricultural University, Hefei, Anhui, China

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Xiao-Meng Wu, 

Xiao-Meng Wu

School of Science, Anhui Agricultural University, Hefei, Anhui, China

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Guang-Jing Qian, 

Guang-Jing Qian

School of Science, Anhui Agricultural University, Hefei, Anhui, China

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Xian Cheng, 

Xian Cheng

School of Science, Anhui Agricultural University, Hefei, Anhui, China

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Yun-Ding Zou, 

Yun-Ding Zou

School of Forestry and Landscape Architecture, Anhui Agricultural University, Hefei, Anhui, China

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Guo-Qing Zhang, 

Guo-Qing Zhang

Bureau of Forestry of Qianshan County, Qianshan, Anhui, China

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Guo-Fei Fang, 

Guo-Fei Fang

Station for Prevention and Control of Forest Disease and Pests, Shenyang, Liaoning, China

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Xia-Zhi Zhou, 

Corresponding Author

Xia-Zhi Zhou

School of Forestry and Landscape Architecture, Anhui Agricultural University, Hefei, Anhui, China

Correspondence

Xiazhi Zhou, School of Forestry and Landscape Architecture, Anhui Agricultural University, No.130 West Changjiang Road, Hefei, China.

Email: [email protected]

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Shou-Dong Bi, 

Shou-Dong Bi

School of Science, Anhui Agricultural University, Hefei, Anhui, China

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First published: 01 July 2024
https://doi.org/10.1111/1748-5967.12753
Citations: 2

Abstract

To improve the prediction accuracy of Dendrolimus punctatus larvae of overwintering, first and second generation and to provide a scientific basis for effective prevention and control of D. punctatus, six mathematical models of fuzzy comprehensive evaluation method were used to predict accumulative amount with the data of 1989–2014. The cumulative amount for the overwintering and the first generation was predicted in 2015, 2016, 2017, and 2018. The forecasted results of six models were all level 1, which was consistent with the actual results. Five forecasted results of six models and the actual results were level 1. The actual accumulative amount of D. punctatus for the second generation was level 1 in 2015, 2016, and 2017, which were consistent with the six models' forecasted results.

Introduction

Dendrolimus punctatus Walker (Lepidoptera Lasiocampidae) is an important global forest pest (Hou 1987). In China, more than 2 million hectares of pine trees are attacked by pine caterpillars every year, which caused damage to forest resources, economy and ecology. It is mainly distributed in the southern areas of the Qinling Mountains and Huaihe River and is one of the main pests in the forest areas of southern China. Generally, the Rampant disaster that D. punctatus caused happens periodically for 3 to 5 years. A severe outbreak of D. punctatus also causes the invasion of pests such as Cerambycidae, causing serious damage to the growth of forest trees (Zou et al. 1990). Therefore, it requires regular monitoring of the pest (Zhang & Li 2008).

The prediction of the occurrence of D. punctatus was essential for the development of comprehensive prevention and control measures. Currently, many studies had used different methods (BP neural network method, LOGIT model method, Markov chains method et al.) to predict its occurrence, pest level, occurrence class and spatial distribution (Zhang et al. 2001; Chen et al. 2011; Tian et al. 2012; Fei et al. 2014), which had provided strong support for the comprehensive prevention and treatment of D. punctatus. In recent years, there had been a large number of reports on the prediction of the occurrence pattern and the occurrence of D. punctatus (Cheng et al. 2019; Qian et al. 2020; Song et al. 2020; Yu et al. 2019; Zhang et al. 2020; Zhou et al. 2017). Park et al. (2003) predicted aquatic insect species richness with an artificial neural network model; Xu et al. (2014) used fisher discriminant analysis to effectively predict different damage levels of D. punctatus. Wang et al. (2016) used partial least squares to predict a spatial pattern of D. punctatus based on meteorological factors. However, these methods had relatively complicated algorithms, which were not convenient for operations. And the prediction accuracy was not very high. These characteristics of its occurrence were not identical in distinct zones because of different climatic conditions, vegetative conditions and topography. The occurrence characteristics of D. punctatus were not exactly the same. The prediction of the growth and decline of the D. punctatus is influenced by a variety of factors, including ecological factors of the inorganic environment and the role of natural enemies. The influence of various factors on the growth of the population varies, from primary to secondary effects. Predictions of pest populations are based on the role of influencing factors. Fuzzy mathematics delineates the relationships between elements that belong and do not belong to a set, and each element belongs to a certain set according to a certain degree of affiliation, thus depicting a large number of fuzzy phenomena. The fuzzy comprehensive evaluation methods to make an overall evaluation of things or phenomena that are affected by multiple factors. The comprehensive evaluation method converts qualitative evaluation into quantitative evaluation based on the affiliation theory of fuzzy mathematics, that is, it uses fuzzy mathematics to make an overall evaluation of things or phenomena affected by multiple factors.

To effectively control D. punctatus, the fuzzy comprehensive evaluation method was used to analyze the accumulative amount for the overwintering, the first and second generation of D. punctatus larvae, to provide a scientific basis for the comprehensive management of D. punctatus.

Materials and methods

Material source

The data on D. punctatus were obtained from the central monitoring and reporting station of Center for Biological Disaster Prevention and Control, National Forestry and Grassland Administration, as well as the Forest Pest Control Station of Qianshan County, Anhui Province (Between 30°27′~31°04′N and 116°14′~116°46′E). The meteorological data were obtained from the National Weather Service. The span of the data was from 1983 to 2018. The information from 1989 to 2014 was used as research information and the information from 2015 to 2018 was used as validation information. According to the survey method developed by FPMDS, different observation methods were adopted for different insect states via a combination of tracing and detailed investigation. The surveys were conducted along forest roads, highways, railways and other lines. An area of standard size was delineated in which observations of damage levels and insect occurrences were recorded. Twenty plants were then sampled for detailed investigation. Cumulative data on the developmental progress provided information on the beginning, peak and end of D. punctatus.

Mathematical analysis methods

  1. Types of models for fuzzy comprehensive evaluation (Li & Peng 1999).
The model of the fuzzy comprehensive evaluation was Y ~ = X~ ⊙ $$ \odot $$ R~. where X~ is the weight vector of evaluation factors, whose elements represent the affiliation of each factor to the evaluated thing; R~ is the fuzzy evaluation matrix, whose elements represent the affiliation of each factor to each grade. To improve accuracy, five fuzzy models are used to predict the occurrence of pest populations. 1/5 of their results are taken and finally a comprehensive decision model is formed.
  • 1. The main factor positive type (model I)
y i = V i = 1 m x i V r ij = max 1 ≤ i ≤ m max x i r ij $$ {y}_i=\overset{\underset{m}{i=1}}{V}\left({x}_i\ \mathrm{V}\ {r}_{ij}\right)=\underset{1\le i\le m}{\mathit{\max}}\left\{\mathit{\max}\left({x}_i,{r}_{ij}\right)\right\} $$
was referred to briefly to indicate the role of prominent factors as M 1 = V , V $$ {M}_1=\left(\mathrm{V},\mathrm{V}\right) $$ . The symbol V represented a large calculation.
  • 2. The main factor determining type (model II)
y i = V i = 1 m x i Λ r ij = max 1 ≤ i ≤ m min x i r ij $$ {y}_i=\underset{i=1}{\overset{m}{\mathrm{V}}}\left({x}_i\ \Lambda\ {r}_{ij}\right)=\underset{1\le i\le m}{\max}\left\{\min \left({x}_i,{r}_{ij}\right)\right\} $$
was referred to briefly to indicate the extent of the main factors as M 2 = Λ V $$ {M}_2=\left(\Lambda, \mathrm{V}\right) $$ . The symbol Λ $$ \Lambda $$ indicated the small calculation.
  • 3. The main factor prominent type (model III)
y i = V i = 1 m x i * r ij = max 1 ≤ i ≤ m x i * r ij $$ {y}_i=\underset{i=1}{\overset{m}{\mathrm{V}}}\left({x_i}^{\ast }{r}_{ij}\right)=\underset{1\le i\le m}{\max}\left\{{x_i}^{\ast }{r}_{ij}\right\} $$
was referred to briefly to indicate the extent of the secondary factor's effect as M 3 = * V $$ {M}_3=\left(\ast, \mathrm{V}\right) $$ .
  • 4. Factor summation type (model IV)
y i = ∑ i = 1 m x i Λ r ij = min 1 , ∑ i = 1 m min x i r ij $$ {y}_i=\sum \limits_{i=1}^m\left({x}_i\ \Lambda\ {r}_{ij}\right)=\min \left\{1,,,\sum \limits_{i=1}^m\min \left({x}_i,{r}_{ij}\right)\right\} $$
was referred to briefly to indicate the effect degree of the overall factor as M 4 = Λ + $$ {M}_4=\left(\Lambda, +\right) $$ .
  • 5. Weighted average type (model V)
y i = ∑ i = 1 m x i * r ij = min 1 , ∑ i = 1 m x i * r ij $$ {y}_i=\sum \limits_{i=1}^m\left({x_i}^{\ast }{r}_{ij}\right)=\min \left(1,,,\sum \limits_{i=1}^m{x_i}^{\ast }{r}_{ij}\right) $$
was referred to briefly to indicate the effect degree of all factors as M 5 = * + $$ {M}_5=\left(\ast, +\right) $$ .
  • 6. Integrated decision type (model VI)
y i = 1 / 5 ∑ i = 1 m M i y i $$ {y}_i=1/5\left(\sum \limits_{i=1}^m{M}_i{y}_i\right) $$
was referred to briefly to indicate the combined effect of all factors as M 6 = 1 / 5 ∑ i = 1 5 M i $$ {M}_6=1/5\sum \limits_{i=1}^5{M}_i $$ .
i = 1, 2, 3, …, m, m was the number of forecasted factors xi, j = 1, 2, 3, …, n, n was the maximum grade of forecasted factors. According to the final calculation result, the maximum value y i $$ {y}_i $$ was used to judge a certain level.
  • 2. Fuzzy comprehensive evaluation analysis method
    • 1. Obtain the fuzzy vector
In the fuzzy comprehensive evaluation method, weight was given to each forecasted factor x i $$ {x}_i $$ to form the fuzzy vector X~. The correlation degree between each forecasted factor and the forecasted object was different, which meant the effect of each forecasted factor. Therefore, the correlation coefficient r xiy $$ {r}_{xiy} $$ between each forecasted factor and the forecasted object y could be used as the weight coefficient of the forecasted factor(i = 1,2…, m). Because ∑ r xiy ≠ 1 $$ \sum {r}_{xiy}\ne 1 $$ needed to be normalized x i = r xiy 2 / ∑ i = 1 m r xiy 2 $$ {x}_i={r}_{xiy}^2/\sum \limits_{i=1}^m{r}_{xiy}^2 $$ . Then the model vector X ~ =(×1, ×2, …, Xm) was obtained.

Establishment of evaluation matrix

The conditional probability P lk i = n lk / n 1 k $$ {P}_{lk}^i={n}_{lk}/{n}_{1k} $$ of each forecasted factor in a × b contingency table was used to replace the fuzzy probability, and the fuzzy evaluation matrix R~ was established.
R = P 1 k 1 P 2 k 1 … P bk 1 P 1 k 2 P 2 k 2 … P bk 2 … … … … P 1 k m P 2 k m … P bk m   $$ R=\left[\begin{array}{cccc}{P}_{1k}^1& {P}_{2k}^1& \dots & {P}_{bk}^1\\ {}{P}_{1k}^2& {P}_{2k}^2& \dots & {P}_{bk}^2\\ {}\dots & \dots & \dots & \dots \\ {}{P}_{1k}^m& {P}_{2k}^m& \dots & {P}_{bk}^m\end{array}\right] $$

Concrete calculation Y ~ =X ~  ⊙ $$ \odot $$ R~.

All calculations in this paper were calculated by the DPS program. DPS program is a Chinese independent intellectual property of statistical software, DPS data processing system has been applied in various fields of natural and social sciences.

Results and analysis

Prediction of overwintering generation larval occurrence of Dendrolimus punctatus

The second generation larvae's population at the beginning of the bloom period in the previous year(x1), Parasitism rate of the Trichogrammatid in eggs of second generation larvae of the previous year(x2), the population of the previous year's second generation larvae(x3), the peak occurrence of the previous year's second generation larvae (x4), which was closely related to the accumulative population of overwintering larvae (y1),The correlation coefficient was 0.6493, 0.5471, 0.6559, 0.5986, df = 23, r0.05 = 0.396, r0.01 = 0.505, indicating that they were all extremely correlated. After normalization, the fuzzy vector X ~ = (0.2793, 0.1983, 0.2850, 0.2374).

The conditional probability of x 1 $$ {x}_1 $$ , x 2 $$ {x}_2 $$ , x 3 $$ {x}_3 $$ , x 4 $$ {x}_4 $$ to the forecasted amount (y) - the accumulative occurrence for the overwintering generation of D. punctatus larvae was listed in Table 1. The accumulative amount for the overwintering generation from 2015 to 2018 was predicted one by one.

TABLE 1. Conditional probability of each factor to the predictor
Series of y1 ∑P
1 2 3 4 5 6
Series of x1 1 1 0 0 0 0 0 1
2 8/11 2/11 1/11 0 0 0 1
3 2/6 1/6 1/6 0 1/6 1/6 1
4 1 0 0 0 0 0 1
5 0 0 1 0 0 0 1
6 0 0 1/3 0 1/3 1/3 1
Series of x2 1 0 0 0 0 1 0 1
2 1/7 1/7 3/7 0 1/7 1/7 1
3 2/3 1/3 0 0 0 0 1
4 7/10 1/10 1/10 0 0 1/10 1
5 3/4 0 1/4 0 0 0 1
Series of x3 1 1 0 0 0 0 0 1
2 3/4 1/6 1/12 0 0 0 1
3 3/7 1/7 1/7 0 1/7 1/7 1
4 0 0 1 0 0 0 1
5 0 0 0 0 1 0 1
6 0 0 1/2 0 0 1/2 1
Series of x4 1 1 0 0 0 0 0 1
2 9/16 0 1/8 0 1/16 1/16 1
3 0 0 1 0 0 0 1
4 0 0 0 0 1 0 1
5 0 0 1 0 0 0 1
6 0 0 0 0 0 1 1
In 2015, x 1 $$ {x}_1 $$ was 1.18 head /strain, x 2 $$ {x}_2 $$ was 22.1%, x 3 $$ {x}_3 $$ was 7.4 head/strain, x 4 $$ {x}_4 $$ was 1.93 head/strain. According to the classification standards in Table 2, x1-x4 was level 1, 4, 1 and 1, and the fuzzy matrix was
1 0 0 0 0 0 0.7 0.1 0.1 0 0 0.1 1 0 0 0 0 0 1 0 0 0 0 0 $$ \left[\begin{array}{cccccc}1& 0& 0& 0& 0& 0\\ {}0.7& 0.1& 0.1& 0& 0& 0.1\\ {}1& 0& 0& 0& 0& 0\\ {}1& 0& 0& 0& 0& 0\end{array}\right] $$
TABLE 2. The occurrence amount of Dendrolimus punctatus overwintering larvae in the classification table of forecasted elements
Series of y and xi
1 2 3 4 5 6
y1 0–8 8.1–16 16.1–24 24.1–32 32.1–40 40.1–48
x1 0–1.25 1.26–2.5 2.51–3.75 3.76–5.00 5.01–6.25 >6.25
x2 <10 10.1–15 15.1–20 20.1–25 25.1–30 >30
x3 0–8 8.1–16 16.1–24 24.1–32 32.1–40 40.1–48
x4 0–3 3.1–6 6.1–9 9.1–12 12.1–15 15.1–18

The actual calculation was

Y = [0.2793, 0.1983, 0.2850, 0.2374]⊙ 1 0 0 0 0 0 0.7 0.1 0.1 0 0 0.1 1 0 0 0 0 0 1 0 0 0 0 0 $$ \left[\begin{array}{cccccc}1& 0& 0& 0& 0& 0\\ {}0.7& 0.1& 0.1& 0& 0& 0.1\\ {}1& 0& 0& 0& 0& 0\\ {}1& 0& 0& 0& 0& 0\end{array}\right] $$ .

According to the evaluation model for calculation:
  • M1 = (1.0000, 0.2850, 0.2850, 0.2850, 0.2850, 0.2850).
  • M2 = (0.2850, 0.1000, 0.1000, 0, 0, 0.1000).
  • M3 = (0.2850, 0.0198, 0.0198, 0, 0, 0.0198).
  • M4 = (1.0000, 0.1000, 0.1000, 0, 0, 0.1000).
  • M5 = (0.9405, 0.0198, 0.0198, 0, 0, 0.0198).
  • M6 = (0.7021, 0.1049, 0.1049, 0.0570, 0.0570, 0.1049).

The final calculation results were: MaxM1yi = 1, MaxM2yi = 0.2850, MaxM3y = 0.2850,MaxM4yi = 1, MaxM5yi = 0.9405, MaxM6yi = 0.7021, and the corresponding levels to be reported for the six models were level 1. The accumulative occurrence of overwintering generation larvae in 2015 was level 1, and the actual occurrence was 6.2 head/strain. According to the classification standard of Table 2, namely, level 1, the forecasted result was accurate.

In 2016, x 1 $$ {x}_1 $$ was 1.14 head /strain, x 2 $$ {x}_2 $$ was 23.5%, x 3 $$ {x}_3 $$ was 7.4 head/strain, x 4 $$ {x}_4 $$ was 1.91 head/strain. According to the classification standards in Table 2, x1-x4 was level 1, 4, 1 and 1, and the fuzzy matrix was
1 0 0 0 0 0 0.7 0.1 0.1 0 0 0.1 1 0 0 0 0 0 1 0 0 0 0 0 $$ \left[\begin{array}{cccccc}1& 0& 0& 0& 0& 0\\ {}0.7& 0.1& 0.1& 0& 0& 0.1\\ {}1& 0& 0& 0& 0& 0\\ {}1& 0& 0& 0& 0& 0\end{array}\right] $$

The final calculation results were: MaxM1yi = 1, MaxM2yi = 0.2850, MaxM3y = 0.2850,MaxM4yi = 1, MaxM5yi = 0.9405, MaxM6yi = 0.7021, and the corresponding levels to be reported for the six models were level 1. The accumulative occurrence of overwintering generation larvae in 2016 was level 1, and the actual occurrence was 0.47 head/strain. According to the classification standard of Table 2, the forecasted result was accurate (Table 3).

TABLE 3. The predicated factors of Dendrolimus punctatus overwintering larvae and their gradation series
Year For overwintering generation larval accumulation population (head/strain) (y1) level number For second-generation beginning period population (head/strain) (x1) level number For second-generation eggs parasite rate (%) (x2) level number For second-generation larval accumulative population (head/strain) (x3) level number For second-generation peak occurrence (head/strain) (x4) level number
1989 42.5 6 2.59 3 10.1 2 16.2 3 3.63 2
1990 37.3 5 5.48 6 6.5 1 34.1 5 9.31 4
1991 18.5 3 2.94 3 10.8 2 18.4 3 4.18 2
1992 12.2 2 2.11 2 12.6 2 13.2 2 3.18 2
1993 7.8 1 1.89 2 12.1 2 11.8 2 2.64 1
1994 18.6 3 4.24 5 11.7 2 26.5 4 6.73 3
1995 18.2 3 6.46 6 11.4 2 40.4 6 12.32 5
1996 38.6 5 3.14 3 12.6 2 19.6 3 5.57 2
1997 42.1 6 8.42 6 20.6 4 52.6 6 15.89 6
1999 6.2 1 1.98 2 18.8 3 12.4 2 3.08 2
2000 7.6 1 1.86 2 24.2 4 11.6 2 3.07 2
2001 6.2 1 1.97 2 25.2 5 12.3 2 3.59 2
2002 7.1 1 2.02 2 22.3 4 12.6 2 3.62 2
2003 15.7 2 2.62 3 19.6 3 16.4 3 4.99 2
2004 7.6 1 3.01 3 18.2 3 18.8 3 5.87 2
2005 6.4 1 3.62 4 20.4 4 22.6 3 5.67 2
2006 6.6 1 2.02 2 20 4 12.6 2 3.11 2
2007 6.4 1 1.81 2 20.3 4 11.8 2 3.14 2
2008 6.6 1 1.94 2 20.3 4 12.1 2 2.93 1
2009 8.4 2 2.11 2 22.6 4 13.2 2 3.47 2
2010 16.2 3 2.21 2 24 4 13.8 2 3.34 2
2011 16.6 3 4.29 5 26.6 5 26.8 4 8.04 3
2012 7.2 1 2.67 3 26.6 5 16.7 3 4.53 2
2013 7.2 1 1.42 1 20.8 4 8.9 2 2.31 1
2014 6.4 1 1.15 1 27.3 5 7.2 1 1.92 1
2015 6.2 1
2016 7.1 1
2017
In 2017, x 1 $$ {x}_1 $$ was 1.3 head /strain, x 2 $$ {x}_2 $$ was 24.8%, x 3 $$ {x}_3 $$ was 8.1 head/strain, x 4 $$ {x}_4 $$ was 2.24 head/strain. According to the classification standards in Table 2, x1-x4 was level 1, 4, 2 and 1, and the fuzzy matrix was
1 0 0 0 0 0 0.7 0.1 0.1 0 0 0.1 0.75 0.1667 0.0813 0 0 0 1 0 0 0 0 0 $$ \left[\begin{array}{cccccc}1& 0& 0& 0& 0& 0\\ {}0.7& 0.1& 0.1& 0& 0& 0.1\\ {}0.75& 0.1667& 0.0813& 0& 0& 0\\ {}1& 0& 0& 0& 0& 0\end{array}\right] $$

The final calculation results were: MaxM1yi = 1, MaxM2yi = 0.2850, MaxM3y = 0.2793,MaxM4yi = 1, MaxM5yi = 0.8693, MaxM6yi = 0.6867, and the corresponding levels to be reported for the six models were level 1. The accumulative occurrence of overwintering generation larvae in 2017 was level 1, and the actual occurrence was 0.65 head/strain. According to the classification standard of Table 2, the forecasted result was accurate.

In 2018, x 1 $$ {x}_1 $$ was 0.18 head /strain, x 2 $$ {x}_2 $$ was 24.8%, x 3 $$ {x}_3 $$ was 1.1 head/strain, x 4 $$ {x}_4 $$ was 0.3 head/strain. According to the classification standards in Table 2, x1-x4 was level 1, 4, 1 and 1, and the fuzzy matrix was
1 0 0 0 0 0 0.7 0.1 0.1 0 0 0.1 1 0 0 0 0 0 1 0 0 0 0 0 $$ \left[\begin{array}{cccccc}1& 0& 0& 0& 0& 0\\ {}0.7& 0.1& 0.1& 0& 0& 0.1\\ {}1& 0& 0& 0& 0& 0\\ {}1& 0& 0& 0& 0& 0\end{array}\right] $$

The final calculation results were MaxM1yi = 1, MaxM2yi = 0.2850, MaxM3y = 0.2850, MaxM4yi = 1, MaM5yi = 0.9405, MaxM6yi = 0.7021, and the corresponding levels to be reported for the six models were level 1. The accumulative occurrence of overwintering generation larvae in 2018 was level 1, and the actual occurrence was 0.12 head/strain. According to the classification standard of Table 2, the forecasted result was consistent with the actual value.

Prediction of the cumulative occurrence of the first-generation larvae of the Dendrolimus punctatus

Parasitism rate of the Trichogrammatidae in eggs of first generation larvae(x5), accumulative occurrence for the overwintering generation larvae (x6), the eggs for the first generation (x7), and peak occurrence for the first generation larvae (x8), were closely related to accumulative occurrence for the first generation larvae (y2), The correlation coefficient was 0.5001, 0.5872, 0.9998, 0.9930, df = 23, r0.05 = 0.396, r0.01 = 0.505, indicating that they were all extremely correlated. After normalization, the fuzzy vector X ~ = (0.0969, 0.1336, 0.3874, 0.3821). For analysis, x1 ~ x4 were graded.

In 2015, x 5 $$ {x}_5 $$ was 17.3%, x 6 $$ {x}_6 $$ was 6.2 head/strain x 7 $$ {x}_7 $$ was 1.01 head/strain, x 8 $$ {x}_8 $$ was 2.12 head/strain. According to the classification standards in Table 4, x5-x8 was level 4, 1, 1 and 1, and the fuzzy matrix was
0.5 0.3333 0.1667 0 0 0 0.6154 0.3077 0.0769 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 $$ \left[\begin{array}{cccccc}0.5& 0.3333& 0.1667& 0& 0& 0\\ {}0.6154& 0.3077& 0.0769& 0& 0& 0\\ {}1& 0& 0& 0& 0& 0\\ {}1& 0& 0& 0& 0& 0\end{array}\right] $$
TABLE 4. The occurrence amount of Dendrolimus punctatus first generation larvae of classification table of forecasted elements
Series of y2 and xi
1 2 3 4 5 6
y2 0–8 8.1–16 16.1–24 24.1–32 32.1–40 40.1–48
x5 <9 9.1–12 12.1–15 15.1–18 18.1–21 >21
x6 0–8 8.1–16 16.1–24 24.1–32 32.1–40 40.1–48
x7 0–1.25 1.26–2.5 2.51–3.75 3.76–5.0 5.01–6.25 >6.25
x8 0–3 3.1–6 6.1–9 9.1–12 12.1–15 15.1–18

The actual calculation was

Y = [0.0969, 0.1336,0.3874, 0.3821] ⊙ 0.5 0.3333 0.1667 0 0 0 0.6154 0.3077 0.0769 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 $$ \left[\begin{array}{cccccc}0.5& 0.3333& 0.1667& 0& 0& 0\\ {}0.6154& 0.3077& 0.0769& 0& 0& 0\\ {}1& 0& 0& 0& 0& 0\\ {}1& 0& 0& 0& 0& 0\end{array}\right] $$ .

According to the evaluation model for calculation:
  • M1 = (1.0000, 0.3874, 0.3874, 0.3874, 0.3874, 0.3874).
  • M2 = (0.3874, 0.1336, 0.0969, 0, 0, 0).
  • M3 = (0.3874, 0.0411, 0.0162, 0, 0, 0).
  • M4 = (1.0000, 0.2305, 0.1738, 0, 0, 0).
  • M5 = (0.9002, 0.0734, 0.0264, 0, 0, 0).
  • M6 = (0.7350, 0.1732, 0.1401, 0.0775, 0.0775, 0.0775).

The final calculation results were: MaxM1yi = 1, MaxM2yi = 0.3874, MaxM3y = 0.3874, MaxM4yi = 1, MaxM5yi = 0.9002, MaxM6yi = 0.7350, and the corresponding levels to be reported for the six models were level 1. The accumulative occurrence of first-generation larvae in 2015 was level 1, and the actual occurrence was 4.95 head/strain. According to the classification standard of Table 4, namely, level 1, the forecasted result was accurate.

In 2016, x 5 $$ {x}_5 $$ was 16.9%, x 6 $$ {x}_6 $$ was 7.1 head/strain x 7 $$ {x}_7 $$ was 1.06 head/strain, x 8 $$ {x}_8 $$ was 2.25 head/strain. According to the classification standards in Table 4, x5-x8 was level 4, 1, 1 and 1, and the fuzzy matrix was
0.5 0.3333 0.1667 0 0 0 0.6154 0.3077 0.0769 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 $$ \left[\begin{array}{cccccc}0.5& 0.3333& 0.1667& 0& 0& 0\\ {}0.6154& 0.3077& 0.0769& 0& 0& 0\\ {}1& 0& 0& 0& 0& 0\\ {}1& 0& 0& 0& 0& 0\end{array}\right] $$

The final calculation results were: MaxM1yi = 1, MaxM2yi = 0.3874, MaxM3y = 0.3874, MaxM4yi = 1, MaxM5yi = 0.9002, MaxM6yi = 0.7350, and the corresponding levels to be reported for the six models were level 1. The accumulative occurrence of first-generation larvae in 2016 was level 1, and the actual occurrence was 6.6 head/strain. According to the classification standard of Table 4, namely, level 1, the forecasted result was accurate.

In 2017, x 5 $$ {x}_5 $$ was 17.9%, x 6 $$ {x}_6 $$ was 12.8 head/strain x 7 $$ {x}_7 $$ was 0.19 head/strain, x 8 $$ {x}_8 $$ was 0.37 head/strain. According to the classification standards in Table 4, x5-x8 was level 4, 2, 1 and 1, and the fuzzy matrix was
0.5 0.3333 0.1667 0 0 0 0.3333 0.3333 0.3333 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 $$ \left[\begin{array}{cccccc}0.5& 0.3333& 0.1667& 0& 0& 0\\ {}0.3333& 0.3333& 0.3333& 0& 0& 0\\ {}1& 0& 0& 0& 0& 0\\ {}1& 0& 0& 0& 0& 0\end{array}\right] $$

The final calculation results were: MaxM1yi = 1, MaxM2yi = 0.3874, MaxM3y = 0.3874, MaxM4yi = 1, MaxM5yi = 0.8625, MaxM6yi = 0.7275, and the corresponding levels to be reported for the six models were level 1. The accumulative occurrence of first-generation larvae in 2017 was level 1, and the actual occurrence was 1.2 head/strain. According to the classification standard of Table 4, namely, level 1, the forecasted result was accurate.

In 2018, x 5 $$ {x}_5 $$ was 18.2%, x 6 $$ {x}_6 $$ was 1.8 head/strain x 7 $$ {x}_7 $$ was 0.26 head/strain, x 8 $$ {x}_8 $$ was 0.54 head/strain. According to the classification standards in Table 4, x5-x8 was level 5, 1, 1 and 1, and the fuzzy matrix was
1 0 0 0 0 0 0.6154 0.3077 0.0769 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 $$ \left[\begin{array}{cccccc}1& 0& 0& 0& 0& 0\\ {}0.6154& 0.3077& 0.0769& 0& 0& 0\\ {}1& 0& 0& 0& 0& 0\\ {}1& 0& 0& 0& 0& 0\end{array}\right] $$

The final calculation results were: MaxM1yi = 1, MaxM2yi = 0.3874, MaxM3y = 0.3874, MaxM4yi = 1, MaxM5yi = 0.9486, MaxM6yi = 0.7447, and the corresponding levels to be reported for the six models were level 1. The accumulative occurrence of first-generation larvae in 2018 was level 1, and the actual occurrence was 1.6 head/strain. According to the classification standard of Table 4, namely, level 1, the forecasted result was accurate.

Predicted cumulative occurrence of second-generation larvae of Dendrolimus punctatus

The population of the beginning period for the second-generation larvae (x9), and peak occurrence for the second generation larvae (x10), were closely related to accumulative occurrence for the second generation larvae (y3), The correlation coefficient was 0.9999, 0.9917, df = 23, r0.05 = 0.396, r0.01 = 0.505, indicating that they were all extremely correlated. After normalization, the fuzzy vector X ~ = (0.5021, 0.4979). For analysis, x9 ~ x10 were graded (Table 5).

TABLE 5. The predication factors of the accumulated Dendrolimus punctatus first generation larvae and their gradation series
Year For first generation larval accumulative population (head/strain) (y2) level number For first generation eggs parasite rate(%) (x5) level number For overwintering generation larval accumulative population (head/strain) (x6) level number For first generation beginning period accumulative population (head/strain) (x7) level number For first generation larvae peak occurrence (head/strain) (x8) level number
1989 18.3 3 7.1 1 42.5 6 2.93 3 5.93 2
1990 42.5 6 8.6 1 37.3 5 6.80 6 15.26 6
1991 7.6 1 10.9 2 18.5 3 1.22 1 1.92 1
1992 7.8 1 12.5 3 12.2 2 1.25 1 2.35 1
1993 7.4 1 10.4 2 7.8 1 1.18 1 2.1 1
1994 38.6 5 10.4 2 18.6 3 6.18 5 4.77 4
1995 19.6 3 13.1 3 18.2 3 3.14 3 5.66 2
1996 40.1 6 14.2 3 38.6 5 6.42 6 13.07 5
1997 7.1 1 12.6 3 42.1 6 1.14 1 2.17 1
1999 6.6 1 16.4 4 6.2 1 1.06 1 2.02 1
2000 7.2 1 20.6 5 7.6 1 1.15 1 2.43 1
2001 6.1 1 22.4 6 6.2 1 0.98 1 2.11 1
2002 8.6 2 16.7 4 7.1 1 1.38 2 3.11 2
2003 18.6 3 14.6 3 15.7 2 2.98 3 6.53 3
2004 7.7 1 16.3 4 7.6 1 1.23 1 2.63 1
2005 16.4 3 14 3 6.4 1 2.62 3 5.25 2
2006 12 2 14.6 3 6.6 1 1.92 2 3.47 2
2007 12.6 2 14.6 3 6.4 1 2.02 2 4.13 2
2008 12.1 2 16.9 4 6.6 1 1.94 2 4.19 2
2009 12.8 2 14.8 3 8.4 2 2.05 2 4.56 2
2010 16.2 3 12.6 3 16.2 3 2.59 3 5.52 2
2011 16.1 3 16.5 4 16.6 3 2.58 3 5.15 2
2012 7.4 1 18.1 5 7.2 1 1.18 1 2.35 1
2013 6.7 1 18.1 5 7.2 1 1.07 1 2.3 1
2014 6.7 1 16.7 4 6.4 1 1.07 1 2.16 1

In 2015, x 9 $$ {x}_9 $$ was 1.14 head/strain, x 10 $$ {x}_{10} $$ was 1.91 head/strain. According to the classification standards in Table 6, x9-x10 was level 1, and the fuzzy matrix was

0.6667 0.3333 0 0 0 0 0.4 0.6 0 0 0 0 $$ \left[\begin{array}{cccccc}0.6667& 0.3333& 0& 0& 0& 0\\ {}0.4& 0.6& 0& 0& 0& 0\end{array}\right] $$

TABLE 6. The occurrence amount of Dendrolimus punctatus second generation larvae of classification table of forecasted elements
Species Classification number
1 2 3 4 5 6
y3 0–8 8.1–16 16.1–24 24.1–32 32.1–40 40.1–48
x9 <1.45 1.46–2.35 2.36–3.25 3.26–4.15 4.16–5.05 >5.05
x10 0–3 3.1–6 6.1–9 9.1–12 12.1–15 >15.1
The actual calculation was
Y = 0.5021 , 0.4979 ⊙ 0.6667 0.3333 0 0 0 0 0.4 0.6 0 0 0 0 . $$ \mathrm{Y}=\left[0.5021,0.4979\right]\odot \left[\begin{array}{cccccc}0.6667& 0.3333& 0& 0& 0& 0\\ {}0.4& 0.6& 0& 0& 0& 0\end{array}\right]. $$
According to the evaluation model for calculation:
  • M1 = (0.6667, 0.6000, 0.5021, 0.5021, 0.5021, 0.5021).
  • M2 = (0.5021, 0.4979, 0, 0, 0, 0).
  • M3 = (0.3348, 0.2987, 0, 0, 0, 0).
  • M4 = (0.9021, 0.8312, 0, 0, 0, 0).
  • M5 = (0.5339, 0.4661, 0, 0, 0, 0).
  • M6 = (0.5879, 0.5388, 0.1004, 0.1004, 0.1004, 0.1004).

The final calculation results were: MaxM1yi = 0.6667, MaxM2yi = 0.5021, MaxM3y = 0.3348, MaxM4yi = 0.9021, MaxM5yi = 0.5339, MaxM6yi = 0.5879, and the corresponding levels to be reported for the six models were level 1 (Table 7). The accumulative occurrence of second-generation larvae in 2015 was level 1, and the actual occurrence was 7.1 head/strain. According to the classification standard in Table 6, the forecasted result was accurate.

TABLE 7. Conditional probability of each factor of first-generation larvae cumulative amount to the predicted quantity
Series of y2 ∑P
1 2 3 4 5 6
Series of x5 1 0 0 1/2 0 0 1/8 1
2 2/3 0 0 0 1/3 0 1
3 1/5 3/10 2/5 0 0 1/10 1
4 8/16 1/3 1/6 0 0 0 1
5 1 0 0 0 0 0
6 1 0 0 0 0 0
Series of x6 1 8/13 4/13 1/13 0 0 0 1
2 1/3 1/3 1/3 0 0 0 1
3 1/5 0 3/5 0 1/5 0 1
4 0 0 0 0 0 0 0
5 0 0 0 0 0 1 1
6 1/2 0 1/2 0 0 0 1
Series of x7 1 1 0 0 0 0 0 1
2 0 1 0 0 0 0 1
3 0 0 1 0 0 0 1
4 0 0 0 0 0 0
5 0 0 0 0 1 0 1
6 0 0 0 0 0 1
Series of x8 1 1 0 0 0 0 0 1
2 0 1/2 1/2 0 0 0 1
3 0 0 1 0 0 0 1
4 0 0 0 0 1 0 1
5 0 0 0 0 0 1 1
6 0 0 0 0 0 1
In 2016, x 9 $$ {x}_9 $$ was 1.30 head/strain, x 10 $$ {x}_{10} $$ was 2.24 head/strain. According to the classification standards in Table 6, x9-x10 was level 1, and the fuzzy matrix was
0.6667 0.3333 0 0 0 0 0.4 0.6 0 0 0 0 $$ \left[\begin{array}{cccccc}0.6667& 0.3333& 0& 0& 0& 0\\ {}0.4& 0.6& 0& 0& 0& 0\end{array}\right] $$

The final calculation results were: MaxM1yi = 0.6667, MaxM2yi = 0.5021, MaxM3y = 0.3348, MaxM4yi = 0.9021, MaxM5yi = 0.5339, MaxM6yi = 0.5879, and the corresponding levels to be reported for the six models were level 1. The accumulative occurrence of second-generation larvae in 2016 was level 1, and the actual occurrence was 7.1 head/strain. According to the classification standard in Table 6, the forecasted result was accurate.

In 2017, x 9 $$ {x}_9 $$ was 0.18 head/strain, x 10 $$ {x}_{10} $$ was 0.3 head/strain. According to the classification standards in Table 6, x9-x10 was level 1, and the fuzzy matrix was
0.6667 0.3333 0 0 0 0 0.4 0.6 0 0 0 0 $$ \left[\begin{array}{cccccc}0.6667& 0.3333& 0& 0& 0& 0\\ {}0.4& 0.6& 0& 0& 0& 0\end{array}\right] $$

The final calculation results were: MaxM1yi = 0.6667, MaxM2yi = 0.5021, MaxM3y = 0.3348, MaxM4yi = 0.9021, MaxM5yi = 0.5339, MaxM6yi = 0.5879, and the corresponding levels to be reported for the six models were level 1. The accumulative occurrence of second-generation larvae in 2017 was level 1, and the actual occurrence was 1.1 head/strain. According to the classification standard in Table 6, the forecasted result was accurate.

Summary

The six models of the fuzzy comprehensive evaluation method were used to predict the accumulative occurrence of D. punctatus larvae for the overwintering, the first and second generation in Qianshan County of Anhui Province, the result was as follows.
  1. The level to be reported for the six models of accumulative occurrence for the overwintering generation larvae in 2015, 2016, 2017 and 2018 was level 1, and the actual result was level 1.
  2. The level to be reported for the 5 models of accumulative occurrence for the first-generation larvae in 2015, 2016, 2017 and 2018 was level 1, and the actual result was level 1 (Table 8).
  3. The level to be reported for the six models of accumulative occurrence for the second-generation larvae in 2015, 2016 and 2017 was level 1, and the actual result was level 1.
TABLE 8. Forecasted factor and classification value from 1989 to 2014
Year For second generation accumulative occurrence (head/strain)(y3) level number For second generation beginning period accumulative population (head/strain) (x9) level number For second generation peak occurrence (head/strain)(x10) level number
1989 34.1 5 5.46 6 9.31 4
1990 18.4 3 2.94 3 4.18 2
1991 13.2 2 2.11 2 3.18 2
1992 11.8 2 1.89 2 2.64 1
1993 26.5 4 4.24 5 6.73 3
1994 40.4 6 6.46 6 12.32 5
1995 19.6 3 3.14 3 5.57 2
1996 52.6 6 8.42 6 15.89 6
1997 12.4 2 1.98 2 3.08 2
1999 11.6 2 1.86 2 3.07 2
2000 12.3 2 1.97 2 3.59 2
2001 12.6 2 2.02 2 3.62 2
2002 16.4 3 2.62 32 4.99 2
2003 18.8 3 3.01 3 5.87 2
2004 22.6 3 3.62 4 5.67 2
2005 12.6 2 2.02 2 3.11 2
2006 11.8 2 1.81 2 3.14 2
2007 12.1 2 1.94 2 2.93 1
2008 13.2 2 2.21 2 3.47 2
2009 13.8 2 2.21 2 3.34 2
2010 26.8 4 4.29 5 8.04 3
2011 16.7 3 2.67 3 4.53 2
2012 8.9 2 1.42 1 2.31 1
2013 7.2 1 1.15 1 1.92 1
2014 7.1 1 1.18 1 1.85 1

The prediction results of the prediction model for the cumulative occurrence of overwintering generation, first and second-generation larvae are in full agreement with the actual situation, and the fuzzy integrated evaluation method is a better prediction method

Discussion

D. punctatus infestation is extremely serious in China, causing huge economic losses and serious harm to forest safety and the forestry economy, and it is necessary to make effective prediction and forecasting work to prepare for the control of D. punctatus infestation.

In this study, the prediction results using the fuzzy comprehensive evaluation method and the actual occurrence results are both level 1, and the historical compliance rate of forecasting the larval period of D. punctatus is 100%, and the results of this study shows that the prediction results of the fuzzy comprehensive evaluation method are accurate.

The fuzzy comprehensive evaluation method is easy to calculate with a low workload and is widely used. Fuzzy mathematics is widely used in mining ecological environment, urban ecology, food sensory evaluation, citrus wine and groundwater environmental quality assessment (Guan et al. 2014; Homik et al. 1989; Huang et al. 2015; Li & Xiao 2016; Ma et al. 2013; Wang & Zhang 2000; Zhang 2006; Zou & Wang 1989). There are six mathematical models to facilitate the choice of forecast analysis, and it can combine the predictions of six mathematical models. The key to the fuzzy comprehensive evaluation method is the selection of predictors that are closely related to the forecast quantity and whether the grading criteria for the forecast quantity are scientific (Table 9). The accuracy of the forecasted results depended largely on the choice of predicted factors. First of all, forecast factors had biological, physical or chemical relationships with the forecast target. The changes in these factors can affect the changes in forecast results; secondly, among many forecast factors the degree of their effects on the forecast results was different, and it was necessary to choose the forecast factors that had a great effect on the forecast results, that was those with high relevance to the forecast results; thirdly, the appropriate amount of forecast factors were chosen for many related forecast factors, not the more forecast factors was chosen the better. The predictors selected in this paper were biologically related to the forecasted target. The relationship between the forecasted targets was related or extremely relevant. In this paper, the occurrence period of D. punctatus larvae was divided into 6 levels, and the difference between adjacent levels was 1. The single correlation analysis method was used to screen x1 ~ x10, which were all factors that were highly correlated with the occurrence period of D. punctatus larvae. Therefore, the weight of the correlation coefficient through normalization helped to improve the accuracy of the forecasted results. The reasons for the accuracy of the forecasted results were also related to the evaluation models. Because the focus of the six mathematical models were different.

TABLE 9. Conditional probability of each factor of second-generation larvae cumulative amount to the predicted quantity
Series of xi Series of y3 ∑P
1 2 3 4 5 6
Series of x1 1 2/3 1/3 0 0 0 0 1
2 0 1 0 0 0 0 1
3 0 0 1 0 0 0 1
4 0 0 1 0 0 0 1
5 0 0 0 1 0 0 1
6 0 0 0 0 1/3 2/3 0
Series of x2 1 2/5 3/5 0 0 0 0 1
2 0 3/5 2/5 0 0 0 1
3 0 0 0 1 0 0 1
4 0 0 0 0 1 0 1
5 0 0 0 0 0 1 1
6 0 0 0 0 0 1 1

The timing of the larval period of the D. punctatus will follow the temperature fluctuations, the growth and development of the D. punctatus must have a certain amount of effective cumulative temperature, but due to the fluctuation of temperature, some forecast factors such as the overwintering generation larval period, if the temperature is significantly lower than normal, the peak of the overwintering generation larvae delayed, if the temperature is significantly higher than normal, the peak of the overwintering generation larvae early, the rest of the occurrence of the same situation will occur in the rest of the occurrence period. The growth and development of D. punctatus are changed by the sequence of egg, larvae, pupae and adults, and the change in the occurrence of the previous insect state will affect the occurrence of the next insect state. If the temperature of the overwintering larval stage (or the rest of the occurrence) is within the range of variation, and the overwintering larval stage and the rest of the occurrence are very small compared with the normal year, the difference between the forecast result of the first-generation larval stage and the actual situation is very small. This is also the case for the second larval stage.

With the application of mathematical models in nonlinear science for forest pests and diseases, the prediction results become more and more accurate. The occurrence of D. punctatus infestation is influenced by a variety of factors, and it is found that the prediction results should be analyzed by combining various factors such as meteorology, ecological environment and natural enemy organisms, and the mathematical model and the grading criteria of forecast quantity should be continuously optimized to improve the prediction accuracy of the model. In this paper, we use the fuzzy comprehensive evaluation method to systematically analyze the peak period of D. punctatus, and in the future, we will combine different mathematical methods to construct prediction models with a broader application prospect.

Acknowledgments

The authors are grateful to the editor and the reviewers for valuable reviews and manuscript improvements. This research is supported by the Support Program for Outstanding Young Talents of Anhui Province Universities (No. gxyq2021165).

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