# Forecasting Model and Related Index of Pig Population in China

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

^{.}Reasonable prediction of the hog supply is fundamental to control fluctuations in pork prices. In recent years, Ref. [31] pointed out that the use of data on the pig population in the pig population management system can improve the prediction accuracy of pig supply. Therefore, the pig population prediction is the basis and premise for understanding and controlling the production capacity of pork. At present, there are few studies on the prediction of pig population. Ref. [32] developed a system dynamics model as a tool for managing and visualizing changes in pig population. The model can be used to simulate the expansion and contraction of the pig population with the influencing factors such as increasing the number of sows. This model can roughly visualize the changes of a pig population without the need for in-depth basic mathematics. There are some scholars concerned with the predictions about certain kinds of pigs such as making a preliminary prediction on the number of breeding sows based on historical data to point out that the number of breeding sows would continue to decline for about 3 months. Some authors also pointed out that there is a quantitative causal relationship between the number of sows and the price of pigs, but the specific quantitative relationship has not been calculated, and no corresponding functional model has been established [33,34].

## 2. Model Building

#### 2.1. Pig Type and Growth Stage

#### 2.2. Derivation and Establishment of the Recursive Model of Pig population and Estimation Model of Pork Supply

- The recurrence formula of the distribution of the number of new born piglets by months of age is as follows:$${z}_{00}(t)=A\lambda (t){\displaystyle \sum _{r={r}_{i}}^{r2}{h}_{r}(t){z}_{r}^{w}(t)}\phantom{\rule{0ex}{0ex}}{Z}_{0}(t)=(1-{d}_{00}){Z}_{00}(t)\phantom{\rule{0ex}{0ex}}{Z}_{1}(t+1)=(1-{d}_{0}){Z}_{0}(t+1)$$
- The recurrence formula for the distribution of sows by months of age is as follows: ${z}_{1}^{w}(t+1)$ is the number of artificially retained.$$\begin{array}{l}{Z}_{2}^{W}(t+1)=(1-{d}_{1}^{W}){z}_{1}^{W}(t)+{x}_{1}(t)\\ \\ {Z}_{3}^{W}(t+1)=(1-{d}_{2}^{W}){z}_{2}^{W}(t)+{x}_{2}(t)\\ \\ \begin{array}{cc}& \end{array}\begin{array}{cc}\begin{array}{cc}& \end{array}& \end{array}\cdots \\ \\ {Z}_{r+1}^{W}(t+1)=(1-{d}_{r}^{W}(t)){z}_{r}^{W}(t)+{x}_{r}(t)\end{array}$$

- 3.
- The recurrence formula for the distribution of boars by months of age is as follows:

- 4.
- The recurrence formula for the distribution of the number of pork pigs per month of age is as follows:

#### 2.3. Estimation Method for New Kept Gilts and Breeding Sows

#### 2.3.1. Estimation of the Sum of Monthly Mortality and Culling Rate of Breeding Sows

#### 2.3.2. Calculation Method for New Gilts in Each Month

#### Construction of the Relationship Model between New Kept Gilts and Pork Prices

#### Parameter Calculation of the Relationship Model between New Kept Gilts and Pork Prices

#### 2.3.3. Estimation of Breeding Sows at Each Month of Age

#### 2.4. Estimate of the Initial Condition of the Pig Population

#### 2.5. Population Index

- (1)
- Number of breeding sows at the end of the year:

- (2)
- Inventory of pigs at the end of the year:

- (3)
- Number of slaughtered fattened hogs

- (4)
- Pork production in the current year:

- (5)
- Number of sows per month at time t:

- (6)
- Number of boars per month age at time t

- (7)
- The number of boars at time t

- (8)
- The total number of slaughter pigs at time t is as follows:

## 3. Example Calculations

#### 3.1. Data Source and Description

#### 3.2. Examples and Results Evaluation

#### 3.2.1. Estimation of New Gilts and Breeding Sows

#### 3.2.2. The Estimation of Initial Pig Population State

#### 3.2.3. Predict the Distribution of Pig Population in China in the Future

#### 3.2.4. The Prediction of the Pig Population Index in China in 2017

## 4. Conclusions

## Author Contributions

^{1}(Fulin Wang), F.W.

^{2}(Fulin Wang) worked collectively. F.Z. conceived and designed the study with the support of F.W.

^{1}(Fulin Wang), F.W.

^{2}(Fulin Wang) gave constructive suggestions for the idea and the writing. All the co-authors drafted and revised the article together. All authors have read and agreed to the published version of the manuscript.

## Funding

## Conflicts of Interest

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**Table 1.**A comparison table between the predicted and the actual value of the number of breeding sows in 2004–2015.

Year | Predictive Value (Ten Thousand) | Actual Value (Ten Thousand) | Relative Error |
---|---|---|---|

2004 | 566 | 566 | |

2005 | 570.9614574 | 589 | 0.030625709 |

2006 | 573.4566575 | 570 | 0.006064311 |

2007 | 574.9350511 | 523 | 0.099302201 |

2008 | 585.8609814 | 587 | 0.001940406 |

2009 | 598.6894485 | 595 | 0.006200754 |

2010 | 603.0519213 | 585 | 0.030857985 |

2011 | 605.5471426 | 591 | 0.024614455 |

2012 | 613.1236142 | 604 | 0.015105322 |

2013 | 618.7693569 | 613 | 0.009411675 |

2014 | 624.2275925 | 596 | 0.047361732 |

2015 | 622.1858153 | 569 | 0.093472435 |

**Table 2.**A comparison table between the predicted and the actual value of the number of finishing pigs in each year.

Year | Predictive Value (Ten Thousand) | Actual Value (Ten Thousand) | Relative Error |
---|---|---|---|

2006 | 7105.02 | 6780.717945 | 0.047827097 |

2007 | 7471.41 | 6804.190631 | 0.098060064 |

2008 | 6360.7 | 6809.446693 | 0.06590061 |

2009 | 6431.4 | 6961.360612 | 0.076128884 |

2010 | 6915.5 | 7108.225114 | 0.027112973 |

2011 | 7178.28 | 7149.174708 | 0.00407114 |

2012 | 7002.6 | 7180.25797 | 0.024742561 |

2013 | 7170.7 | 7276.110933 | 0.014487263 |

2014 | 7314.1 | 7344.67785 | 0.004163266 |

2015 | 7445 | 7404.611788 | 0.005454467 |

Time | Number (Ten Thousand) | Time | Number (Ten Thousand) | Time | Number (Ten Thousand) |
---|---|---|---|---|---|

January 2016 | 27.9298 | October 2016 | 28.0708 | July 2017 | 27.2512 |

February 2016 | 28.1523 | November 2016 | 27.9799 | August 2017 | 27.3216 |

March 2016 | 28.1672 | December 2016 | 28.0318 | September 2017 | 27.4218 |

April 2016 | 28.4008 | January 2017 | 28.1690 | October 2017 | 27.3939 |

May 2016 | 28.5436 | February 2017 | 28.0986 | November 2017 | 27.3531 |

June 2016 | 28.6029 | March 2017 | 27.3272 | December 2017 | 27.4570 |

July 2016 | 28.7791 | April 2017 | 27.7314 | January 2018 | 27.5219 |

August 2016 | 28.3081 | May 2017 | 27.4792 | February 2018 | 27.4329 |

September 2016 | 28.2896 | June 2017 | 27.2716 | March 2018 | 26.9971 |

Time | Number (Ten Thousand) | Time | Number (Ten Thousand) | Time | Number (Ten Thousand) |
---|---|---|---|---|---|

January 2016 | 665.2360 | October 2016 | 665.3340 | July 2017 | 672.4522 |

February 2016 | 664.3963 | November 2016 | 665.8391 | August 2017 | 673.1802 |

March 2016 | 663.9295 | December 2016 | 666.4881 | September 2017 | 673.8585 |

April 2016 | 663.4213 | January 2017 | 667.2831 | October 2017 | 674.4909 |

May 2016 | 663.0983 | February 2017 | 668.0141 | November 2017 | 675.0584 |

June 2016 | 663.0819 | March 2017 | 668.9140 | December 2017 | 675.6828 |

July 2016 | 663.7822 | April 2017 | 669.9261 | January 2018 | 676.1457 |

August 2016 | 664.3333 | May 2017 | 670.8922 | February 2018 | 675.9240 |

September 2016 | 664.8637 | June 2017 | 671.8684 | March 2018 | 676.0462 |

Time | Number (Ten Thousand) | Time | Number (Ten Thousand) | Time | Number (Ten Thousand) |
---|---|---|---|---|---|

January 2016 | 579.3772 | October 2016 | 575.9535917 | July 2017 | 579.6922849 |

February 2016 | 579.65269 | November 2016 | 575.5439568 | August 2017 | 580.9896057 |

March 2016 | 579.7294325 | December 2016 | 575.4801702 | September 2017 | 581.4689223 |

April 2016 | 579.7225285 | January 2018 | 576.3562409 | October 2017 | 582.5915294 |

May 2016 | 597.6500583 | February 2017 | 576.8695025 | November 2017 | 583.6358593 |

June 2016 | 122.7583752 | March 2017 | 577.5293108 | December 2017 | 584.5347175 |

July 2016 | 577.9820714 | April 2017 | 578.0292742 | January 2018 | 585.0040278 |

August 2016 | 577.0397165 | May 2017 | 578.4427404 | February 2018 | 585.5790734 |

September 2016 | 576.6056677 | June 2017 | 578.9158294 | March 2018 | 586.2149126 |

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**MDPI and ACS Style**

Zhang, F.; Wang, F.; Wang, F.
Forecasting Model and Related Index of Pig Population in China. *Symmetry* **2021**, *13*, 114.
https://doi.org/10.3390/sym13010114

**AMA Style**

Zhang F, Wang F, Wang F.
Forecasting Model and Related Index of Pig Population in China. *Symmetry*. 2021; 13(1):114.
https://doi.org/10.3390/sym13010114

**Chicago/Turabian Style**

Zhang, Fan, Fulin Wang, and Fulin Wang.
2021. "Forecasting Model and Related Index of Pig Population in China" *Symmetry* 13, no. 1: 114.
https://doi.org/10.3390/sym13010114