# Statistical Evaluations of Variations in Dairy Cows’ Milk Yields as a Precursor of Earthquakes

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## Abstract

**:**

## Simple Summary

## Abstract

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Milk Yields

_{t}is the expected milk yield in time t, n

_{t}is the number of days after calving, e is natural logarithm, and a, b and c are parameters. These parameters were estimated using a general linear model (glm function in R; version 3.3.0, The R Foundation for Statistical Computing, Vienna, Austria) after a logarithmic transformation [35,36]. Table 1 shows estimated parameters for individual lactation curves. Then, residual values I of milk yields (dM-I) were calculated by subtracting these predicted values from the actual measurement values of the current day:

_{t}= M

_{t}− pM-I

_{t},

_{t}is the milk yield for a current day and pM-I

_{t}is the predicted value for the current day estimated by Wood’s model.

_{t}= (1.8 T

_{t}+ 32) − (5.5 + 0.055 H

_{t}) × (1.8 T

_{t}− 26),

_{t}is the mean dM-I at time t, x

_{t−2}is the THI at the relevant lag, x0 is the critical point in THI, and a, b and c are parameters. The estimated model was used to calculate the expected daily milk yields from the THI values. Table 2 shows estimated parameters and the critical point. The residual values of the milk yields (dM-II) were calculated by subtracting these predicted values from dM-I:

_{t}= dM-I

_{t}− pM-II

_{t},

_{t}is the milk yield after removing the effect of calving time and pM-II

_{t}is the predicted value based on the THI values. The dM-II data might have trend variation, which is inappropriate for time-series analyses. Therefore, final variations in milk yields were calculated by the partly-changed equation described by Maekawa et al. [14] and Hayakawa et al. [33]. That is, we calculated residual values in the milk yields as:

_{t}= dM-II

_{t}− <dM-II

_{t}>,

_{t}is the milk yield after removal of two effects at time t and <dM-II

_{t}> is the 7-day backward moving average at the same time t. These final variations (dM-III) were used in analyses regarding the relevance of the data to earthquakes.

#### 2.2. Cross-Correlation Analyses

^{0.43M},

^{(4.8+1.5M)},

#### 2.3. Performance Evaluations of Binary Earthquake Forecasts

#### 2.4. Comparison with Anomalies of VLF/LF Propagation Data

## 3. Results

#### 3.1. Cross-Correlation Analyses

#### 3.2. Binary Earthquake Forecasts

#### 3.3. Comparison with Anomalies in VLF/LF Propagation Data

## 4. Discussion

#### 4.1. Cross-Correlation Analyses

#### 4.2. Binary Earthquake Forecasts

#### 4.3. Comparison with Anomalies of VLF/LF Propagation Data

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**The radius (km) calculated according to the Dobrovolsky radius condition with magnitudes (Ms) = 5.0, 5.5 and 6.0. The red circles represent the maximum range for earthquakes of each M. The solid green circle represents the location of the farm used to observe milk yields.

**Figure 2.**The location of the farm used to observe milk yields, eight observatories and the Japanese low frequency transmitting station (JJY) for very low frequency/low frequency (VLF/LF) propagation data. Red lines represent the propagation path from JJY to the eight observatories. NSB = Nakashibetsu; AKT = Akita; IMZ = Imizu; KTU = Katsuura; KMK = Kamakura; TYH = Toyohashi ANA = Anan; STU = Suttu.

**Figure 4.**The variations of milk yields in the total observation period (Mean ± Standard deviation). The blank area indicates no observation.

**Figure 5.**The detail of earthquakes which occurred during the days exceeding effective magnitude (Meff) 5.0. The red stars represent the locations of earthquakes. The green circle represents the location of the farm used to observe milk yields. The upper table shows the detail of earthquakes. The alphabets in the map correspond with those in the table. Lat = Latitude; Lon = Longitude; D = Distance from epicenters; DRC = Dobrovolsky radius condition.

**Figure 6.**The results of cross-correlation analyses between milk yields and the dates exceeding each Meff; CI = confidence interval.

**Figure 7.**The scores used to estimate the cross-tabulation tables using the twelve criteria. (

**a**) shows hit rate (H, %); (

**b**) shows probability gain (PG) and (

**c**) shows the successful rate of earthquake prediction (SEP, %). The lower table shows the details of the criteria.

**Table 1.**Estimated parameters in Equation (1) for individual lactation curves (Mean ± Standard deviation).

a | b | c |
---|---|---|

27.1 ± 15.9 | 0.183 ± 0.520 | 0.00644 ± 0.01981 |

**Table 2.**Estimated parameters in Equation (4) and the critical point in the temperature–humidity index (x0).

a | b | c | x0 |
---|---|---|---|

−0.24 | 17.86 | 0.27 | 74.60 |

**Table 3.**The format of cross-tabulation tables consisting of the presence or absence of earthquakes and anomalies in milk yields; a represents the number of earthquakes occurring in alarm days, b represents the number of earthquakes occurring in no alarm days; c represents the number of alarm days without targeted earthquakes; d represents the number of no alarm days without targeted earthquakes.

Earthquake | Alarm | Total | |
---|---|---|---|

Yes | No | ||

Yes | a | b | a + b |

No | c | d | c + d |

Total | a + c | b + d | a + b + c + d |

**Table 4.**The definitions in anomalies of milk yields and targeted earthquakes based on each criterion; M = magnitude; DRC = Dobrovolsky radius condition;

**σ**= standard deviation.

Anomalies in Milk Yields | Targeted Earthquakes | |||
---|---|---|---|---|

σ < | Duration (Days) ≥ | M > | Distance from Epicenters < | |

Criterion 1 | −1.5 | 1 | 5.0 | DRC |

Criterion 2 | −1.5 | 1 | 5.5 | DRC |

Criterion 3 | −1.5 | 1 | 6.0 | DRC |

Criterion 4 | −1.5 | 2 | 5.0 | DRC |

Criterion 5 | −1.5 | 2 | 5.5 | DRC |

Criterion 6 | −1.5 | 2 | 6.0 | DRC |

Criterion 7 | −1.5 | 1 | 5.0 | DRC + 250 km |

Criterion 8 | −1.5 | 1 | 5.5 | DRC + 250 km |

Criterion 9 | −1.5 | 1 | 6.0 | DRC + 250 km |

Criterion 10 | −1.5 | 2 | 5.0 | DRC + 250 km |

Criterion 11 | −1.5 | 2 | 5.5 | DRC + 250 km |

Criterion 12 | −1.5 | 2 | 6.0 | DRC + 250 km |

Criterion 1 | Criterion 7 | ||||||

Earthquake | Alarm | Total | Earthquake | Alarm | Total | ||

Yes | No | Yes | No | ||||

Yes | 7 | 3 | 10 | Yes | 11 | 21 | 32 |

No | 103 | 231 | 334 | No | 66 | 246 | 312 |

Total | 110 | 234 | 344 | Total | 77 | 267 | 344 |

Criterion 2 | Criterion 8 | ||||||

Earthquake | Alarm | Total | Earthquake | Alarm | Total | ||

Yes | No | Yes | No | ||||

Yes | 6 | 1 | 7 | Yes | 7 | 8 | 15 |

No | 109 | 228 | 337 | No | 90 | 239 | 329 |

Total | 115 | 229 | 344 | Total | 97 | 247 | 344 |

Criterion 3 | Criterion 9 | ||||||

Earthquake | Alarm | Total | Earthquake | Alarm | Total | ||

Yes | No | Yes | No | ||||

Yes | 3 | 1 | 4 | Yes | 4 | 2 | 6 |

No | 124 | 216 | 340 | No | 116 | 222 | 338 |

Total | 127 | 217 | 344 | Total | 120 | 224 | 344 |

Criterion 4 | Criterion 10 | ||||||

Earthquake | Alarm | Total | Earthquake | Alarm | Total | ||

Yes | No | Yes | No | ||||

Yes | 6 | 4 | 10 | Yes | 7 | 25 | 32 |

No | 35 | 299 | 334 | No | 30 | 282 | 312 |

Total | 41 | 303 | 344 | Total | 37 | 307 | 344 |

Criterion 5 | Criterion 11 | ||||||

Earthquake | Alarm | Total | Earthquake | Alarm | Total | ||

Yes | No | Yes | No | ||||

Yes | 6 | 1 | 7 | Yes | 6 | 9 | 15 |

No | 37 | 300 | 337 | No | 33 | 296 | 329 |

Total | 43 | 301 | 344 | Total | 39 | 305 | 344 |

Criterion 6 | Criterion 12 | ||||||

Earthquake | Alarm | Total | Earthquake | Alarm | Total | ||

Yes | No | Yes | No | ||||

Yes | 3 | 1 | 4 | Yes | 3 | 3 | 6 |

No | 52 | 288 | 340 | No | 52 | 286 | 338 |

Total | 55 | 289 | 344 | Total | 55 | 289 | 344 |

**Table 6.**The correspondence table of the anomalous milk yields, the observed targeted earthquakes and VLF data. Lat = Latitude, Lon = Longitude, D = Distance from epicenters, DRC = Dobrovolsky radius condition.

Anomalies of Milk Yields | Earthquake Data | VLF Data | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Start | End | Duration (Days) | Lead Time (Days) | σ (min) | Date (dd/mm/yyyy) | Lat | Lon | D (km) | DRC (km) | Depth (km) | M | Anomalies (Yes or No) | Lead Time (Days) | Path (Anomalous Day) |

11/4/2014 | 12/4/2014 | 2 | - | −3.57 | - | - | - | - | - | - | - | - | - | - |

16/04/2014 | 17/04/2014 | 2 | 18–19 | −3.30 | 5/5/2014 | 34.95 | 139.48 | 132 | 380 | 156 | 6.0 | Yes | 13 | JJY-KTU (22/04/2014) |

31/05/2014 | 2/6/2014 | 3 | 14–16 | −2.13 | 16/06/2014 | 36.62 | 141.80 | 165 | 282 | 37 | 5.7 | Yes | 10 | JJY-KTU (06/06/2014) |

16/06/2014 | 37.07 | 141.16 | 149 | 312 | 52 | 5.8 | Yes | 10 | JJY-NSB (06/06/2014) | |||||

23/06/2014 | 27/06/2014 | 5 | 15–19 | −4.78 | 12/7/2014 | 37.05 | 142.32 | 228 | 1023 | 33 | 7.0 | Yes | 11 | JJY-IMZ (01/07/2014) |

29/07/2014 | 31/07/2014 | 3 | - | −2.31 | - | - | - | - | - | - | - | - | - | - |

24/08/2014 | 26/08/2014 | 3 | 21–23 | −1.90 | 16/09/2014 | 36.09 | 139.86 | 24 | 256 | 47 | 5.6 | Yes | 11 | JJY-TYH (05/09/2014) |

4/11/2014 | 5/11/2014 | 2 | 17–18 | −2.93 | 22/11/2014 | 36.69 | 137.89 | 213 | 760 | 5 | 6.7 | Yes | 10 | JJY-IMZ (12/11/2014) |

- | - | - | - | - | 20/12/2014 | 37.43 | 141.61 | 205 | 380 | 44 | 6.0 | Yes | 11 | JJY-STU (09/12/2014) |

8/12/2014 | 9/12/2014 | 2 | 16–17 | −1.74 | 25/12/2014 | 37.23 | 141.65 | 191 | 256 | 36 | 5.6 | Yes | 8 | JJY-NSB (17/12/2014) |

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**MDPI and ACS Style**

Yamauchi, H.; Hayakawa, M.; Asano, T.; Ohtani, N.; Ohta, M.
Statistical Evaluations of Variations in Dairy Cows’ Milk Yields as a Precursor of Earthquakes. *Animals* **2017**, *7*, 19.
https://doi.org/10.3390/ani7030019

**AMA Style**

Yamauchi H, Hayakawa M, Asano T, Ohtani N, Ohta M.
Statistical Evaluations of Variations in Dairy Cows’ Milk Yields as a Precursor of Earthquakes. *Animals*. 2017; 7(3):19.
https://doi.org/10.3390/ani7030019

**Chicago/Turabian Style**

Yamauchi, Hiroyuki, Masashi Hayakawa, Tomokazu Asano, Nobuyo Ohtani, and Mitsuaki Ohta.
2017. "Statistical Evaluations of Variations in Dairy Cows’ Milk Yields as a Precursor of Earthquakes" *Animals* 7, no. 3: 19.
https://doi.org/10.3390/ani7030019