Araştırma Makalesi
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New approaches in choosing a suitable growth model: Mean Curvature and Arc Length Values

Yıl 2022, Cilt: 12 Sayı: 2, 691 - 702, 15.12.2022
https://doi.org/10.31466/kfbd.1105995

Öz

Logistic, Gompertz and Bertalanffy sigmoid growth models are widely used to study the growth dynamics of populations such as living plants, animals and bacteria. Appropriate model selection and parameter estimation are very important as these models will be used to make practical inferences. Because different growth models are modeled biologically, regardless of whether the parameters are definable or not. Applications that do not take into account parameter identifiability can lead to unreliable parameter estimates and misleading interpretations. Therefore, first the most suitable model should be determined and then the parameters should be defined. In this study, two new suitable model determination criteria such as mean curvature and arc length are proposed. For this, firstly, the definition of curvature was given. Then, the mean curvature and arc length values of the data belonging to two different species (kangal dog growth and eucalyptus plant growth) were calculated. For this purpose, a comparison was made with model selection criteria available in the literature such as coefficient of determination, error sum of squares and Akaike information criterion (AIC). It has been determined that the results obtained from the mean curvature and arc length values are in accordance with the existing criteria. In the two datasets, it was seen that the fit model ranking for both the existing criteria and the criteria we proposed was the same. For this reason, it is thought that the mean curvature and arc length values can be accepted as suitable model selection criteria.

Kaynakça

  • Akaike, H. (1974). A new look at the statistical model identification. IEEE transactions on automatic control, 19(6), 716-723.
  • Akaike, H. (1970). Statistical predictor identification. Ann. Inst. Statist. Math, 22, 203-217.
  • Bertalanffy, Von L. (1957). Quantitative laws in metabolism and growth. Quart. Rev. Biol,. 32(3), 217-231.
  • Bianco, F., Şenol, H., Papirio, S., Zenk, H., Kara, A., and Atasoy, S. (2022). Combined ultrasonic–hydrothermal pretreatment to improve the biomethane potential of hazelnut shell. Biomass and Bioenergy, 165, 106554.
  • Castro, I., and Castro-Infantes, I. (2016). Plane curves with curvature depending on distance to a line. Differential Geometry and its Applications, 44, 77-97.
  • Çoban, Ö., Yıldız, A., Sabuncuoğlu, N., Laçin, E., and Yıldırım, F., 2011. Use of non-linear growth curves to describe the body weight changes in Kangal puppies. J.Vet.Sci., University of Atatürk, Turkey, 6(1), 17-22.
  • Draper, N. R., and Smith, H. (2014). Applied regression analysis. John Wiley & Sons.
  • Hernandez, H. (2021). Testing for normality: what is the best method. ForsChem Research Reports, 6, 2021- 05.
  • Kara, A., Şenol, H.(2022) Endüstriyel Anaerobik Reaktörler İçin Enerji Dönüşümünün Hızlandırılmasına Yönelik Bir Çalışma. Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi, 17(2), 349-358.
  • Kara, A. (2019). Determination of nuclear excitation functions of zirconium using certain level density parameters for neutron-induced reactions. Indian Journal of Physics, 93(11), 1485-1488.
  • Khatun, N. (2021). Applications of normality test in statistical analysis. Open Journal of Statistics, 11(01), 113.
  • Lady, E. L. Curvature [PDF document]. Retrieved from Online Web site: http://www.math.hawaii.edu/~lee/calculus/curvature.pdf.
  • Nutbourne, A. W., McLellan, P. M., and Kensit, R. M. L. (1972). Curvature profiles for plane curves. Computer-aided design, 4(4), 176-184.
  • Oda, V., Korkmaz, M., and Özkurt, E. (2016). Some sigmoidal model used in estimating growth curve and biological parameters obtained: bertalanffy pattern sample. Ordu University Journal of Science Tecnology, 6(1), 54-66. (in Turkish, with abstract in English).
  • Oda, V. (2017). Convertion of some sigmoidal growth models into biologcally meaningful mechanical models, MSc Thesis, Ordu University, Institute of science and technology, Ordu.
  • Posada O, S., Gomez O, L., and Rosero N. R. (2014). Application of the logistic model to describe the growth curve in dogs of different breeds. Revista MVZ Córdoba, 19(1), 4015-4022.
  • Ricker, W.E. (1979). Growth rates and models. Fish Physiol, 8, 677-743.
  • Salt, C., Morris, P. J., Butterwick, R. F., Lund, E. M., Cole, T. J., and German, A. J. (2020). Comparison of growth patterns in healthy dogs and dogs in abnormal body condition using growth standards. PloS one, 15(9), e0238521.
  • Şenol, H., Açıkel, Ü., Demir, S., and Oda, V. (2020). Anaerobic digestion of cattle manure, corn silage and sugar beet pulp mixtures after thermal pretreatment and kinetic modeling study. Fuel, 263, 116651.
  • Şenol, H., Kara. A., Atasoy, S., and Erşan, M. (2022) Anaerobik Sindirimde Nanopartikül Konsantrasyonunun Cevap Yüzey Yöntemi İle Optimizasyonu. Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi, 17(1), 211-221.
  • Ucal, M.Ş. (2006). A brief survey of econometrics model selection criteria. J. Econom. and Adm. Sci.,
  • University of Cumhuriyet, Turkey, 7(2), 41-57 (in Turkish, with abstract in English).
  • Winsor, C.P. (1932). The Gompertz curve as a growth curve, Proc. Natl. Acad. Sci.,18(1), 1-8.
  • Yıldızbakan, A. (2005). Analysis on mathematical models of tree growth and comparison of these models,
  • MSc Thesis, Cukurova University, Institute of science and technology, Adana.

En uygun model seçimi için yeni yaklaşımlar: Ortalama Eğrilik ve Yay Uzunluğu Değerleri

Yıl 2022, Cilt: 12 Sayı: 2, 691 - 702, 15.12.2022
https://doi.org/10.31466/kfbd.1105995

Öz

Lojistik, Gompertz ve Bertalanffy sigmoid büyüme modelleri, canlı bitki, hayvan ve bakteri gibi populasyonların büyüme dinamiklerini incelemek için yaygın olarak kullanılmaktadır. Bu modeller pratik çıkarımlar yapmak için kullanılacağından, uygun model seçimi ve parametre tahmini çok önemlidir. Çünkü farklı büyüme modelleri, parametrelerin tanımlanabilir olup olmadığı dikkate alınmadan biyolojik olarak modellenmiştir. Parametre tanımlanabilirliğini dikkate almayan uygulamalar, güvenilir olmayan parametre tahminlerine ve yanıltıcı yorumlara yol açabilir. Bu yüzden, öncelikle en uygun model belirlenmeli ve sonrasında parametreler tanımlanmalıdır. Bu çalışmada ortalama eğrilik ve yay uzunluğu gibi iki yeni uygun model belirleme kriteri önerilmiştir. Bunun için öncelikle eğriliğin tanımı verildi. Daha sonra iki farklı canlı türüne ait verilerin ortalama eğrilik ve yay uzunluğu değerleri hesaplandı. Bu amaçla belirleme katsayısı, hata kareler toplamı ve Akaike bilgi kriteri (AIC) gibi literatürde mevcut olan model seçim kriterleri ile karşılaştırma yapıldı. Ortalama eğrilik ve yay uzunluğu değerlerinden elde edilen sonuçların mevcut kriterlere uygun olduğu tespit edilmiştir. İki veri setinde, hem mevcut kriterler, hem de önerdiğimiz kriterler için uygun model sıralamasının aynı olduğu görüldü. Bu nedenle ortalama eğrilik ve yay uzunluğu değerlerinin uygun model seçim kriterleri olarak kabul edilebileceği düşünülmektedir.

Kaynakça

  • Akaike, H. (1974). A new look at the statistical model identification. IEEE transactions on automatic control, 19(6), 716-723.
  • Akaike, H. (1970). Statistical predictor identification. Ann. Inst. Statist. Math, 22, 203-217.
  • Bertalanffy, Von L. (1957). Quantitative laws in metabolism and growth. Quart. Rev. Biol,. 32(3), 217-231.
  • Bianco, F., Şenol, H., Papirio, S., Zenk, H., Kara, A., and Atasoy, S. (2022). Combined ultrasonic–hydrothermal pretreatment to improve the biomethane potential of hazelnut shell. Biomass and Bioenergy, 165, 106554.
  • Castro, I., and Castro-Infantes, I. (2016). Plane curves with curvature depending on distance to a line. Differential Geometry and its Applications, 44, 77-97.
  • Çoban, Ö., Yıldız, A., Sabuncuoğlu, N., Laçin, E., and Yıldırım, F., 2011. Use of non-linear growth curves to describe the body weight changes in Kangal puppies. J.Vet.Sci., University of Atatürk, Turkey, 6(1), 17-22.
  • Draper, N. R., and Smith, H. (2014). Applied regression analysis. John Wiley & Sons.
  • Hernandez, H. (2021). Testing for normality: what is the best method. ForsChem Research Reports, 6, 2021- 05.
  • Kara, A., Şenol, H.(2022) Endüstriyel Anaerobik Reaktörler İçin Enerji Dönüşümünün Hızlandırılmasına Yönelik Bir Çalışma. Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi, 17(2), 349-358.
  • Kara, A. (2019). Determination of nuclear excitation functions of zirconium using certain level density parameters for neutron-induced reactions. Indian Journal of Physics, 93(11), 1485-1488.
  • Khatun, N. (2021). Applications of normality test in statistical analysis. Open Journal of Statistics, 11(01), 113.
  • Lady, E. L. Curvature [PDF document]. Retrieved from Online Web site: http://www.math.hawaii.edu/~lee/calculus/curvature.pdf.
  • Nutbourne, A. W., McLellan, P. M., and Kensit, R. M. L. (1972). Curvature profiles for plane curves. Computer-aided design, 4(4), 176-184.
  • Oda, V., Korkmaz, M., and Özkurt, E. (2016). Some sigmoidal model used in estimating growth curve and biological parameters obtained: bertalanffy pattern sample. Ordu University Journal of Science Tecnology, 6(1), 54-66. (in Turkish, with abstract in English).
  • Oda, V. (2017). Convertion of some sigmoidal growth models into biologcally meaningful mechanical models, MSc Thesis, Ordu University, Institute of science and technology, Ordu.
  • Posada O, S., Gomez O, L., and Rosero N. R. (2014). Application of the logistic model to describe the growth curve in dogs of different breeds. Revista MVZ Córdoba, 19(1), 4015-4022.
  • Ricker, W.E. (1979). Growth rates and models. Fish Physiol, 8, 677-743.
  • Salt, C., Morris, P. J., Butterwick, R. F., Lund, E. M., Cole, T. J., and German, A. J. (2020). Comparison of growth patterns in healthy dogs and dogs in abnormal body condition using growth standards. PloS one, 15(9), e0238521.
  • Şenol, H., Açıkel, Ü., Demir, S., and Oda, V. (2020). Anaerobic digestion of cattle manure, corn silage and sugar beet pulp mixtures after thermal pretreatment and kinetic modeling study. Fuel, 263, 116651.
  • Şenol, H., Kara. A., Atasoy, S., and Erşan, M. (2022) Anaerobik Sindirimde Nanopartikül Konsantrasyonunun Cevap Yüzey Yöntemi İle Optimizasyonu. Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi, 17(1), 211-221.
  • Ucal, M.Ş. (2006). A brief survey of econometrics model selection criteria. J. Econom. and Adm. Sci.,
  • University of Cumhuriyet, Turkey, 7(2), 41-57 (in Turkish, with abstract in English).
  • Winsor, C.P. (1932). The Gompertz curve as a growth curve, Proc. Natl. Acad. Sci.,18(1), 1-8.
  • Yıldızbakan, A. (2005). Analysis on mathematical models of tree growth and comparison of these models,
  • MSc Thesis, Cukurova University, Institute of science and technology, Adana.
Toplam 25 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Volkan Oda 0000-0001-5724-7678

Mehmet Korkmaz 0000-0002-7488-0552

Halil Şenol 0000-0003-3056-5013

Yayımlanma Tarihi 15 Aralık 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 12 Sayı: 2

Kaynak Göster

APA Oda, V., Korkmaz, M., & Şenol, H. (2022). New approaches in choosing a suitable growth model: Mean Curvature and Arc Length Values. Karadeniz Fen Bilimleri Dergisi, 12(2), 691-702. https://doi.org/10.31466/kfbd.1105995