Discrete-Time Gompertz Model for Adana Breed Pigeons

Year 2023, Volume: 36 Issue: 3, 1382 - 1390, 01.09.2023

Levent Özbek

https://doi.org/10.35378/gujs.809156

Abstract

The mathematical animal growth models in the literature are not in the form of linear models. These growth models in the literature are not in linear form. There are different numerical analysis methods for the estimation of the parameters found in these functions and specific software have been produced to estimate the unknown parameters in these mathematical models and to apply these methods. In these nonlinear mathematical growth models, there may be more than one parameter. For these and other reasons, the number of mathematical numerical operations in estimating parameters is quite high. In this study, the discrete time stochastic Gompertz model (DTSGM) was considered to determine the growth of Adana pigeons. A model is used in which the parameter in the model is estimated by an adaptive Kalman filter (AKF). The aim of this research is to reveal the validity of both the model and the estimation method for Adana breed domestic pigeons. Daily weight measurements of 28 Adana pigeons were considered and estimated using DTSGM and AKF methods in this framework. DTSGM in conjunction with AKF has been shown to provide a convenient analysis tool for modeling daily weight estimates of Adana pigeons.

Keywords

Adana pigeons, Stochastic Gompertz model, Adaptive Kalman filter, Time-series

References

• [1] Secord, J.A., “Charles Darwin and the breeding of pigeons”, Nature's Fancy, 72(2): 162-186. University of Chicago Press, (1981).
• [2] Shapiro, M., “Genomic diversity and evolution of the head crest in the rock pigeon”, Science, 339(6123): 1063-1067, (2013).
• [3] Yılmaz, O., Ertuğrul, M., “Importance of pigeon husbandry in history”, Journal of Harran University Faculty of Agriculture, 16(2): 1-7, (2012).
• [4] Yılmaz, O., Savaş, S., Ertuğrul, M., “Pigeon and pigeon rearing in the Turkish culture”, Nevşehir Üniversitesi Fen Bilimleri Enstitü Dergisi, 2: 79-86, (2012).
• [5] https://guvercinadana.tr.gg/, Access date: 8.8.2020.
• [6] Gompertz, B., “On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies”, Philosophical Transactions of the Royal Society of London, 115: 513-583, (1825).
• [7] Bertalanffy, L., “Problems of organic growth”, Nature 163, 156–158, (1949).
• [8] Richards, F.A., “Flexible growth function for empirical use”, Journal of Experimental Botany, 10: 280-300, (1959).
• [9] Zwietering, M., Jongenburger, I., Rombouts, F., Van’t, R.K., “Modeling of the bacterial growth curve”, Applied and Environmental Microbiology, 56(6): 1875–1881, (1990).
• [10] Gerlee, P., “The model muddle: in search of tumor growth laws”, Cancer Research, 73(8): 2407–2411, (2013).
• [11] Kathleen, M.C., Tjørve, E., “The use of Gompertz models in growth analyses, and new Gompertz-model approach: An addition to the unified-Richards family”, PLoS ONE, 12(6): e0178691, (2017).
• [12] Topal, M., Ozdemir, M., Aksakal, V., Yildiz, N., Dogru, U., “Determination of the best non-linear function in order to estimate growth in Morkaraman and Awassi lambs”, Small Ruminant Research, 55: 229-232, (2004).
• [13] Şengul, T., Kiraz, S., “Non-linear models for growth curves in large white turkeys”, Turkish Journal of Veterinary and Animal Sciences, 29: 331-337, (2005).
• [14] Sezer, M., Tarhan, S., “Model parameters of growth curves of three meat-type lines of Japanese quail”, Czech Journal Animal Science, 50: 22-30 (2005).
• [15] Kizilkaya, K., Balcioglu, M., Yolcu H., Karabag, K., Genc I., “Growth curve analysis using nonlinear mixed model in divergently selected Japanese quails”, European Poultry Sciences, , 70: 181-186, (2006).
• [16] Topal, M., Bolukbasi, Ş., “Comparison of nonlinear growth curve models in broiler chickens”, J Applied Animal Research, 34: 149-152, (2008).
• [17] Gbangboche, A.B., Glele, K.R., Salifou, S., Albuquerque, L.G., “Comparison of non-linear growth models to describe the growth curve in West African Dwarf sheep”, Animal, 2: 1003-1012, (2008).
• [18] Narinc, D., Karaman, E., Firat, M.Z., Aksoy, T., “Comparison of nonlinear growth models to describe the growth in Japanese quail”, Journal Animal Veterinary Advences , 9: 1961-1966, (2010).
• [19] Özçelik, R., Yavuz, H., Karatepe, Y., Gürlevik, N., Kırış, R., “Development of ecoregion-based height–diameter models for 3 economically important tree species of southern Turkey”, Turkish Journal of Veterinary and Animal Sciences, 38: 399-412, (2014).
• [20] Ghaderi, Z.M., Rafeie, F., Bahreini, B.M.R., “Simple hierarchical and general nonlinear growth modeling in sheep”, Turkish Journal Of Veterinary And Animal Sciences, 42(4), 326-334, (2018).
• [21] Faraji, A.H, Rokouei, M., Ghazaghi, M., “Comparative study of growth patterns in seven strains of Japanese quail using nonlinear regression modeling”, Turkish Journal of Veterinary And Animal Sciences, 42: 441-451, (2018).
• [22] Sariyel, V., Aygun, A., Keskin, I., “Comparison of growth curve models in partridge, Growth curves for ostriches (Struthio camelus) in a Brazilian population”, Poultry Science, 96: 1635–1640, (2017).
• [23] Ramos, S. B., Caetano, S., Savegnago, R.P., Nunes, B.N., Ramos, A.A., Munari. D.P., “Production, Modeling and Education”. Poultry Science, 92: 277–282, (2013).
• [24] Gon, A.¸ Gotuzzo, C., Piles, M., Pillon, R., “Genetics and genomics, Bayesian hierarchical model for comparison of different nonlinear function and genetic parameter estimates of meat quails”, Poultry Science, 98:1601–1609, (2019).
• [25] Aggrey, S.E., “Comparison of three nonlinear and spline regression models for describing chicken growth curves”, Poultry Science, 81:1782–1788, (2002).
• [26] Kuhleitner, M., Brunner, N., Nowak, W.G., “Best-fitting growth curves of the von Bertalanffy type”, Poultry Science, 98: 3587–3592, (2019).
• [27] Gao, C.Q., Yang, J.X., Chen, M.X., Yan, H.C., Wang, X.Q., “Growth curves and age-related changes in carcass characteristics, organs, serum parameters, and intestinal transporter gene expression in domestic pigeon (Columba livia)”, Poultry Science, 95: 867–877, (2016).
• [28] Vincek, D., Kralik, G., Kušec, G., Sabo, K., Scitovski, R., “Application of growth functions in the prediction of live weight of domestic animals”, CEJOR, 20: 719–733, (2012).
• [29] Aerts, J.M., Lippens, M., Groote, G., Buyse, J., Decuypere, E., Vranken, E., Berckmans, D., “Recursive prediction of broiler growth response to feed intake by using a time-variant parameter estimation method”, Poultry Science, 82(1): 40-49, (2003).
• [30] Zheng, Z., Robert, M., Nowierski, M., Taper, L., Dennis, B., William, P.K., “Complex Populatıon Dynamıcs In The Real World: Modeling the Influence of Time‐Varying Parameters and Time Lags”, Ecology, 79(6): 2193–2209, (1998).
• [31] Harvey, AC., “Forecasting, structural time series models, and Kalman filter”, Cambridge University Press, New York, USA, (1989).
• [32] Harvey, AC., “The econometric analysis of time series. Second edition. Massachusetts Institute of Technology Press, Cambridge, Massachusetts, USA, (1989).
• [33] Jonas, K., Perry, V., “Are patterns of density dependence in the Global Population Dynamics Database driven by uncertainty about population abundance?”, Ecology Letters, 15: 17–23, (2012).
• [34] Dennis, B., Ponciano, J.M., Subhash, R., Traper, L.M.L, Staples D.F., “Estimating Density Dependence, Process Noise and Observation Erros”, Ecological Monographs, 76(3): 323–341, (2006).
• [35] Jazwinski, A.H., “Stochastic Processes and Filtering Theory”, Academic Press, (1970).
• [36] Anderson, B.D.O., Moore, J.B., “Optimal Filtering”, Prentice Hall, (1979).
• [37] Chui, C.K., Chen, G., “Kalman Filtering with Real-time Applications”, Springer Verlag, (1991).
• [38] Ljung, L., Söderström, T., “Theory and Practice of Recursive Identification”, The MIT Press, (1983).
• [39] Chen, G., “Approximate Kalman Filtering”, World Scientific, (1993).
• [40] Grewal, S., Andrews, A.P.,” Kalman Filtering Theory and Practice”, Prentice Hall, (1993).
• [41] Özbek, L., “Kalman Filtresi”, Akademisyen Kitabevi, (in Turkish), (2016).
• [42] Kalman, R.E., “A new Approach to linear Filtering and Prediction Problems”, Journal of Basic Engineering, 82: 35-45, (1960).
• [43] Özbek, L., “A study on modelling and estimation of growth functions Adana pigeons”, Communications Faculty of Sciences University of Ankara Series A2-A3 Physical Sciences and Engineering, 64(2): 95-103 (2022).
• [44] Özbek, L., Aliev, F.A., “Comments on Adaptive Fading Kalman Filter with an Application”, Automatica, 34(12): 1663-1664, (1998).
• [45] Efe, M., Özbek, L.,” Fading Kalman Filter for Manoeuvring Target Tracking”, Journal of the Turkish Statistical Assocation, 2(3): 193-206, (1999).
• [46] Özbek, L., Efe, M., “An Adaptive Extended Kalman Filter with Application to Compartment Models”, Communications in Statistics-Simulation and Computation, 33(1): 145-158, (2004).