Abstract
The optimization of perennial plant breeding necessarily involves the evaluation of multi-harvest and/or multi-site trials. In these situations, modeling covariance structures can elevate accuracy. This study aimed to evaluate different covariance structures for multi-harvest and multi-site trial analyses, using two datasets (D1 and D2). In D1, 25 hybrids of Theobroma grandiflorum were evaluated in a complete randomized block design, during twelve consecutive harvest years. In D2, 215 clones of Eucalyptus spp. were evaluated in a complete randomized block design, in four sites. For both datasets, the covariance structures of the random effects were modeled, and their adequacy was tested by the Akaike and Bayesian information criteria. From the selected model, the variance components and genetic parameters were estimated. We also compared the expected genetic gains and the rankings of genotypes based on the genotypic values provided by the basic and the selected models. For D1, the third-order factor analytic model was the most suitable for genetic effects, while for D2, the unstructured model showed the best fit for such effects. The models provided a better insight into the variances dynamics over the harvest years/sites. The genetic gains were 3.52 percentage points higher in D1 and did not change in D2. Despite similar results, the standard model, modeled with covariance structures that assume homogeneity of co-variances, was not the most statistically appropriate model for D2 according to the information criteria. Therefore, the modeling of covariance structures can and should be used in the genetic evaluation of perennial plants.
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Data availability
The datasets generated during and/or analyzed during the current study are available in the GitHub repository, at https://github.com/saulo-chaves/MHT_MET_MM.
Code availability
The codes are also available at https://github.com/saulo-chaves/MHT_MET_MM.
References
Akaike H (1974) A new look at the statistical model identification. IEEE Trans Autom Control 19:716–723. https://doi.org/10.1109/TAC.1974.1100705
Alves RS, Resende MDV, Azevedo CF et al (2020) Optimization of Eucalyptus breeding through random regression models allowing for reaction norms in response to environmental gradients. Tree Genet Genomes 16:38. https://doi.org/10.1007/s11295-020-01431-5
Armstrong RA (2017) Recommendations for analysis of repeated-measures designs: testing and correcting for sphericity and use of MANOVA and mixed model analysis. Ophthalmic Physiol Opt 37:585–593. https://doi.org/10.1111/opo.12399
Atlin GN, Cairns JE, Das B (2017) Rapid breeding and varietal replacement are critical to adaptation of cropping systems in the developing world to climate change. Glob Food Secur 12:31–37. https://doi.org/10.1016/j.gfs.2017.01.008
Baker B (2017) Can modern agriculture be sustainable?: perennial polyculture holds promise. Bioscience 67:325–331. https://doi.org/10.1093/biosci/bix018
Berlin M, Jansson G, Högberg K-A, Helmersson A (2019) Analysis of non-additive genetic effects in Norway spruce. Tree Genet Genomes 15:42. https://doi.org/10.1007/s11295-019-1350-9
Burgueño J (2018) Spatial Analysis of Field Experiments. In: Glaz B, Yeater KM (eds) ASA, CSSA, and SSSA Books. American Society of Agronomy, Crop Science Society of America, and Soil Science Society of America, Inc., Madison, WI, USA, pp 319–344
Butler DG, Cullis BR, Gilmour AR et al (2018) ASReml-R reference manual Version 4. VSN International, Hemel Hempstead, UK
Cavanaugh JE, Neath AA (2019) The Akaike information criterion: background, derivation, properties, application, interpretation, and refinements. Wires Comput Stat 11:e1460. https://doi.org/10.1002/wics.1460
Chaves SFS, Gama MAP, Alves RM et al (2020) Evaluation of physicochemical attributes of a yellow latosol under agroforestry system as compared to secondary forest in the Eastern Amazon. Agrofor Syst 94:1903–1912. https://doi.org/10.1007/s10457-020-00513-6
Chaves SFS, Alves RM, Alves RS et al (2021) Theobroma grandiflorum breeding optimization based on repeatability, stability and adaptability information. Euphytica 217:211. https://doi.org/10.1007/s10681-021-02944-3
Cobb JN, Juma RU, Biswas PS et al (2019) Enhancing the rate of genetic gain in public-sector plant breeding programs: lessons from the breeder’s equation. Theor Appl Genet 132:627–645. https://doi.org/10.1007/s00122-019-03317-0
Coelho IF, Peixoto MA, Evangelista JSPC et al (2020) Multiple-trait, random regression, and compound symmetry models for analyzing multi-environment trials in maize breeding. PLoS One 15:e0242705. https://doi.org/10.1371/journal.pone.0242705
Crews TE, Cattani DJ (2018) Strategies, advances, and challenges in breeding perennial grain crops. Sustainability 10:2192. https://doi.org/10.3390/su10072192
Crews TE, Blesh J, Culman SW et al (2016) Going where no grains have gone before: from early to mid-succession. Agric Ecosyst Environ 223:223–238. https://doi.org/10.1016/j.agee.2016.03.012
Crowder MJ, Hand DJ (2020) Analysis of repeated measures. Routledge, New York
Cullis BR, Smith AB, Coombes NE (2006) On the design of early generation variety trials with correlated data. J Agric Biol Environ Stat 11:381–393. https://doi.org/10.1198/108571106X154443
Cullis BR, Smith AB, Beeck CP, Cowling WA (2010) Analysis of yield and oil from a series of canola breeding trials. Part II. Exploring variety by environment interaction using factor analysis. Genome 53:1002–1016. https://doi.org/10.1139/G10-080
Cullis BR, Jefferson P, Thompson R, Smith AB (2014) Factor analytic and reduced animal models for the investigation of additive genotype-by-environment interaction in outcrossing plant species with application to a Pinus radiata breeding programme. Theor Appl Genet 127:2193–2210. https://doi.org/10.1007/s00122-014-2373-0
Dias LAS, Kageyama PY (1998) Repeatability and minimum harvest period of cacao (Theobroma cacao L.) in Southern Bahia. Euphytica 102:29–35. https://doi.org/10.1023/A:1018373211196
Dias KOG, Gezan SA, Guimarães CT et al (2018) Estimating genotype × environment interaction for and genetic correlations among drought tolerance traits in maize via factor analytic multiplicative mixed models. Crop Sci 58:72–83. https://doi.org/10.2135/cropsci2016.07.0566
Drton M, Plummer M (2017) A Bayesian information criterion for singular models. J R Stat Soc Ser B Stat Methodol 79:323–380. https://doi.org/10.1111/rssb.12187
Elias AA, Robbins KR, Doerge RW, Tuinstra MR (2016) Half a century of studying genotype × environment interactions in plant breeding experiments. Crop Sci 56:2090–2105. https://doi.org/10.2135/cropsci2015.01.0061
Elli EF, Sentelhas PC, Bender FD (2020) Impacts and uncertainties of climate change projections on Eucalyptus plantations productivity across Brazil. For Ecol Manag 474:118365. https://doi.org/10.1016/j.foreco.2020.118365
Faveri J, Verbyla AP, Pitchford WS et al (2015) Statistical methods for analysis of multi-harvest data from perennial pasture variety selection trials. Crop Pasture Sci 66:947. https://doi.org/10.1071/CP14312
Ferrão LFV, Ferrão RG, Ferrão MAG et al (2017) A mixed model to multiple harvest-location trials applied to genomic prediction in Coffea canephora. Tree Genet Genomes 13:95. https://doi.org/10.1007/s11295-017-1171-7
Gezan SA, Carvalho MP, Sherrill J (2017) Statistical methods to explore genotype-by-environment interaction for loblolly pine clonal trials. Tree Genet Genomes 13:1. https://doi.org/10.1007/s11295-016-1081-0
Gilmour AR, Cullis BR, Verbyla AP (1997) Accounting for natural and extraneous variation in the analysis of field experiments. J Agric Biol Environ Stat 2:269–293. https://doi.org/10.2307/1400446
Gu Z, Eils R, Schlesner M (2016) Complex heatmaps reveal patterns and correlations in multidimensional genomic data. Bioinforma Oxf Engl 32:2847–2849. https://doi.org/10.1093/bioinformatics/btw313
Halldorsdottir T, Binder EB (2017) Gene × environment interactions: from molecular mechanisms to behavior. Annu Rev Psychol 68:215–241. https://doi.org/10.1146/annurev-psych-010416-044053
Haverkamp N, Beauducel A (2017) Violation of the sphericity assumption and its effect on type-I error rates in repeated measures ANOVA and Multi-Level Linear Models (MLM). Front Psychol 8:1841. https://doi.org/10.3389/fpsyg.2017.01841
Henderson CR (1975) Best linear unbiased estimation and prediction under a selection model. Biometrics 31:423. https://doi.org/10.2307/2529430
Hu X, Yan S, Shen K (2013) Heterogeneity of error variance and its influence on genotype comparison in multi-location trials. Field Crops Res 149:322–328. https://doi.org/10.1016/j.fcr.2013.05.011
Hunt CH, Hayes BJ, van Eeuwijk FA et al (2020) Multi-environment analysis of sorghum breeding trials using additive and dominance genomic relationships. Theor Appl Genet 133:1009–1018. https://doi.org/10.1007/s00122-019-03526-7
Isabel N, Holliday JA, Aitken SN (2020) Forest genomics: advancing climate adaptation, forest health, productivity, and conservation. Evol Appl 13:3–10. https://doi.org/10.1111/eva.12902
Isik F, Holland J, Maltecca C (2017) Genetic data analysis for plant and animal breeding. Springer International Publishing, Cham
Kelly AM, Smith AB, Eccleston JA, Cullis BR (2007) The accuracy of varietal selection using factor analytic models for multi-environment plant breeding trials. Crop Sci 47:1063–1070. https://doi.org/10.2135/cropsci2006.08.0540
Krause MD, Dias KOG, Santos J et al (2020) Boosting predictive ability of tropical maize hybrids via genotype-by-environment interaction under multivariate GBLUP models. Crop Sci 60:3049–3065. https://doi.org/10.1002/csc2.20253
Lahive F, Hadley P, Daymond AJ (2019) The physiological responses of cacao to the environment and the implications for climate change resilience A Review. Agron Sustain Dev 39:5. https://doi.org/10.1007/s13593-018-0552-0
Malosetti M, Ribaut J-M, van Eeuwijk FA (2013) The statistical analysis of multi-environment data: modeling genotype-by-environment interaction and its genetic basis. Front Physiol 4:44. https://doi.org/10.3389/fphys.2013.00044
Melo VL, Marçal TS, Rocha JRASC et al (2020) Modeling (co)variance structures for genetic and non-genetic effects in the selection of common bean progenies. Euphytica 216:77. https://doi.org/10.1007/s10681-020-02607-9
Meyer K (2009) Factor-analytic models for genotype × environment type problems and structured covariance matrices. Genet Sel Evol 41:21. https://doi.org/10.1186/1297-9686-41-21
Monteverde E, Rosas JE, Blanco P et al (2018) Multienvironment models increase prediction accuracy of complex traits in advanced breeding lines of rice. Crop Sci 58:1519–1530. https://doi.org/10.2135/cropsci2017.09.0564
Mrode RA (2014) Linear models for the prediction of animal breeding values, 3rd edn. CABI, Boston, MA
Neath AA, Cavanaugh JE (2012) The Bayesian information criterion: background, derivation, and applications. Wires Comput Stat 4:199–203. https://doi.org/10.1002/wics.199
Pastina MM, Malosetti M, Gazaffi R et al (2012) A mixed model QTL analysis for sugarcane multiple-harvest-location trial data. Theor Appl Genet 124:835–849. https://doi.org/10.1007/s00122-011-1748-8
Patterson HD, Thompson R (1971) Recovery of inter-block information when block sizes are unequal. Biometrika 58:545–554. https://doi.org/10.1093/biomet/58.3.545
Piepho H-P (1997) Analyzing genotype-environment data by mixed models with multiplicative terms. Biometrics 53:761–766. https://doi.org/10.2307/2533976
Piepho H-P (1998) Empirical best linear unbiased prediction in cultivar trials using factor-analytic variance-covariance structures. Theor Appl Genet 97:195–201. https://doi.org/10.1007/s001220050885
Piepho H-P, Eckl T (2014) Analysis of series of variety trials with perennial crops. Grass Forage Sci 69:431–440. https://doi.org/10.1111/gfs.12054
Piepho H-P, Möhring J, Melchinger AE, Büchse A (2008) BLUP for phenotypic selection in plant breeding and variety testing. Euphytica 161:209–228. https://doi.org/10.1007/s10681-007-9449-8
R Core Team (2021) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Viena, Áustria
Rai MK, Shekhawat NS (2014) Recent advances in genetic engineering for improvement of fruit crops. Plant Cell Tissue Organ Cult PCTOC 116:1–15. https://doi.org/10.1007/s11240-013-0389-9
Redpath LE, Gumpertz M, Ballington JR et al (2021) Genotype, environment, year, and harvest effects on fruit quality traits of five blueberry (Vaccinium corymbosum L.) cultivars. Agronomy 11:1788. https://doi.org/10.3390/agronomy11091788
Schmidt P, Hartung J, Bennewitz J, Piepho H-P (2019) Heritability in plant breeding on a genotype-difference basis. Genetics 212:991–1008. https://doi.org/10.1534/genetics.119.302134
Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6:461–464
Shalizi MN, Isik F (2019) Genetic parameter estimates and GxE interaction in a large cloned population of Pinus taeda L. Tree Genet Genomes 15:46. https://doi.org/10.1007/s11295-019-1352-7
Silva PHM, Marco M, Alvares CA et al (2019) Selection of Eucalyptus grandis families across contrasting environmental conditions. Crop Breed Appl Biotechnol 19:47–54. https://doi.org/10.1590/1984-70332019v19n1a07
Singh M, Tadesse W, Sarker A et al (2013) Capturing the heterogeneity of the error variances of a group of genotypes in crop cultivar trials. Crop Sci 53:811–818. https://doi.org/10.2135/cropsci2012.11.0637
Smith AB, Cullis BR (2018) Plant breeding selection tools built on factor analytic mixed models for multi-environment trial data. Euphytica 214:143. https://doi.org/10.1007/s10681-018-2220-5
Smith AB, Cullis BR, Thompson R (2001) Analyzing variety by environment data using multiplicative mixed models and adjustments for spatial field trend. Biometrics 57:1138–1147. https://doi.org/10.1111/j.0006-341X.2001.01138.x
Smith AB, Stringer JK, Wei X, Cullis BR (2007) Varietal selection for perennial crops where data relate to multiple harvests from a series of field trials. Euphytica 157:253–266. https://doi.org/10.1007/s10681-007-9418-2
Smith AB, Ganesalingam A, Kuchel H, Cullis BR (2015) Factor analytic mixed models for the provision of grower information from national crop variety testing programs. Theor Appl Genet 128:55–72. https://doi.org/10.1007/s00122-014-2412-x
Smith AB, Norman A, Kuchel H, Cullis B (2021) Plant variety selection using interaction classes derived from factor analytic linear mixed models: models with independent variety effects. Front Plant Sci 12:1857. https://doi.org/10.3389/fpls.2021.737462
Snowdon RJ, Wittkop B, Chen T-W, Stahl A (2021) Crop adaptation to climate change as a consequence of long-term breeding. Theor Appl Genet 134:1613–1623. https://doi.org/10.1007/s00122-020-03729-3
Souza VF, Ribeiro PCO, Vieira Júnior IC et al (2021) Exploring genotype × environment interaction in sweet sorghum under tropical environments. Agron J 113:3005–3018. https://doi.org/10.1002/agj2.20696
Stringer JK, Atkin FC, Gezan SA (2017) Statistical approaches in plant breeding: maximising the use of the genetic information. Genetic Improvement of Tropical Crops. Springer International Publishing, Cham, pp 3–17
van Eeuwijk FA, Bustos-Korts D, Millet EJ et al (2019) Modelling strategies for assessing and increasing the effectiveness of new phenotyping techniques in plant breeding. Plant Sci 282:23–39. https://doi.org/10.1016/j.plantsci.2018.06.018
Velazco JG, Rodríguez-Álvarez MX, Boer MP et al (2017) Modelling spatial trends in sorghum breeding field trials using a two-dimensional P-spline mixed model. Theor Appl Genet 130:1375–1392. https://doi.org/10.1007/s00122-017-2894-4
Verbyla AP (2019) A note on model selection using information criteria for general linear models estimated using REML. Aust N Z J Stat 61:39–50. https://doi.org/10.1111/anzs.12254
Verbyla AP, Faveri J, Deery DM, Rebetzke GJ (2021) Modelling temporal genetic and spatio-temporal residual effects for high-throughput phenotyping data. Aust N Z J Stat 63:284–308. https://doi.org/10.1111/anzs.12336
Weißhuhn P, Reckling M, Stachow U, Wiggering H (2017) Supporting agricultural ecosystem services through the integration of perennial polycultures into crop rotations. Sustainability 9:2267. https://doi.org/10.3390/su9122267
Wickham H (2016) ggplot2: elegant graphics for data analysis, 2nd edn. Springer, Cham
Wolfinger RD (1996) Heterogeneous variance: covariance structures for repeated measures. J Agric Biol Environ Stat 1:205–230. https://doi.org/10.2307/1400366
Zhang R, Han D, Hu X (2020) Analyzing the performance of corn in China using a factor-analytic variance-covariance structure with multiple factors. Crop Sci 60:190–201. https://doi.org/10.1002/csc2.20090
Acknowledgements
We acknowledge the financial support from the National Institute of Science and Technology of Coffee (INCT Café), Minas Gerais State Agency for Research and Development (FAPEMIG), Brazilian National Council for Scientific and Technological Development (CNPq), and Coordination for the Improvement of Higher Education Personnel (CAPES)—Finance Code 001.
Funding
This research was supported by the National Institute of Science and Technology of Coffee (INCT Café), Minas Gerais State Agency for Research and Development (FAPEMIG), Brazilian National Council for Scientific and Technological Development (CNPq), and Coordination for the Improvement of Higher Education Personnel (CAPES)—Finance Code 001.
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All authors contributed to the study conception and design. K.O.G. Dias and R.S. Alves were responsible for the conceptualization of this work. S.F.S. Chaves and J.S.P.C. Evangelista performed the material preparation and analysis. S.F.S. Chaves, J.S.P.C. Evangelista, and F.M. Ferreira wrote the first draft. All authors commented on the previous version of the manuscript. All authors read and approved the final manuscript.
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Data and scripts used in this work are publicly available at GitHub (https://github.com/saulo-chaves/MHT_MET_MM).
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Chaves, S.F.S., Evangelista, J.S.P.C., Alves, R.S. et al. Application of linear mixed models for multiple harvest/site trial analyses in perennial plant breeding. Tree Genetics & Genomes 18, 44 (2022). https://doi.org/10.1007/s11295-022-01576-5
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DOI: https://doi.org/10.1007/s11295-022-01576-5