Richards Büyüme Modelinin Parametrelerinin Biyolojik Olarak Anlamlı Parametrelere Dönüşümü Üzerine Bir Çalışma

Year 2022, Volume: 12 Issue: 2, 159 - 166, 31.12.2022

Volkan Oda , Mehmet Korkmaz , Halil Şenol

https://doi.org/10.54370/ordubtd.1183760

Abstract

Bu çalışmada, sigmoid büyüme modellerinden biri olan Richards modelinin maksimum büyüme değeri, gecikme süresi ve maksimum spesifik büyüme hızı gibi biyolojik olarak önemli parametrelerle mekanik bir modele nasıl dönüştürüldüğü anlatılmaktadır. Birinci ve ikinci türevler yardımıyla hesaplanan biyolojik olarak önemli 4 parametre içeren Richards büyüme modelinin detay dönüşümleri verildi. Bu modelin doğruluğunu test etmek için E. Camaldulensis Dehn ağacının yıllara göre yükseklik verileri kullanılarak model tahmin değerleri analiz edilmiştir. Biyolojik olarak önemli 4 parametreli Richards büyüme modelinin tahmini değerleri, diğer 3 parametreyi içeren modifiye Gompertz, Logistic ve Bertalanffy modellerinin tahmin değerleri ile karşılaştırıldı. Önerilen tüm modeller için model değerlendirme kriterleri olarak Hata Kareler Toplamı, Belirleme Katsayıları ve Akaike Bilgi Kriterleri kullanılmış ve 4 parametreli Richards büyüme modelinin diğer modellere göre nispeten daha iyi tahmin ettiği sonucuna varılmıştır.

Keywords

richards büyüme modeli, sigmoidal büyüme modeli, mekanik model, akaike bilgi kriterleri, belirleme katsayıları

A Study over Transformations of the Parameters of Richards Growth Model into the Biologically Meaningful Parameters

Abstract

In this study, it is explained how the Richards model, which is one of the sigmoid growth models, is transformed into a mechanical model with biologically significant parameters such as maximum growth value, lag time and maximum specific growth rate. Detail transformations of the Richards growth model containing 4 parameters with biologically significant parameters calculated with the help of the first and second derivatives were given. In order to test the accuracy of this model, the model prediction values were analyzed by using the height data of the E. Camaldulensis Dehn tree by years. The estimated values of the biologically significant parameters of Richards growth model containing 4 parameters were compared with the estimated values of the modified Gompertz, Logistic and Bertalanffy models containing the other 3 parameters. Error Sum of Squares, Coefficients of Determination and Akaike Information Criteria were used as model evaluation criteria for all proposed models, and it was concluded that the Richards growth model containing 4-parameters predicted relatively better than other models.

Keywords

richards growth model, sigmoidal growth model, mechanical model, akaike information criteria, coefficients of determination

References

• Akaike, H. (1974). A new look at the statistical model identification, IEEE Transactions on Automatic Control, 19(6), 716-723. http://dx.doi.org/10.1109/TAC.1974.1100705
• Bertalanffy, Von L. (1957). Quantitative laws in metabolism and growth, Quart. Rev. Biol. 32 (3), 217-231. https://doi.org/10.1086/401873
• Draper, N. R., & Smith, H. (2014). Applied regression analysis, John Wiley & Sons.
• Gregorczyk, A. (1998). Richards plant growth model. J. Agron. Crop. Sci. 181, 243-247. https://doi.org/10.1111/j.1439-037X.1998.tb00424.x
• Korkmaz M. (2017). An applied study on converting some sigmoidal models in empirical form to meaningful parameterized mechanistic models, J. Sci. Eng. Res., 4(7) 82-92. https://doi.org/10.21597/jist.1095933
• Korkmaz, M. (2021). A study over with four‐parameter Logistic and Gompertz growth models. Numerical Methods for Partial Differential Equations, 37(3), 2023-2030. https://doi.org/10.1002/num.22641
• Narinc, D., Aksoy, T., & Karaman, E. (2010) Genetic parameters of growth curve parameters and weekly body weights in Japanese quails (Coturnix coturnix japonica). J. Anim. Vet. Adv., 9, 501–507. https://doi.org/10.3923/javaa.2010.501.507
• Narinc, D., & Karaman, E., First, M. Z. Aksoy T (2010) Comparison of non-linear growth models to describe the growth in Japanese quail. J. Anim. Vet. Adv., 9, 1961–1966. https://doi.org/10.3923/javaa.2010.1961.1966
• Oda, V., Korkmaz, M., & Özkurt, E. (2016). Some sigmoidal models used in estimating growth curve and biological parameters obtained : Bertalanffy pattern sample, Ordu Univ. J. Sci. Tech., 6(1), 54-66. https://dergipark.org.tr/tr/download/article-file/227497 Richards, J. F. (1959). A flexible growth function for empirical use. J Exp Bot, 1(10), 290–310. http://dx.doi.org/10.1093/jxb/10.2.290
• Ricker, W. E. (1979). Growth rates and models. Fish Physiology, 8, 677-743. http://dx.doi.org/10.1016/S1546-5098(08)60034-5
• Şenol, H. (2020). Anaerobic digestion of hazelnut (Corylus colurna) husks after alkaline pretreatment and determination of new important points in Logistic model curves. Bioresource Technology, 300, 122660. https://doi.org/10.1016/j.biortech.2019.122660
• Şenol, H., Açıkel, Ü., & Oda, V. (2021). Anaerobic digestion of sugar beet pulp after acid thermal and alkali thermal pretreatments. Biomass Conversion and Biorefinery, 11(3), 895-905. https://doi.org/10.1007/s13399-019-00539-6
• Winsor, C. P. (1932). The Gompertz curve as a growth curve, Proc. Natl. Acad. Sci. U. S. A., 18(1), 1-8. https://doi.org/10.1073/pnas.18.1.1
• Yıldızbakan, A. (2005). Analysis on mathematical models of tree growth and comparison of these models [MSc Thesis]. University of Cukurova.
• Zwietering, M. H., Jongenburger, I., Rombouts, F. M., & Riet, K. V. (1990). Modeling of the bacterial growth curve. Appl. Environ. Microbiol., 56(6), 1875-1881. https://doi.org/10.1128/aem.56.6.1875-1881.1990