Method of individual forecasting of sow reproductive performance on the basis of a non-linear canonical model of a random sequence

Keywords: pig; individual forecasting of sow reproduction; non-linear canonical model of the random sequence


Improvement of sow reproductive performance is a key factor determining the efficiency of the pig production cycle and profitability of pork production. This article presents the solution of an important scientific and practical problem of individual forecasting of sow reproduction . The population used for the present study is from a pig farm managed by the Limited Liability Company (LLC) ‘Tavriys’kisvyni’ located in Skadovsky district (Kherson region, Ukraine). The experimental materials used for this study consisted of 100 inds. of productive parent sows of the Large White breed.The litter size traits – the total number of piglets born (TNB), number of piglets born alive (NBA) and number of weaned piglets (NW) – were monitored in the first eight parities over an eleven year period (2007–2017). The method of the forecasting of sow litter size is developed based on the non-linear canonical model of the random sequence of a litter size change. The proposed method allows us to take maximum account of stochastic peculiarities of sow reproductive performance and does not impose any restrictions on the random sequence of a litter size change (linearity, stationarity, Markov property, monotony, etc.). The block diagram of the algorithm presented in this work reflects the peculiarities of calculation of the parameters of a predictive model. The expression for the calculation of an extrapolation error allows us to estimate the necessary volume of a priori and a posteriori information for achieving the required quality of solving the forecasting problem. The results of the numerical experiment confirmed the high accuracy of the proposed method of forecasting of sow reproduction. The method offered by us almost doubles the accuracy of forecasting of sow litter size compared to the use of the Wiener and Kalman methods. Thus, average forecast error decreases across the range of features TNB (1.71), NBA (1.68) and NW (1.25 piglets). Apparently, this may reflect a higher level of manifestation of the genetically determined level of individual sow fertility at the moment of piglet weaning. The higher adequacy of the developed mathematical model with regard to NW can be also due to the fact that the relations between sow litter size in different farrowings primarily have a non-linear character, which is taken into maximum account in our offered model. Given non-linearity, on the other hand, turns out to be a significant factor determining a lower estimation of the repeatability value for NW compared to the estimations for TNB and NBA. The use of the developed method will help to improve the efficiency of pig farming.


Atamanyuk, I. P. (2005). Algorithm of extrapolation of a nonlinear random process on the basis of its canonical decomposition. Cybernetics and Systems Analysis, 41(2), 267–273.

Atamanyuk, I. P. (2009). Optimal polynomial extrapolation of realization of a random process with a filtration of measurement errors. Journal of Automation and Information Sciences, 41(8), 38–48.

Atamanyuk, I. P., Kondratenko, V. Y., Kozlov, O. V., & Kondratenko, Y. P. (2012). The algorithm of optimal polynomial extrapolation of random processes. In: International conference on modeling and simulation in engineering, economics and management. Springer, Berlin, Heidelberg. Pp. 78–87.

Atamanyuk, I., Kondratenko, Y., Shebanin, V., & Mirgorod, V. (2015). Method of polynomial predictive control of fail-safe operation of technical systems. In: The experience of designing and application of CAD systems in microelectronics. IEEE, Lviv, Polyana. Pp. 248–251.

Biermann, A. D. M., Pimentel, E. C. G., Tietze, M., Pinent, T., & König, S. (2014). Implementation of genetic evaluation and mating designs for the endangered local pig breed ‘Bunte Bentheimer’. Journal of Animal Breeding and Genetics, 131(1), 36–45.

Bono, C., Cornou, C., & Kristensen, A. (2012). Dynamic production monitoring in pig herds I: Modeling and monitoring litter size at herd and sow level. Livestock Science, 149(3), 289–300.

Borges, V. F., Bernardi, M. L., Bortolozzo, F. P., & Wentz, I. (2005). Risk factors for stillbirth and foetal mummification in four Brazilian swine herds. Preventive Veterinary Medicine, 70(3–4), 165–176.

Box, G. E., Jenkins, G. M., Reinsel, G. C., & Ljung, G. M. (2015). Time series analysis: Forecasting and control. John Wiley & Sons Inc., Hoboken, New Jersey.

Canario, L., Cantoni, E., Le Bihan, E., Caritez, J. C., Billon, Y., Bidanel, J. P., & Foulley, J. L. (2006). Between-breed variability of stillbirth and its relationship with sow and piglet characteristics. Journal of Animal Science, 84(12), 3185–3196.

Glen, J. (1983). A dynamic programming model for pig production. Journal of the Operational Research Society, 34, 511–519.

Huirne, R. B. M., Hendriks, T. H., Dijkhuizen, A. A., & Giesen, G. W. J. (1988). The economic optimisation of sow replacement decisions by stochastic dynamic programming. Journal of Agricultural Economics, 39(3), 426–438.

Iida, R., Piñeiro, C., & Koketsu, Y. (2015). High lifetime and reproductive performance of sows on southern European Union commercial farms can be predicted by high numbers of pigs born alive in parity one. Journal of Animal Science, 93(5), 2501–2508.

Jørgensen, E. (1993). The influence of weighing precision on delivery decisions in slaughter pig production. Acta Agriculturae Scandinavica, Section A: Animal Science, 43(3), 181–189.

Kramarenko, S. S., & Lugovoy, S. I. (2013). Ispol'zovanie entropiyno-informatsionnogo analiza dlya otsenki vosproizvoditel'nykh kachestv svinomatok [The use of entropy and informational analysis for the estimation of sow reproductive performance]. The Altai State Agrarian University Herald, 107, 58–62 (in Russian).

Lavery, A., Lawlor, P. G., Magowan, E., Miller, H. M., O’Driscoll, K., & Berry, D. P. (2019). An association analysis of sow parity, live-weight and back-fat depth as indicators of sow productivity. Animal, 13(3), 622–630.

Leenhouwers, J. I., van der Lende, T., & Knol, E. F. (1999). Analysis of stillbirth in different lines of pig. Livestock Production Science, 57(3), 243–253.

Lucia Jr., T., Dial, G. D., & Marsh, W. E. (2000). Lifetime reproductive performance in female pigs having distinct reasons for removal. Livestock Production Science, 63(3), 213–222.

Małopolska, M. M., Tuz, R., Lambert, B. D., Nowicki, J., & Schwarz, T. (2018). The replacement gilt: Current strategies for improvement of the breeding herd. Journal of Swine Health and Production, 26(4), 208–214.

Pourmoayed, R., Nielsen, L. R., & Kristensen, A. R. (2016). A hierarchical Markov decision process modelling feeding and marketing decisions of growing pigs. European Journal of Operational Research, 250(3), 925–938.

Pugachev, V. S. (1965). Theory of random functions. Pergamon, New York.

Radojković, D., Savić, R., Popovac, M., Radović, Č., & Gogić, M. (2018). The share of variance components and correlations between sow production traits in different treatments of the litter size (The repeatability and multi-trait models). Contemporary Agriculture, 67(3–4), 207–214.

Roehe, R., & Kennedy, B. W. (1995). Estimation of genetic parameters for litter size in Canadian Yorkshire and Landrace swine with each parity of farrowing treated as a different trait. Journal of Animal Science, 73(10), 2959–2970.

Schwarz, T., Kopyra, M. (2006). Influence of age on insemination process, and reproductive performance in sows. Animal Science Papers and Reports, 24(suppl. 3), 229–239.

Strang, G. S., & Smith, C. (1979). A note on the heritability of litter traits in pigs. Animal Production, 28(3), 403–406.

Szyndler-Nędza, M. (2016). Coefficients of repeatability for colostrum and milk composition of PLW and PL sows over three consecutive lactations. Livestock Science, 185, 56–60.

Tantasuparuk, W., Lundeheim, N., Dalin, A. M., Kunavongkrit, A., & Einarsson, S. (2000). Reproductive performance of purebred Landrace and Yorkshire sows in Thailand with special reference to seasonal influence and parity number. Theriogenology, 54(3), 481–496.

Toft, N., & Jørgensen, E. (2002). Estimation of farm specific parameters in a longitudinal model for litter size with variance components and random dropout. Livestock Production Science, 77(2–3), 175–185.

Toft, N., Kristensen, A., & Jørgensen, E. (2005). A framework for decision support related to infectious diseases in slaughter pig fattening units. Agricultural Systems, 85(2), 120–137.

Tummaruk, P., Lundeheim, N., Einarsson, S., & Dalin, A. M. (2000). Reproductive performance of purebred Swedish Landrace and Swedish Yorkshire sows: I. Seasonal variation and parity influence. Acta Agriculturae Scandinavica Section A – Animal Science, 50(3), 205–216.

Wiener, N. (1970). Extrapolation, interpolation, and smoothing of stationary time series. MIT Press, New-York.

Ye, J., Tan, C., Hu, X., Wang, A., & Wu, Z. (2018). Genetic parameters for reproductive traits at different parities in Large White pigs. Journal of Animal Science, 96(4), 1215–1220.

Zaleski, H. M., & Hacker, R. R. (1993). Effect of oxygen and neostigmine on stillbirth and pig viability. Journal of Animal Science, 71(2), 298–305.