Up hill, down dale: Quantitative genetics of curvaceous traits

Philosophical Transactions of the Royal Society B: Biological Sciences

Volumn 360, Issue 1459, 2005, Pages 1443-1455

  Meyer, Karin ^a   Kirkpatrick, Mark ^b  

^a UNIVERSITY OF NEW ENGLAND   (Australia)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

Covariance function; Function valued traits; Quantitive genetics; Random regression model

Indexed keywords

GENETICS;

EID: 24944487129     PISSN: 09628436     EISSN: None     Source Type: Journal    
DOI: 10.1098/rstb.2005.1681     Document Type: Review

References (98)

1. Albuquerque, L. G. & Meyer, K. 2001 Estimates of covariance functions for growth from birth to 630 days of age in Nelore cattle. J. Anim. Sci. 79, 2776-2789.
2. Beder, J. H. & Gomulkiewicz, R. 1998 Computing the selection gradient and evolutionary response of an infinite-dimensional trait. J. Math. Biol. 36, 299-319.
3. Calus, M. P. L. & Veerkamp, R. F. 2003 Estimation of environmental sensitivity of genetic merit for milk production traits using a random regression model. J. Dairy Sci. 86, 3756-3764.
4. Chase, K., Carrier, D. R., Adler, F. R., Jarvik, T., Ostrander, E. A., Lorentzen, T. D. & Lark, K. G. 2002 Genetic basis for systems of skeletal quantitative traits: principal component analysis of the canid skeleton. Proc. Natl Acad. Sci. USA 99, 9930-9935.
5. de Boor, C. 2001 A practical guide to splines. Springer series in applied mathematics, vol. 27, 2nd edn. New York: Springer.
6. de Jong, G. & Bijma, P. 2002 Selection and phenotypic plasticity in evolutionary biology and animal breeding. Livest. Prod. Sci. 78, 195-214.
7. DeGroot, B. J., Keown, J. F., Kachman, S. D. & Van Vleck, L. D. 2003 Estimates of genetic parameters and lactation curves with a cubic spline model for Holstein cows treated with bovine somatotropin. J. Anim. Sci. 81(Suppl. 1), 37. (Abstr.)
8. Emmerling, R., Mäntysaari, E.A., Lidauer, M. 2002 Reduced rank covariance functions for a multi-lactation test-day model. In Proc. Seventh World Congress on Genetics Applied to Livestock Production. Communication No. 17-03. (CD-ROM)
9. Falconer, D. S. 1952 The problem of environment and selection. Am. Nat. 86, 293-298.
10. Foulley, J. L. & van Dyk, D. A. 2000 The PX-EM algorithm for fast stable fitting of Henderson's mixed model. Genet. Select. Evol. 32, 143-163.
11. Foulley, J. L., Jaffrézic, F. & Robert-Granié, C. 2000 EM-REML estimation of covariance parameters in Gaussian mixed models for longitudinal data analysis. Genet. Select. Evol. 32, 129-141.
12. Gengler, N., Tijani, A., Wiggans, G. R. & Misztal, I. 1999 Estimation of (co)variance function coefficients for test day yield with an expectation-maximization restricted maximum likelihood algorithm. J. Dairy Sci. 82, 1849. (See http://jds.fass.org/cgi/content/abstract/82/8/1849.)
13. Gengler, N., Tijani, A. & Wiggans, G. R. 2000 Use of sequential estimation of regressions and effects on regressions to solve large multi-trait test day models. J. Dairy Sci. 83, 369. (See http://jds.fass.org/cgi/content/ abstract/83/2/369.)
14. Gilmour, A. R., Thompson, R. & Cullis, B. R. 1995 Average information REML, an efficient algorithm for variance parameter estimation in linear mixed models. Biometrics 51, 1440-1450.
15. Gomulkiewicz, R. & Beder, J. H. 1996 The selection gradient of an infinite-dimensional trait. SIAM J. Appl. Math. 56, 509-523.
16. Gomulkiewicz, R. & Kirkpatrick, M. 1992 Quantitative genetics and the evolution of reaction norms. Evolution 46, 390-411.
17. Graser, H. U., Smith, S. P. & Tier, B. 1987 A derivative-free approach for estimating variance components in animal models by restricted maximum likelihood. J. Anim. Sci. 64, 1362-1370.
18. Groeneveld, E. 1994 A reparameterisation to improve numerical optimisation in multivariate REML (co)variance component estimation. Genet. Select. Evol. 26, 537-545.
19. Harville, D. A. 1977 Maximum likelihood approaches to variance component estimation and related problems. J. Am. Stat. Assoc. 72, 320-338.
20. Harville, D. A. 1997 Matrix algebra from a statistician's perspective. Berlin: Springer.
21. Henderson, C. R. 1973 Sire evaluation and genetic trends. In Proc. Animal Breeding Genetics Symposium in Honor of Dr. J. L. Lush, pp. 10-41. Champaign, Illinois: ASAS and ADSA.
22. Henderson, C. R. 1976 A simple method for computing the inverse of a numerator relationship matrix used in prediction of breeding values. Biometrics 32, 69-83.
23. Henderson Jr, C. R. 1982 Analysis of covariance in the mixed model: higher-level, non-homogeneous and random regressions. Biometrics 38, 623-640.
24. Hill, W. G. 1998 Inferences from evolutionary biology to livestock breeding. In Proc. Sixth World Congress on Genetics Applied to Livestock Production 23, 32-39. Australia: Armidale.
25. Hill, W. G. 2002 Direct effects of selection on phenotypic variability of quantitative traits. In Seventh World Congress on Genetics Applied to Livestock Production. Communication no. 19-02. (CD-ROM)
26. Hill, W. G. & Zhang, X.-S. 2004 Effects of phenotypic variability of directional selection arising through genetic differences in residual variability. Genet. Res. 83, 121-132.
27. Hofer, A. 1998 Variance component estimation in animal breeding: a review. J. Anim. Breed. Genet. 115, 247-265.
28. Huisman, A. E., Veerkamp, R. F. & van Arendonk, J. A. M. 2002 Genetic parameters for various random regression models to describe the weight data of pigs. J. Anim. Sci. 80, 575-582.
29. Jaffrézic, F. & Pletcher, S. D. 2000 Statistical models for estimating the genetic basis of repeated measures and other function-valued traits. Genetics 156, 913-922.
30. James, G. M., Hastie, T. J. & Sugar, C. A. 2000 Principal component models for sparse functional data. Biometrika 87, 587-602.
31. Jamrozik, J. 2004 Implementation issues for Markov Chain Monte Carlo methods in random regression test-day models. J. Anim. Breed. Genet. 121, 1-13.
32. Jamrozik, J. & Schaeffer, L. R. 1997 Estimates of genetic parameters for a test day model with random regressions for yield traits of first lactation Holsteins. J. Dairy Sci. 80, 762-770.
33. Jamrozik, J. & Schaeffer, L. R. 2000 Comparison of two computing algorithms for solving mixed model equations for multiple trait random regression test day models. Livest. Prod. Sci. 67, 143-153.
34. Jamrozik, J., Schaeffer, L. R. & Dekkers, J. C. M. 1997 Genetic evaluation of dairy cattle using test day yields and random regression model. J. Dairy Sci. 80, 1217-1226.
35. Jamrozik, J., Schaeffer, L. R. & Jansen, G. B. 2000 Approximate accuracies of prediction from random regression models. Livest. Prod. Sci. 66, 85-92.
36. Jennrich, R. I. & Sampson, P. F. 1976 Newton-Raphson and related algorithms for maximum likelihood variance component estimation. Technometrics 18, 11-17.
37. Jensen, J., Mäntysaari, E. A., Madsen, P. & Thompson, R. 1997 Residual maximum likelihood estimation of (co)variance components in multivariate mixed linear models using average information. J. Ind. Soc. Agric. Stat. 49, 215-225.
38. Jollife, I. T. 1986 Principal component analysis. Springer series in statistics. New York: Springer.
39. Kettunen, A., Mäntysaari, E. A. & Pösö, J. 2000 Estimation of genetic parameters for daily milk yield of primiparous Ayrshire cows by random regression test-day models. Livest. Prod. Sci. 66, 251-261.
40. Kingsolver, J. G. & Gomulkiewicz, R. 2003 Environmental variation and selection on performance curves, Integr. Comp. Biol. 43, 470-477.
41. Kirkpatrick, M. 1993 The evolution of size in size-structured populations. In The dynamics of size-structured populations (ed. B. Ebenman & L. Persson), pp. 13-28. Heidelberg: Springer.
42. Kirkpatrick, M. 2002 Selection on age dependent traits. In Seventh World Congress on Genetics Applied to Livestock Production. Communication no. 19-06. (CD-ROM)
43. Kirkpatrick, M. & Bataillon, T. 1999 Artificial selection on phenotypically plastic traits. Genet. Res. 74, 265-270.
44. Kirkpatrick, M. & Heckman, N. 1989 A quantitative genetic model for growth, shape, reaction norms, and other infinite-dimensional characters. J. Math. Biol. 27, 429-450.
45. Kirkpatrick, M. & Lofsvold, D. 1992 Measuring selection and constraint in the evolution of growth. Evolution 46, 954-971.
46. Kirkpatrick, M. & Meyer, K. 2004 Simplified analysis of complex phenotypes: direct estimation of genetic principal components. Genetics 168, 2295-2306.
47. Kirkpatrick, M., Lofsvold, D. & Bulmer, M. 1990 Analysis of the inheritance, selection and evolution of growth trajectories. Genetics 124, 979-993.
48. Kirkpatrick, M., Hill, W. G. & Thompson, R. 1994 Estimating the covariance structure of traits during growth and aging, illustrated with lactations in dairy cattle. Genet. Res. 64, 57-69.
49. Koivula, M., Negussie, E. & Mäntysaari, E. A. 2004 Genetic parameters for test-day somatic cell count at different lactation stages of Finnish dairy cattle. Livest. Prod. Sci. 90, 145-157.
50. Kolmodin, R. & Bijma, P. 2004 Response to mass selection when genotype by environment interaction is modelled as a linear reaction norm. Genet. Select. Evol. 36, 435-454.
51. Kolmodin, R., Strandberg, E., Madsen, P., Jensen, J. & Jorjani, H. 2002 Genotype by environment interactions in Nordic dairy cattle studied using reaction norms. Acta Agric. Scand. A 52, 11-24.
52. Kolmodin, R., Strandberg, E., Jorjani, H. & Danell, B. 2003 Selection in the presence of a genotype by environment interaction: response in environmental sensitivity. Anim. Sci. 76, 375-385.
53. Lande, R. & Arnold, S. J. 1983 The measurement of selection on correlated characters. Evolution 37, 1210-1226.
54. Legarra, A., Misztal, I. & Bertrand, J. K. 2004 Constructing covariance functions for random regression models for growth in Gelbvieh beef cattle. J. Anim. Sci. 82, 1564-1571.
55. Lidauer, M., Stranden, I., Mäntysaari, E. A., Pösö, J. & Kettunen, A. 1999 Solving large test-day models by iteration on data and preconditioned conjugate gradient. J. Dairy Sci. 82, 2788-2796.
56. Lopez-Romero, P., Rekaya, R. & Carabano, M. J. 2004 Bayesian comparison of test-day models under different assumptions of heterogeneity for the residual variance: the change point technique versus arbitrary intervals. J. Anim. Breed. Genet. 121, 14-25.
57. Mäntysaari, E. A. 1999 Derivation of multiple trait reduced random regression (RR) model for the first lactation test day records of milk, protein and fat. 50th Annual Meeting of the European Association for Animal Production, Mimeo.
58. Meyer, K. 1998a Estimating covariance functions for longitudinal data using a random regression model. Genet. Select. Evol. 30, 221-240.
59. Meyer, K. 1998b Modeling 'repeated' records: covariance functions and random regression models to analyse animal breeding data. In Proc. Sixth World Congress on Genetics Applied to Livestock Production 25, 517-520. Australia: Armidale.
60. Meyer, K. 2001a Estimates of direct and maternal covariance functions for growth of Australian beef calves from birth to weaning. Genet. Select. Evol. 33, 487-514.
61. Meyer, K. 2001b Estimating genetic covariance functions assuming a parametric correlation structure for environmental effects. Genet. Select. Evol. 33, 557-585.
62. Meyer, K. 2005 Random regression analyses using B-splines to model growth of Australian Angus cattle. Genet. Select. Evol. 37. (In the press.)
63. Meyer, K. & Hill, W. G. 1997 Estimation of genetic and phenotypic covariance functions for longitudinal data by restricted maximum likelihood. Livest. Prod. Sci. 47, 185-200.
64. Meyer, K. & Kirkpatrick, M. 2005 Restricted maximum likelihood estimation of genetic principal components and smoothed covariance matrices. Genet. Select. Evol. 37, 1-30.
65. Meyer, K. & Smith, S. P. 1996 Restricted maximum likelihood estimation for animal models using derivatives of the likelihood. Genet. Select. Evol. 28, 23-49.
66. Misztal, I., Strabel, T., Jamrozik, J., Mäntysaari, E. A. & Meuwissen, T. H. E. 2000 Strategies for estimating the parameters needed for different test-day models. J. Dairy Sci. 83, 1125-1134.
67. Nobre, P. C. R., Misztal, I., Tsuruta, S., Bertrand, J. K., Silva, L. O. C. & Lopes, P. S. 2003 Analyses of growth curves of Nellore cattle by multiple-trait and random regression models. J. Anim. Sci. 81, 918-926.
68. Núñez-Antón, V. & Zimmerman, D. L. 2000 Modelling non-stationary longitudinal data. Biometrics 56, 699-705.
69. Pinheiro, J. C. & Bates, D. M. 1996 Unconstrained parameterizations for variance-covariance matrices. Stat. Comput. 6, 289-296.
70. Pletcher, S. D. & Geyer, C. J. 1999 The genetic analysis of age-dependent traits: modeling the character process. Genetics 153, 825-835.
71. Quaas, R. L. 1976 Computing the diagonal elements of a large numerator relationship matrix. Biometrics 32, 949-953.
72. Ramsay, J. O. 2000 Functional components of variation in handwriting. J. Am. Stat. Assoc. 95, 9-15.
73. Ramsay, J. O. & Silverman, B. W. 1997 Functional data analysis. New York: Springer.
74. Ramsay, J. O. & Silverman, B. W. 2001 Functional data analysis. In International encyclopedia of the social & behavioural sciences (ed. J. Smelsen & P. B. Baltes), pp. 5822-5828. New York: Pergamon Press.
75. Ramsay, J. O. & Silverman, B. W. 2002 Applied functional data analysis. Berlin: Springer.
76. Rekaya, R., Carabaño, M. J. & Toro, M. A. 1999 Use of test day yields for the genetic evaluation of production traits in Holstein-Friesian cattle. Livest. Prod. Sci. 57, 203-217.
77. Rice, J. A. & Silverman, B. W. 1991 Estimating the mean and covariance structure nonparametrically when the data are curves. J. R. Stat. Soc. B 53, 233-243.
78. Rice, J. A. & Wu, C. O. 2001 Nonparametric mixed effects models for unequally sampled noisy curves. Biometrics 57, 253-259.
79. Ruppert, D., Wand, M. P. & Carroll, R. J. 2003 Semiparametric regression. New York: Cambridge University Press.
80. Schaeffer, L. R. 2004 Application of random regression models in animal breeding. Livest. Prod. Sci. 86, 35-45.
81. Schaeffer, L. R. & Dekkers, J. C. M. 1994 Random regressions in animal models for test-day production in dairy cattle. In Proc. Fifth World Congress on Genetics Applied to Livestock Production 18, 443-446.
82. Schnyder, U., Hofer, A., Labroue, F. & Künzi, N. 2001 Genetic parameters of a random regresion model for daily feed intake of performance tested French Landrace and large white growing pigs. Genet. Select. Evol. 33, 635-658.
83. Schnyder, U., Hofer, A., Labroue, F. & Künzi, N. 2002 Multiple trait model combining random regressions for daily feed intake with single measured performance traits of growing pigs. Genet. Select. Evol. 34, 61-81.
84. Smith, S. P. 1995 Differentiation of the Cholesky algorithm. J. Comput. Graph. Stat. 4, 134-147.
85. Smith, A. B., Cullis, B. R. & Thompson, R. 2001 Analysing variety by environment data using multiplicative mixed models and adjustments for spatial field trends. Biometrics 57, 1138-1147.
86. Sorensen, D. & Gianola, D. 2002 Likelihood, Bayesian and MCMC methods in quantitative genetics. Berlin: Springer.
87. Spitzner, D. J., Marron, J. S. & Essick, G. K. 2003 Mixed-model functional ANOVA for studying human tactile perception. J. Am. Stat. Assoc. 98, 263-272.
88. Thompson, R. 1976 The estimation of maternal genetic variance. Biometrics 32, 903-917.
89. Thompson, R. & Mäntysaari, E. A. 1999 Prospects for statistical methods in dairy cattle breeding. Interbull Bull. 20, 70-77.
90. Tier, B. & Meyer, K. 2004 Approximating prediction error covariances in multiple-trait and random regression models. J. Anim. Breed. Genet. 121, 77-89.
91. Togashi, K. & Lin, C. Y. 2003 Modifying the lactation curve to improve lactation milk and persistency. J. Dairy Sci. 86, 1487-1493.
92. Torres, R. A. A. & Quaas, R. L. 2001 Determination of covariance functions for lactation traits on dairy cattle using random-coefficient regressions on B-splines. J. Anim. Sci. 79(Suppl. 1), 112. Abstract.
93. van der Werf, J. H. J. 2002 Optimising selection for traits along trajectories. In Seventh World Congress on Genetics Applied to Livestock Production. Communication no. 16-07. (CD-ROM)
94. van der Werf, J. H. J., Goddard, M. & Meyer, K. 1998 The use of covariance functions and random regression for genetic evaluation of milk production based on test day records. J. Dairy Sci. 81, 3300-3308.
95. Veerkamp, R. F. & Goddard, M. E. 1998 Covariance functions across herd production levels for test day records on milk, fat and protein yields. J. Dairy Sci. 81, 1690-1701.
96. Veerkamp, R. F. & Thompson, R. 1999 A covariance function for feed intake, live weight and milk yield estimated using a random regression model. J. Dairy Sci. 82, 1565-1573.
97. Via, S. & Lande, R. 1985 Genotype-environment interaction and the evolution of phenotypic plasticity. Evolution 39, 505-522.
98. White, I. M. S., Thompson, R. & Brotherstone, S. 1999 Genetic and environmental smoothing of lactation curves with cubic splines. J. Dairy Sci. 82, 632-638.