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

Silvae Genetica

Volumn 60, Issue 1, 2011, Pages 25-35

  Cappa, E P ^a   Lstiburek, M ^b   Yanchuk, A D ^c,d   El Kassaby, Y A ^d  

^a INSTITUTO NACIONAL DE TECNOLOGÍA AGROPECUARIA INTA   (Argentina)

^b CZECH UNIVERSITY OF LIFE SCIENCES PRAGUE   (Czech Republic)

^c RESEARCH BRANCH   (Canada)

^d UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Accuracy; Error variance; Genetic parameters; Genetics trials; Spatial variability; Tensor product of b spline

Indexed keywords

ERRORS; FORESTRY; INTERPOLATION; TENSORS;

ACCURACY; B SPLINES; ERROR VARIANCE; GENETIC PARAMETERS; GENETICS TRIALS; SPATIAL VARIABILITY;

DESIGN OF EXPERIMENTS;

ACCURACY; CHROMOSOMES; FORESTRY; VARIANCE;

EID: 79953217070     PISSN: 00375349     EISSN: None     Source Type: Journal    
DOI: 10.1515/sg-2011-0004     Document Type: Article

References (52)

1. 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.
7. CORNILLON, P. A., L. SAINT-ANDRE, J. M. BOUVET, P. VIGNERON, A. SAYA and R. GOUMA (2003): Using Bsplines for growth curve classification: applications to selection of eucalypt clones. Forest Ecology and Management 176: 75-85.
8. DE BOOR, C. (1993): B(asic)-spline basics. Fundamental Developments of Computer-Aided Geometric Modeling. Edited by L. PIEGL, Academic Press, San Diego, CA.
9. DURBAN, M., I. CURRIE and R. KEMPTON (2001): Adjusting for fertility and competition in variety trials. J Agric Sci (Camb) 136: 129-140.
10. 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.
11. 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.
12. 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.
13. 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.
14. 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.
15. ERICSSON, T. (1997): Enhanced heritabilities and best linear unbiased predictors through appropriate blocking of progeny trials. Can J For Res 27: 2097-2101.
16. FEDERER, W. T. (1998): Recovery of interblock, intergradient, and intervarietal information in incomplete block and lattice rectangle designed experiments. Biometrics 54: 471-481.
17. 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.
18. 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.
19. 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.
20. GREEN, P. J. and B. W SILVERMAN (1994): Nonparametric Regression and Generalized Linear Model. Chapman & Hall, London, UK.
21. GRONDONA, M. O., J. CROSSA, P. N. FOX and W H. PFEIFFER (1996): Analysis of variety yield trials using twodimensional separable ARIMA processes. Biometrics 52: 763-770.
22. HENDERSON, C. R. (1984): Applications of Linear Models in Animal Breeding. Canada, University of Guelph, Guelph, Ont.
23. 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.
24. HARVILLE, D. A. (1997): Matrix algebra from a statistician's perspective. Springer-Verlag. New York.
25. 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.
26. 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.
27. 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.
28. 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.
29. 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.
30. 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.
31. 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.
32. 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.
33. MAGNUSSEM, S. (1990): Application and comparison of spatial models in analyzing tree-genetics field trials. Can J For Res 20: 536-546.
34. MAGNUSSEN, S. (1993): Bias in genetic variance estimates due to spatial autocorrelation. Theor Appl Genet 86: 349-355.
35. 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.
36. MEYER, K. (2005): Random regression analyses using Bsplines to model growth of Australian Angus cattle. Genet Sel Evol 37: 473-500.
37. REHFELDT, G. E. (1995): Genetic variation, climate models and the ecological genetics of Larix occidentalis. For Ecol Manage 78: 21-37.
38. RUPPERT, D. (2002): Selecting the number of knots for penalized splines. Journal of Computational and Graphical Statistics 11: 735-757.
39. RUPPERT, D., M. P. WAND and R. J. CARROLL (2003): Semiparametric Regression. Cambridge Univ Press, Cambridge, UK.
40. 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.
41. SCHABENBERGER, O. and C. A. GOTWAY (2005): Statistical Methods for Spatial Data Analysis. Boca Raton: Chapman & Hall.
42. SILVERMAN, B. (1986): Density Estimation for Statistics and Data Analysis. Chapman and Hall, London.
43. 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.
44. 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.
45. 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.
46. THOMSON, A. J. and Y. A. EL-KASSABY (1988): Trend surface analysis of provenance-progeny transfer data. Can J For Res 18: 515-520.
47. 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.
48. WAND, M. P. (2003): Smoothing and mixed models. Cornput Stat 18: 223-249.
49. 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.
50. 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.
51. 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.
52. ZAS, R. (2006): Iterative kriging for removing spatial autocorrelation in analysis of forest genetic trials. Tree Genet Genomics 2: 177-185.