Two-dimensional penalized splines via Gibbs sampling to account for spatial variability in forest genetic trials with small amount of information available

Anekonda, T. S. and W. J. Libby (1996): Effectiveness of nearestneighbor data adjustment in a clonal test of Redwood. Silvae Genet. 45(1): 46–51.Search in Google Scholar

Bohmanova, J., I. Misztal and J. K. Bertrand (2005): Studies on multiple trait and random regression models for genetic evaluation of beef cattle for growth. J Anim Sci 83: 62–67.10.2527/2005.83162xSearch in Google Scholar

Cantet, R. J. C., A. N. Birchmeier, A. W. Canaza Cayo and C. Fiorett (2005): Semiparametric animal models via penalized splines as alternatives to models with contemporary groups. J Anim Sci 83: 2482–2494.10.2527/2005.83112482xSearch in Google Scholar

Cappa, E. P. and R. J. C. Cantet (2006): Bayesian inference for normal multiple-trait individual-tree models with missing records via full conjugate Gibbs. Can J For Res 36: 1276–1285.10.1139/x06-024Search in Google Scholar

Cappa, E. P. and R. J. C. Cantet (2007): Bayesian estimation of a surface to account for a spatial trend using penalized splines in an individual-tree mixed model. Can J For Res 37: 2677–2688.10.1139/X07-116Search in Google Scholar

Costa e Silva, J., G. W. Dutkowski and A. R. Gilmour (2001): Analysis of early tree height in forest genetic trials is enhanced by including a spatially correlated residual. Can J For Res 31: 1887–1893.10.1139/x01-123Search in Google Scholar

Cornillon, P. A., L. Saint-Andre, J. M. Bouvet, P. Vigneron, A. Saya and R. Gouma (2003): Using B-splines for growth curve classification: applications to selection of eucalypt clones. Forest Ecology and Management 176: 75–85.10.1016/S0378-1127(02)00276-1Search in Google Scholar

De Boor, C. (1993): B(asic)-spline basics. Fundamental Developments of Computer-Aided Geometric Modeling. Edited by L. Piegl, Academic Press, San Diego, CA.Search in Google Scholar

Durban, M., I. Currie and R. Kempton (2001): Adjusting for fertility and competition in variety trials. J Agric Sci (Camb) 136: 129–140.10.1017/S0021859601008541Search in Google Scholar

Dutkowski, G. W., J. Costa e Silva, A. R. Gilmour and G. A. Lopez (2002): Spatial analysis methods for forest genetic trials. Can J For Res 32: 2201–2214.10.1139/x02-111Search in Google Scholar

Dutkowski, G. W., J. Costa e Silva, A. R. Gilmour, H. Wellendorf and A. Aguiar (2006): Spatial analysis enhances modeling of a wide variety of traits in forest genetic trials. Can J For Res 36: 1851–1870.10.1139/x06-059Search in Google Scholar

Eilers, P. H. C. and B. D. Marx (1996): Flexible smoothing with B-splines and penalties (with comments and rejoinder). Stat Sci 11: 89–121.10.1214/ss/1038425655Search in Google Scholar

Eilers, P. H. C. and B. D. Marx (2003): Multivariate calibration with temperature interaction using two-dimensional penalized signal regression. Chemometr. Intell Lab Syst 66: 159–174.10.1016/S0169-7439(03)00029-7Search in Google Scholar

El-Kassaby, Y. A. and Y. S. Park (1993): Genetic variation and correlation in growth, biomass traits, and vegetative phenology of a 3-year-old Douglas-fir common garden at different spacings. Silvae Genet 42: 289–297.Search in Google Scholar

Ericsson, T. (1997): Enhanced heritabilities and best linear unbiased predictors through appropriate blocking of progeny trials. Can J For Res 27: 2097–2101.10.1139/x97-153Search in Google Scholar

Federer, W. T. (1998): Recovery of interblock, intergradient, and intervarietal information in incomplete block and lattice rectangle designed experiments. Biometrics 54: 471–481.10.2307/3109756Search in Google Scholar

Finley, A. O., S. Banerjee, P. Waldmann and T. Ericsson (2009): Hierarchical spatial modeling of additive and dominance genetic variance for large spatial trial data sets. Biometrics 65: 441–451.10.1111/j.1541-0420.2008.01115.x277509518759829Search in Google Scholar

Gilmour, A. R., B. R. Cullis and A. P. Verbyla (1997): Accounting for natural and extraneous variation in the analysis of field experiments. J Agric Biol Environ Stat 2: 269–293.10.2307/1400446Search in Google Scholar

Gezan, S. A., D. A. Huber and T. L. White (2006): Post hoc blocking to improve heritability and precision of best linear unbiased genetic predictions. Can J For Res 36: 2141–2147.10.1139/x06-112Search in Google Scholar

Green, P. J. and B. W. Silverman (1994): Nonparametric Regression and Generalized Linear Model. Chapman & Hall, London, UK.10.1007/978-1-4899-4473-3Search in Google Scholar

Grondona, M. O., J. Crossa, P. N. Fox and W. H. Pfeiffer (1996): Analysis of variety yield trials using two-dimensional separable ARIMA processes. Biometrics 52: 763–770.10.2307/2532916Search in Google Scholar

Henderson, C. R. (1984): Applications of Linear Models in Animal Breeding. Canada, University of Guelph, Guelph, Ont.Search in Google Scholar

Hamann, A., M. Koshy and G. Namkoong (2002): Improving precision of breeding values by removing spatially autocorrelated variation in forestry field experiments. Silvae Genet 51: 210–215.Search in Google Scholar

Harville, D. A. (1997): Matrix algebra from a statistician’s perspective. Springer-Verlag. New York.10.1007/b98818Search in Google Scholar

Iwaisaki, H., S. Tsuruta, I. Misztal and J. K. Bertrand (2005): Genetic parameters estimated with multi-trait and linear spline-random regression models using Gelbvieh early growth data. J Anim Sci 83: 499–506.10.2527/2005.834757x15753329Search in Google Scholar

Joyce, D., R. Ford and Y. B. Fu (2002): Spatial patterns of tree height variations in a black spruce farm-field progeny test and neighbors-adjusted estimations of genetic parameters. Silvae Genet 51: 13–18.Search in Google Scholar

Krakowski, J, Y. S. Park and Y. A. El-Kassaby (2005): Early testing of Douglas-fir: wood density and ring width. For Genet 12: 99–105.Search in Google Scholar

Kroon, J., B. Andersson and T. J. Mullin (2008): Genetic variation in the diameter-height relationship in Scots pine (Pinus sylvestris). Can J For Res 38: 1493–1503.10.1139/X07-233Search in Google Scholar

Kusnandar, D. and N. Galwey (2000): A Proposed Method for Estimation of Genetic Parameters on Forest Trees Without Raising Progeny: Critical Evaluation and Refinement. Silvae Genet 49: 15–21.Search in Google Scholar

Loo-Dinkins, J. A. and C. G. Tauer (1987): Statistical efficiency of six progeny test field designs on three loblolly pine (Pinus taeda L.) site types. Can J For Res 17: 1066–1070.10.1139/x87-163Search in Google Scholar

Loo-Dinkins, J. (1992): Field test design. In: Handbook of quantitative forest genetics. Edited by L. Fins, S. Friedman, and J.V. Brotschol. Kluwer Academic Publishers, Dordrecht, the Netherlands. pp. 96–139.10.1007/978-94-015-7987-2_4Search in Google Scholar

Lopez, G. A., B. M. Potts, G. W. Dutkowski, L. A. Apiolaza and P. Gelid (2002): Genetic variation and intertrait correlations in Eucalyptus globulus base population trials in Argentina. Forest Genetics 9: 223–237.Search in Google Scholar

Magnussem, S. (1990): Application and comparison of spatial models in analyzing tree-genetics field trials. Can J For Res 20: 536–546.10.1139/x90-070Search in Google Scholar

Magnussen, S. (1993): Bias in genetic variance estimates due to spatial autocorrelation. Theor Appl Genet 86: 349–355.10.1007/BF00222101Search in Google Scholar

Magnussen, S. and A. D. Yanchuk (1994): Time trends of predicted breeding values in selected crosses of coastal Douglas-fir in British Columbia: a methodological study. For Sci 40: 663–685.Search in Google Scholar

Meyer, K. (2005): Random regression analyses using B-splines to model growth of Australian Angus cattle. Genet Sel Evol 37: 473–500.10.1186/1297-9686-37-6-473Search in Google Scholar

Rehfeldt, G. E. (1995): Genetic variation, climate models and the ecological genetics of Larix occidentalis. For Ecol Manage 78: 21–37.10.1016/0378-1127(95)03602-4Search in Google Scholar

Ruppert, D. (2002): Selecting the number of knots for penalized splines. Journal of Computational and Graphical Statistics 11: 735–757.10.1198/106186002853Search in Google Scholar

Ruppert, D., M. P. Wand and R. J. Carroll (2003): Semiparametric Regression. Cambridge Univ Press, Cambridge, UK.10.1017/CBO9780511755453Search in Google Scholar

Saenz-Romero, C., E. V. Nordheim, R. P. Guries and P. M. Crump (2001): A case study of a provenance/progeny test using trend analysis with correlated errors and SAS PROC MIXED. Silvae Genet 50: 127–135.Search in Google Scholar

Schabenberger, O. and C. A. Gotway (2005): Statistical Methods for Spatial Data Analysis. Boca Raton: Chapman & Hall.Search in Google Scholar

Silverman, B. (1986): Density Estimation for Statistics and Data Analysis. Chapman and Hall, London.10.1007/978-1-4899-3324-9Search in Google Scholar

Smith, B. J. (2003): Bayesian Output Analysis Program (BOA) version 1.0 user’s manual. http://www.publichealth.uiowa.edu/boa/Home.html. Cited 14 Aug 2008.Search in Google Scholar

Spiegelhalter, D. J., N. G. Best, B. P. Carlin and A. Van der Linde (2002): Bayesian measures of model complexity and fit (with discussion). Journal of the Royal Statistical Society Series B 64: 583–639.10.1111/1467-9868.00353Search in Google Scholar

St. Clair, J. B. (2006): Genetic variation in fall cold hardiness in coastal Douglas-fir in western Oregon and Washington. Can J Bot 84: 1110–1121.10.1139/b06-084Search in Google Scholar

Thomson, A. J. and Y. A. El-Kassaby (1988): Trend surface analysis of provenance-progeny transfer data. Can J For Res 18: 515–520.10.1139/x88-075Search in Google Scholar

Verbyla, A. P., B. R. Cullis, M. G. Kenward and S. J. Welham (1999): The analysis of designed experiments and longitudinal data by using smoothing splines (with discussion). Applied Statistics 48: 69–311.Search in Google Scholar

Wand, M. P. (2003): Smoothing and mixed models. Comput Stat 18: 223–249.10.1007/s001800300142Search in Google Scholar

Woods, J. H., D. Kolotelo and A. D. Yanchuk (1995): Early selection of coastal Douglas-fir in a farm-field environment. Silvae Genet 44: 178–186.Search in Google Scholar

White, I. M. S., R. Thompson and S. Brotherstone (1999): Genetic and environmental smoothing of lactation curves with cubic splines. J Dairy Sci 82: 632–638.10.3168/jds.S0022-0302(99)75277-XSearch in Google Scholar

Ye, T. Z. and K. J. S. Jayawickrama (2008): Efficiency of using spatial analysis in firest-generation coastal Douglas-fir progeny tests in the US Pacific Northwest. Tree Genet Genomics 4: 677–692.10.1007/s11295-008-0142-4Search in Google Scholar

Zas, R. (2006): Iterative kriging for removing spatial autocorrelation in analysis of forest genetic trials. Tree Genet Genomics 2: 177–185.10.1007/s11295-006-0042-4Search in Google Scholar