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Linear mixed model selection in forest tree breeding studies

Year 2023, Volume: 24 Issue: 1, 218 - 226, 15.05.2023
https://doi.org/10.17474/artvinofd.1260542

Abstract

In forest tree breeding studies, genetic parameters are estimated for breeding programs with long-term genetic tests. Since the estimations of these parameters will affect the breeding program, the selection of the linear mixed model to be used for the estimation is of great importance. In linear mixed models used for the estimation of these parameters, the estimation is usually obtained by using the residual or restricted maximum likelihood (REML) methods. In order to compare the models with different fixed effects with the information criteria based on likelihood, it is suggested that the models should be estimated using maximum likelihood. In forest tree breeding studies, different models should be tried in linear mixed model selection and the most useful model that increases model fit should be selected. It is generally recommended to use the Akaike (AIC) information criterion to compare the fit of models in forest tree breeding studies. In this study, it is aimed to reveal the necessity and importance of linear mixed model selection. For this purpose, the models were compared by using the twelfth year diameter at breast height data of the trees in the red pine progeny trial field established with 168 open pollinated families (half-sib) in Muğla-Marmaris. In the analysis of this data set, a total of 32 different models were tested, which include traditional (simple), spatial component, and assume that the residual is an independent or 1st order 2-dimensional separable autoregressive correlation error structure. The AIC value of the traditional model (Model-1=5594.1) was found to be higher than the models with the spatial component and the residual autoregressive correlation structure (Model-20=5447).

References

  • Alan M, Öztürk H, Şıklar S, Ezen T, Korkmaz B, Doğan B, Keskin S, Tulukçu M, Derilgen SI, Çalışkan B (2005) Ege bölgesi alt yükselti kuşağı ıslah zonunda (0-400 m) Kızılçam (Pinus brutia ten.) döl denemeleri 4. yaş sonuçları. (Teknik Bülten:13), Orman Ağaçları ve Tohumları Islah Araştırma Enstitüsü Müdürlüğü, Ankara.
  • Aparicio J, Ariza-Suarez D, Raatz B (2019) Web application for spatial modelling of field trials. Paper presented at the XXIX Simposio Internacional de Estadística, Barranquilla
  • Borges A, González-Reymundez A, Ernst O, Cadenazzi M, Terra J, Gutiérrez L (2019) Can spatial modeling substitute for experimental design in agricultural experiments? Crop Science, 59(1):44-53
  • Bozdogan H (1987) Model selection and Akaike's information criterion (AIC): The general theory and its analytical extensions. Psychometrika, 52(3):345-370
  • Brown H, Prescott R (2015) Applied mixed models in medicine. John Wiley & Sons, New York
  • Burgueño J, Cadena A, Crossa J, Banziger M, Gilmour A, Cullis B (2000) User's guide for spatial analysis of field variety trials using ASREML. International Maize and Wheat Improvement Center (CIMMYT), Mexico
  • Caliński T, Czajka S, Kaczmarek Z, Krajewski P, Pilarczyk W (2005) Analyzing multi‐environment variety trials using randomization‐derived mixed models. Biometrics, 61(2):448-455
  • Casler MD (2015) Fundamentals of experimental design: Guidelines for designing successful experiments. Agronomy Journal, 107(2):692-705
  • Chen Z, Karlsson B, Wu H (2017) Patterns of additive genotype-by environment interaction in tree height of Norway spruce in southern and central Sweden. Tree Genetics & Genomes, 13(1):1-14
  • Cullis BR, Smith AB, Coombes NE (2006) On the design of early generation variety trials with correlated data. Journal of Agricultural, Biological, Environmental Statistics, 11(4):381-393
  • Dutkowski GW, Costa e Silva J, Gilmour AR, Wellendorf H, Aguiar A (2006) Spatial analysis enhances modelling of a wide variety of traits in forest genetic trials. Canadian Journal of Forest Research, 36(7):1851-1870
  • Dutkowski GW, Silva JCe, Gilmour AR, Lopez GA (2002) Spatial analysis methods for forest genetic trials. Canadian Journal of Forest Research, 32(12):2201-2214
  • Fisher RA (1936) Design of experiments. British Medical Journal 1(3923):554
  • Galwey NW (2014) Introduction to mixed modelling: beyond regression and analysis of variance. John Wiley & Sons, New York
  • Gezan SA, White TL, Huber DA (2010) Accounting for spatial variability in breeding trials: a simulation study. Agronomy Journal, 102(6):1562-1571
  • Gilmour A, Gogel B, Cullis B, Thompson R (2009) ASReml user guide release 3.0 VSN International Ltd, Hemel Hempstead
  • Gilmour A, Gogel B, Cullis B, Welham S, Thompson R (2015) ASReml user guide release 4.1 functional specification. VSN International Ltd, Hemel Hempstead
  • Grondona M, Crossa J, Fox P, Pfeiffer W (1996) Analysis of variety yield trials using two-dimensional separable ARIMA processes. Biometrics, 763-770
  • Guerin L, Stroup WW (2000) A simulation study to evaluate PROC MIXED analysis of repeated measures data Isik F, Holland J, Maltecca C (2017) Genetic data analysis for plant and animal breeding. Springer International Publishing, Switzerland
  • Kehel Z, Habash D, Gezan S, Welham S, Nachit MJAJ (2010) Estimation of spatial trend and automatic model selection in augmented designs. Agronomy Journal, 102(6):1542-1552
  • Legendre P (1993) Spatial autocorrelation: trouble or new paradigm? Ecology, 74(6):1659-1673
  • Little R, Milliken GA, Stroup WW, Wolfinger RD, Schabenberger O (2006) SAS for mixed models. SAS Institute Inc, North Carolina
  • Matheson A, Gapare W, Ilic J, Wu H (2008) Inheritance and genetic gain in wood stiffness in radiata pine assessed acoustically in young standing trees. Silvae Genetica, 57(2):56-64
  • Mathew B, Holand AM, Koistinen P, Léon J, Sillanpää MJ (2016) Reparametrization-based estimation of genetic parameters in multi-trait animal model using Integrated Nested Laplace Approximation. Theoretical Applied Genetics, 129(2):215-225
  • Mramba LK (2016) Optimal experimental designs for spatially and genetically correlated data using linear mixed models. University of Florida
  • Piepho HP, Möhring J, Melchinger AE, Büchse A (2008) BLUP for phenotypic selection in plant breeding and variety testing. Euphytica, 161(1-2):209-228
  • Piepho HP, Williams ER, Michel V (2015) Beyond latin squares: a brief tour of row‐column designs. Agronomy Journal, 107(6):2263-2270 Schutz W, Cockerham CC (1966) The effect of field blocking on gain from selection. Biometrics, 22(4):843-863 Shalizi MN, Gezan SA, McKeand SE, Sherrill JR, Cumbie WP, Whetten RW, Isik F (2020) Correspondence between breeding values of the same Pinus taeda L. genotypes from clonal trials and half-sib seedling progeny trials. Forest Science, 66(5):600-611
  • Smith A, Cullis B, Thompson R (2001) Analyzing variety by environment data using multiplicative mixed models and adjustments for spatial field trend. Biometrics, 57(4):1138-1147
  • Spilke J, Richter C, Piepho HJPb (2010) Model selection and its consequences for different split‐plot designs with spatial covariance and trend. Plant Breeding, 129(6):590-598
  • Stroup WW (2012) Generalized linear mixed models: modern concepts, methods and applications. CRC Press, Boca Raton.
  • Urhan OS, Kolpak SE, Jayawickrama KJS, Howe GT (2014) Early genetic selection for wood stiffness in juvenile Douglas-fir and western hemlock. Forest Ecology and Management, 320:104-117
  • Verbyla AP (2019) A note on model selection using information criteria for general linear models estimated using REML. Australian & New Zealand Journal of Statistics, 61(1):39-50
  • VSNI T (2021) A brief look at spatial modelling. In. /, (01.10.2022).
  • Welham SJ, Gezan SA, Clark SJ, Mead A (2014) Statistical methods in biology: design and analysis of experiments and regression. CRC Press, London.
  • Welham SJ, Gogel BJ, Smith AB, Thompson R, Cullis BR (2010) A comparison of analysis methods for late‐stage variety evaluation trials. Australian and New Zealand Journal of Statistics, 52(2):125-149
  • White TL, Adams WT, Neale DB (2007) Forest genetics. Cabi, United Kingdom.
  • Yates F (1939) The recovery of inter‐block information in variety trials arranged in three‐dimensional lattices. Annals of Eugenics, 9(2):136-156
  • Ye TZ, Jayawickrama KJ (2008) Efficiency of using spatial analysis in first-generation coastal Douglas-fir progeny tests in the US Pacific Northwest. Tree Genetics & Genomes, 4(4):677-692

Orman ağacı ıslah çalışmalarında doğrusal karma model seçimi

Year 2023, Volume: 24 Issue: 1, 218 - 226, 15.05.2023
https://doi.org/10.17474/artvinofd.1260542

Abstract

Orman ağacı ıslah çalışmalarında, uzun süre gözlemlenen genetik testler ile ıslah programları için genetik parametreler tahmin edilmektedir. Söz konusu parametrelerin tahminleri ıslah programını etkileyeceğinden tahmin için kullanılacak doğrusal karma modelin seçimi büyük önem taşımaktadır. Kullanılan doğrusal karma modellerde tahmin, genellikle artık (residual) veya kısıtlı maksimum olabilirlik (REML) yöntemi kullanılarak elde edilir. Farklı sabit etkileri olan modellerin olabilirliğe (likelihood) dayalı bilgi kriterleri ile kıyaslanabilmesi için, modellerin maksimum olabilirlik (maximum likelihood) kullanılarak tahmin edilmesi önerilmektedir. Orman ağaçları ıslahı çalışmalarında doğrusal karma model seçiminde farklı modeller denenerek model uyumunu arttıran en kullanışlı model seçilmelidir. Orman ağaçları ıslah çalışmalarında modellerin uyumunu kıyaslamak için ise genellikle Akaike (AIC) bilgi kriterinin kullanılması önerilmektedir. Bu çalışmada, doğrusal karma model seçiminin gerekliliğini ve önemini ortaya koymak amaçlanmıştır. Bu amaç için, Muğla-Marmaris’te açık tozlaşma ürünü 168 aile (üvey kardeş) ile tesis edilmiş olan Kızılçam döl deneme sahasındaki ağaçların on ikinci yaş göğüs yüksekliği çap verileri kullanılarak modeller kıyaslanmıştır. Verilerin analizinde geleneksel (basit), mekânsal bileşen içeren, artığın bağımsız veya birinci dereceden iki boyutlu ayrılabilir otoregresif korelasyon hata yapısı olduğunu varsayan toplamda otuziki farklı model denenmiştir. Geleneksel modelin AIC değeri (Model-1=5594.1), mekânsal bileşen ve artığın otoregresif korelasyon yapısı içeren modellere kıyasla (Model-20=5447) daha yüksek bulunmuştur

References

  • Alan M, Öztürk H, Şıklar S, Ezen T, Korkmaz B, Doğan B, Keskin S, Tulukçu M, Derilgen SI, Çalışkan B (2005) Ege bölgesi alt yükselti kuşağı ıslah zonunda (0-400 m) Kızılçam (Pinus brutia ten.) döl denemeleri 4. yaş sonuçları. (Teknik Bülten:13), Orman Ağaçları ve Tohumları Islah Araştırma Enstitüsü Müdürlüğü, Ankara.
  • Aparicio J, Ariza-Suarez D, Raatz B (2019) Web application for spatial modelling of field trials. Paper presented at the XXIX Simposio Internacional de Estadística, Barranquilla
  • Borges A, González-Reymundez A, Ernst O, Cadenazzi M, Terra J, Gutiérrez L (2019) Can spatial modeling substitute for experimental design in agricultural experiments? Crop Science, 59(1):44-53
  • Bozdogan H (1987) Model selection and Akaike's information criterion (AIC): The general theory and its analytical extensions. Psychometrika, 52(3):345-370
  • Brown H, Prescott R (2015) Applied mixed models in medicine. John Wiley & Sons, New York
  • Burgueño J, Cadena A, Crossa J, Banziger M, Gilmour A, Cullis B (2000) User's guide for spatial analysis of field variety trials using ASREML. International Maize and Wheat Improvement Center (CIMMYT), Mexico
  • Caliński T, Czajka S, Kaczmarek Z, Krajewski P, Pilarczyk W (2005) Analyzing multi‐environment variety trials using randomization‐derived mixed models. Biometrics, 61(2):448-455
  • Casler MD (2015) Fundamentals of experimental design: Guidelines for designing successful experiments. Agronomy Journal, 107(2):692-705
  • Chen Z, Karlsson B, Wu H (2017) Patterns of additive genotype-by environment interaction in tree height of Norway spruce in southern and central Sweden. Tree Genetics & Genomes, 13(1):1-14
  • Cullis BR, Smith AB, Coombes NE (2006) On the design of early generation variety trials with correlated data. Journal of Agricultural, Biological, Environmental Statistics, 11(4):381-393
  • Dutkowski GW, Costa e Silva J, Gilmour AR, Wellendorf H, Aguiar A (2006) Spatial analysis enhances modelling of a wide variety of traits in forest genetic trials. Canadian Journal of Forest Research, 36(7):1851-1870
  • Dutkowski GW, Silva JCe, Gilmour AR, Lopez GA (2002) Spatial analysis methods for forest genetic trials. Canadian Journal of Forest Research, 32(12):2201-2214
  • Fisher RA (1936) Design of experiments. British Medical Journal 1(3923):554
  • Galwey NW (2014) Introduction to mixed modelling: beyond regression and analysis of variance. John Wiley & Sons, New York
  • Gezan SA, White TL, Huber DA (2010) Accounting for spatial variability in breeding trials: a simulation study. Agronomy Journal, 102(6):1562-1571
  • Gilmour A, Gogel B, Cullis B, Thompson R (2009) ASReml user guide release 3.0 VSN International Ltd, Hemel Hempstead
  • Gilmour A, Gogel B, Cullis B, Welham S, Thompson R (2015) ASReml user guide release 4.1 functional specification. VSN International Ltd, Hemel Hempstead
  • Grondona M, Crossa J, Fox P, Pfeiffer W (1996) Analysis of variety yield trials using two-dimensional separable ARIMA processes. Biometrics, 763-770
  • Guerin L, Stroup WW (2000) A simulation study to evaluate PROC MIXED analysis of repeated measures data Isik F, Holland J, Maltecca C (2017) Genetic data analysis for plant and animal breeding. Springer International Publishing, Switzerland
  • Kehel Z, Habash D, Gezan S, Welham S, Nachit MJAJ (2010) Estimation of spatial trend and automatic model selection in augmented designs. Agronomy Journal, 102(6):1542-1552
  • Legendre P (1993) Spatial autocorrelation: trouble or new paradigm? Ecology, 74(6):1659-1673
  • Little R, Milliken GA, Stroup WW, Wolfinger RD, Schabenberger O (2006) SAS for mixed models. SAS Institute Inc, North Carolina
  • Matheson A, Gapare W, Ilic J, Wu H (2008) Inheritance and genetic gain in wood stiffness in radiata pine assessed acoustically in young standing trees. Silvae Genetica, 57(2):56-64
  • Mathew B, Holand AM, Koistinen P, Léon J, Sillanpää MJ (2016) Reparametrization-based estimation of genetic parameters in multi-trait animal model using Integrated Nested Laplace Approximation. Theoretical Applied Genetics, 129(2):215-225
  • Mramba LK (2016) Optimal experimental designs for spatially and genetically correlated data using linear mixed models. University of Florida
  • Piepho HP, Möhring J, Melchinger AE, Büchse A (2008) BLUP for phenotypic selection in plant breeding and variety testing. Euphytica, 161(1-2):209-228
  • Piepho HP, Williams ER, Michel V (2015) Beyond latin squares: a brief tour of row‐column designs. Agronomy Journal, 107(6):2263-2270 Schutz W, Cockerham CC (1966) The effect of field blocking on gain from selection. Biometrics, 22(4):843-863 Shalizi MN, Gezan SA, McKeand SE, Sherrill JR, Cumbie WP, Whetten RW, Isik F (2020) Correspondence between breeding values of the same Pinus taeda L. genotypes from clonal trials and half-sib seedling progeny trials. Forest Science, 66(5):600-611
  • Smith A, Cullis B, Thompson R (2001) Analyzing variety by environment data using multiplicative mixed models and adjustments for spatial field trend. Biometrics, 57(4):1138-1147
  • Spilke J, Richter C, Piepho HJPb (2010) Model selection and its consequences for different split‐plot designs with spatial covariance and trend. Plant Breeding, 129(6):590-598
  • Stroup WW (2012) Generalized linear mixed models: modern concepts, methods and applications. CRC Press, Boca Raton.
  • Urhan OS, Kolpak SE, Jayawickrama KJS, Howe GT (2014) Early genetic selection for wood stiffness in juvenile Douglas-fir and western hemlock. Forest Ecology and Management, 320:104-117
  • Verbyla AP (2019) A note on model selection using information criteria for general linear models estimated using REML. Australian & New Zealand Journal of Statistics, 61(1):39-50
  • VSNI T (2021) A brief look at spatial modelling. In. /, (01.10.2022).
  • Welham SJ, Gezan SA, Clark SJ, Mead A (2014) Statistical methods in biology: design and analysis of experiments and regression. CRC Press, London.
  • Welham SJ, Gogel BJ, Smith AB, Thompson R, Cullis BR (2010) A comparison of analysis methods for late‐stage variety evaluation trials. Australian and New Zealand Journal of Statistics, 52(2):125-149
  • White TL, Adams WT, Neale DB (2007) Forest genetics. Cabi, United Kingdom.
  • Yates F (1939) The recovery of inter‐block information in variety trials arranged in three‐dimensional lattices. Annals of Eugenics, 9(2):136-156
  • Ye TZ, Jayawickrama KJ (2008) Efficiency of using spatial analysis in first-generation coastal Douglas-fir progeny tests in the US Pacific Northwest. Tree Genetics & Genomes, 4(4):677-692

Details

Primary Language Turkish
Subjects Forest Industry Engineering
Journal Section Research Article
Authors

Mehmet ACET
Orman Ağaçları ve Tohumları Islah Araştırma Enstitüsü Müdürlüğü
0000-0001-6901-7554
Türkiye


Zafer ÖLMEZ
ARTVİN ÇORUH ÜNİVERSİTESİ, ORMAN FAKÜLTESİ, ORMAN MÜHENDİSLİĞİ BÖLÜMÜ
0000-0001-6199-6284
Türkiye

Supporting Institution Orman Genel Müdürlüğü Orman Ağaçları ve Tohumları Islah Araştırma Enstitüsü Müdürlüğü
Project Number Diğer Çalışmalar
Thanks Bu çalışmaya katkısı olan başta Oğuz Şerif URHAN olmak üzere bireysel ve kurumsal katkılar için teşekkür ederiz.
Publication Date May 15, 2023
Published in Issue Year 2023Volume: 24 Issue: 1

Cite

Bibtex @research article { artvinofd1260542, journal = {Artvin Çoruh Üniversitesi Orman Fakültesi Dergisi}, issn = {2146-1880}, eissn = {2146-698X}, address = {}, publisher = {Artvin Çoruh University}, year = {2023}, volume = {24}, number = {1}, pages = {218 - 226}, doi = {10.17474/artvinofd.1260542}, title = {Orman ağacı ıslah çalışmalarında doğrusal karma model seçimi}, key = {cite}, author = {Acet, Mehmet and Ölmez, Zafer} }
APA Acet, M. & Ölmez, Z. (2023). Orman ağacı ıslah çalışmalarında doğrusal karma model seçimi . Artvin Çoruh Üniversitesi Orman Fakültesi Dergisi , 24 (1) , 218-226 . DOI: 10.17474/artvinofd.1260542
MLA Acet, M. , Ölmez, Z. "Orman ağacı ıslah çalışmalarında doğrusal karma model seçimi" . Artvin Çoruh Üniversitesi Orman Fakültesi Dergisi 24 (2023 ): 218-226 <http://ofd.artvin.edu.tr/en/pub/issue/77285/1260542>
Chicago Acet, M. , Ölmez, Z. "Orman ağacı ıslah çalışmalarında doğrusal karma model seçimi". Artvin Çoruh Üniversitesi Orman Fakültesi Dergisi 24 (2023 ): 218-226
RIS TY - JOUR T1 - Linear mixed model selection in forest tree breeding studies AU - MehmetAcet, ZaferÖlmez Y1 - 2023 PY - 2023 N1 - doi: 10.17474/artvinofd.1260542 DO - 10.17474/artvinofd.1260542 T2 - Artvin Çoruh Üniversitesi Orman Fakültesi Dergisi JF - Journal JO - JOR SP - 218 EP - 226 VL - 24 IS - 1 SN - 2146-1880-2146-698X M3 - doi: 10.17474/artvinofd.1260542 UR - https://doi.org/10.17474/artvinofd.1260542 Y2 - 2023 ER -
EndNote %0 Artvin Coruh University Journal of Forestry Faculty Orman ağacı ıslah çalışmalarında doğrusal karma model seçimi %A Mehmet Acet , Zafer Ölmez %T Orman ağacı ıslah çalışmalarında doğrusal karma model seçimi %D 2023 %J Artvin Çoruh Üniversitesi Orman Fakültesi Dergisi %P 2146-1880-2146-698X %V 24 %N 1 %R doi: 10.17474/artvinofd.1260542 %U 10.17474/artvinofd.1260542
ISNAD Acet, Mehmet , Ölmez, Zafer . "Orman ağacı ıslah çalışmalarında doğrusal karma model seçimi". Artvin Çoruh Üniversitesi Orman Fakültesi Dergisi 24 / 1 (May 2023): 218-226 . https://doi.org/10.17474/artvinofd.1260542
AMA Acet M. , Ölmez Z. Orman ağacı ıslah çalışmalarında doğrusal karma model seçimi. ACUJFF. 2023; 24(1): 218-226.
Vancouver Acet M. , Ölmez Z. Orman ağacı ıslah çalışmalarında doğrusal karma model seçimi. Artvin Çoruh Üniversitesi Orman Fakültesi Dergisi. 2023; 24(1): 218-226.
IEEE M. Acet and Z. Ölmez , "Orman ağacı ıslah çalışmalarında doğrusal karma model seçimi", Artvin Çoruh Üniversitesi Orman Fakültesi Dergisi, vol. 24, no. 1, pp. 218-226, May. 2023, doi:10.17474/artvinofd.1260542
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