A novel individual-tree mixed model to account for competition and environmental heterogeneity: a Bayesian approach
Eduardo Pablo Cappa1,2,5 & Facundo Muñoz3 & Leopoldo Sanchez3 &
Rodolfo J. C. Cantet2,4
Received: 19 May 2015 /Revised: 19 August 2015 /Accepted: 28 August 2015 /Published online: 26 October 2015 # Springer-Verlag Berlin Heidelberg 2015
Abstract 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.
Keywords Individual-tree mixedmodel . Genetic and environmental competition effects . Environmental heterogeneity . Two-dimensional smoothing surface . Gibbs sampling
Advanced forest genetic evaluation involves analyzing data from progeny tests using mixed linear models to calculate
Communicated by R. Burdon
This article is part of the Topical Collection on Breeding
Electronic supplementary material The online version of this article (doi:10.1007/s11295-015-0917-3) contains supplementary material, which is available to authorized users. * Eduardo Pablo Cappa firstname.lastname@example.org 1 Instituto Nacional de Tecnología Agropecuaria (INTA), Instituto de
Recursos Biológicos, De Los Reseros y Dr. Nicolás Repetto s/n, 1686 Hurlingham, Buenos Aires, Argentina 2 Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Buenos Aires, Argentina 3 Institut National de la Recherche Agronomique (INRA) Orléans,
Unité Amélioration, Génétique et Physiologie Forestières, 2163
Avenue de la Pomme de Pin, CS 40001 ARDON, 45075, Orleans
Cedex 02, France 4 Departamento de Producción Animal, Facultad de Agronomía,
Universidad de Buenos Aires, Avenida San Martín 4453,
C1417DSQ Buenos Aires, Argentina 5 Bosques Cultivados, Instituto de Recursos Biológicos, Centro de
Investigación en Recursos Naturales, Instituto Nacional de
Tecnología Agropecuaria, De Los Reseros y Dr. Nicolás Repetto s/n, 1686 Hurlingham, Buenos Aires, Argentina
Tree Genetics & Genomes (2015) 11: 120
Bbest linear unbiased predictors^ (BLUP) of tree breeding values (BVs). As BLUP prediction depends on the values of the covariance matrices for the assumed model, the specification of the dispersion parameters should take into account the negative correlation caused by competition among individuals and the positive spatial correlation due to the environmental heterogeneity. In field trials with perennial plants, both phenomena (i.e., competition and environmental heterogeneity) are dynamic and coexist simultaneously (Magnussen 1994). Therefore, statistical genetic analyses neglecting these factors or considering only one of them can lead to biases in the estimation of genetic parameters and in the prediction of individual additive genetic effects (i.e., BLUP of BVs). Simulation studies have shown that positive spatial correlation inflates the additive genetic variance, while moderate levels of negative correlation caused by competition depress it (Magnussen 1994). Therefore, when both competition and environmental heterogeneity are present in a forest genetic trial, a complete model approach that allows fitting simultaneously both processes is necessary (Resende et al. 2005). However, appropriate choice of the model is likely to influence how well the two processes can be separated analytically (Durban et al. 2001).
Competition reflects the impairing interplay of closely neighboring trees, often when local resources are limiting. It depends on the genetic composition and the spatial arrangement of neighboring trees (Hinson and Hanson 1962), and it can be decomposed into genetic and environmental sources (Magnussen 1989).
Cappa and Cantet (2008) presented an approach to account for competition effects in forest genetic evaluation. The mixed linear model included direct and indirect (i.e., competition) genetic effects, as well as environmental competition effects. Competition effects, either genetic or environmental, are identified in the phenotype of a competitor tree by means of the Bintensity of competition^ (IC) elements. The ICs are inverse functions of the distance and the number of competing individuals, either row/column-wise or diagonally. The
ICs allow standardization of the variance of competition effects, so that the model accounts for unequal number of neighbors in locations with mortality and borders.