A novel individual-tree mixed model to account for competition and environmental heterogeneity: a Bayesian approach
- 340 Downloads
Negative correlation caused by competition among individuals and positive spatial correlation due to environmental heterogeneity may lead to biases in estimating genetic parameters and predicting breeding values (BVs) from forest genetic trials. Former models dealing with competition and environmental heterogeneity did not account for the additive relationships among trees or for the full spatial covariance. This paper extends an individual-tree mixed model with direct additive genetic, genetic, and environmental competition effects, by incorporating a two-dimensional smoothing surface to account for complex patterns of environmental heterogeneity (competition + spatial model (CSM)). We illustrate the proposed model using simulated and real data from a loblolly pine progeny trial. The CSM was compared with three reduced individual-tree mixed models using a real dataset, while simulations comprised only CSM versus true-parameters comparisons. Dispersion parameters were estimated using Bayesian techniques via Gibbs sampling. Simulation results showed that the CSM yielded posterior mean estimates of variance components with slight or negligible biases in the studied scenarios, except for the permanent environment variance. The worst performance of the simulated CSM was under a scenario with weak competition effects and small-scale environmental heterogeneity. When analyzing real data, the CSM yielded a lower value of the deviance information criterion than the reduced models. Moreover, although correlations between predicted BVs calculated from CSM and from a standard model with block effects and direct genetic effects only were high, the ranking among the top 5 % ranked individuals showed differences which indicated that the two models will have quite different genotype selections for the next cycle of breeding.
KeywordsIndividual-tree mixed model Genetic and environmental competition effects Environmental heterogeneity Two-dimensional smoothing surface Gibbs sampling
This research was supported by grants of Agencia Nacional de Ciencia y Tecnología (FONCyT PICT 00321) of Argentina, under the Programa de Modernización Tecnológica III, Contrato de Préstamo BID 1728/OC-AR. The authors would like to thank to Forestry Research and Experimentation Centre (CIEF, Buenos Aires, Argentina) for kindly providing the P. taeda L. dataset used in this study. FM and LS received funding from the European Union’s Seventh Framework Programme for research, technological development, and demonstration under grant agreement no. 284181 (“Trees4Future”).
Data archiving statement
We followed standard Tree Genetics and Genomes policy. Simulated dataset used in this manuscript is available in the Zenodo repository, http://dx.doi.org/10.5281/zenodo.32036. Supplementary information of the P. taeda L. trial and family numbers is also available in the Zenodo repository, http://dx.doi.org/10.5281/zenodo.32040. In addition, diameter at breast height of the P. taeda L. dataset will be available upon request.
- Brotherstone S, White IMS, Sykes R, Thompson R, Connolly T, Lee S, Woolliams J (2011) Competition effects in a young sitka spruce (Picea sitchensis, Bong. Carr) clonal trial. Silvae Genet 60:149–155Google Scholar
- Cappa EP, Cantet RJC (2008) Direct and competition additive effects in tree breeding: Bayesian estimation from an individual tree mixed model. Silvae Genet 57:45–56Google Scholar
- Cappa EP, Lstiburek M, Yanchuk AD, El-Kassaby YA (2011) Two-dimensional penalized splines via Gibbs sampling to account for spatial variability in forest genetic trials with small amount of information available. Silvae Genet 60:25–35Google Scholar
- De Boor C (1993) B(asic)-spline basics. Fundamental developments of computer-aided geometric modeling. L. Piegl, ed. Academic Press, San Diego, CAGoogle Scholar
- Geweke J (1992) Evaluating the accuracy of sampling-based approaches to calculating posterior moments. In: Bernardo JM, Berger JO, Dawid AP, Smith AFM (eds) Bayesian statistics 4. Oxford University Press, OxfordGoogle Scholar
- Gilmour AR, Gogel BJ, Cullis BR, Thompson R (2006) ASReml user guide release 2.0 VSN International Ltd, Hemel Hempstead, HP1 1ES, UK. p 267Google Scholar
- Hannrup B, Wilhelmsson L, Danell Ö (1998) Time trends for genetic parameters of wood density and growth traits in Pinus sylvestris L. Silvae Gene 47:214–219Google Scholar
- Henderson CR (1984) Applications of linear models in animal breeding. University of Guelph, Guelph, Ont, CanadaGoogle Scholar
- Kass RE, Carlin BP, Gelman A, Neal RM (1998) Markov chain Monte Carlo in practice: a roundtable discussion. Am Stat 52:93–100Google Scholar
- Kusnandar D (2001) The identification and interpretation of genetic variation in forestry plantation. PhD Thesis, University of Western Australia, Crawley, Australia.Google Scholar
- Magnussen S (1989) Effects and adjustments of competition bias in progeny trials with single-tree plots. For Sci 35:532–547Google Scholar
- Muir WM (2005) Incorporation of competitive effects in forest tree or animal breeding programs. Genetics 170:1247–1259Google Scholar
- Muñoz F, Sanchez L (2014) breedR: statistical methods for forest genetic resources analysts. R package version 0.7-16. https://github.com/famuvie/breedR
- R Development Core Team (2011) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. http://www.R-project.org/. Accessed 4 May 2015
- Resende MDV, Stringer J, Cullis B, Thompson R (2005) Joint modelling of competition and spatial variability in forest field trials. Rev Mat Estat 23:7–22Google Scholar
- Smith BJ (2003) Bayesian Output Analysis Program (BOA) version 1.0 user’s manual. Available from http://www.public-health.uiowa.edu/boa/.
- Stringer JK, Cullis BR, Thompson R (2005) Joint modelling of spatial variability and interplot competition to improve the efficiency of plant improvement. In Proceedings of the: Thredbo Statistical Meeting. Canberra, 6–11 February 2005. Australian National University/Australasian Region of the International Biometric Society v. 1, p.41.Google Scholar
- Verbyla AP, Cullis BR, Kenward MG, Welham SJ (1999) The analysis of designed experiments and longitudinal data by using smoothing splines (with discussion). Appl Stat 48:69–311Google Scholar