Comparing parent-offspring regression with frequentist and Bayesian animal models to estimate heritability in wild populations: A simulation study for Gaussian and binary traits

Methods in Ecology and Evolution

Volumn 4, Issue 3, 2013, Pages 260-275

  De Villemereuil, Pierre ^a,b   Gimenez, Olivier ^b   Doligez, Blandine ^a,b  

^a UNIVERSITÉ DE LYON   (France)

^b CNRS   (France)

Author keywords

Bayesian methods < Statistics; Quantitative genetics < Population Genetics; Statistics

Indexed keywords

EID: 84875248934     PISSN: None     EISSN: 2041210X     Source Type: Journal    
DOI: 10.1111/2041-210X.12011     Document Type: Article

References (91)

1. Authier, M., Cam, E. & Guinet, C. (2011) Selection for increased body length in subantarctic fur seals on amsterdam island. Journal of Evolutionary Biology, 24(3), 607-616.
2. Backström, N., Karaiskou, N., Leder, E.H., Gustafsson, L., Primmer, C.R., Qvarnström, A. & Ellegren, H. (2008) A gene-based genetic linkage map of the collared flycatcher (Ficedula albicollis) reveals extensive synteny and gene-order conservation during 100 million years of avian evolution. Genetics, 179(3), 1479-1495.
3. Bers, N.E.M.V., Oers, K.V., Kerstens, H.H.D., Dibbits, B.W., Crooijmans, R.P.M.A., Visser, M.E. & Groenen, M.a.M. (2010) Genome-wide SNP detection in the great tit parus major using high throughput sequencing. Molecular Ecology, 19, 89-99.
4. Bolker, B. (2008) Ecological Models and Data in R. Princeton University Press, Princeton, New Jersey, USA.
5. Bolker, B.M., Brooks, M.E., Clark, C.J., Geange, S.W., Poulsen, J.R., Stevens, M.H.H. & White, J.S.S. (2009) Generalized linear mixed models: a practical guide for ecology and evolution. Trends in Ecology & Evolution, 24(3), 127-135.
6. Breslow, N.E. & Clayton, D.G. (1993) Approximate inference in generalized linear mixed models. Journal of the American Statistical Association, 88(421), 9-25.
7. Breslow, N.E. & Lin, X. (1995) Bias correction in generalised linear mixed models with a single component of dispersion. Biometrika, 82(1), 81-91.
8. Callens, M. & Croux, C. (2005) Performance of likelihood-based estimation methods for multilevel binary regression models. Journal of Statistical Computation and Simulation, 75(12), 1003-1017.
9. Cam, E. (2009) Contribution of capture-mark-recapture modeling to studies of evolution by natural selection. Modeling Demographic Processes In Marked Populations, (eds D.L. Thomson, E.G. Cooch & M.J. Conroy), pp. 83-129. Springer, Boston, Massachusetts, USA.
10. Charmantier, A. & Réale, D. (2005) How do misassigned paternities affect the estimation of heritability in the wild? Molecular Ecology, 14(9), 2839-2850.
11. Charmantier, A., Keyser, A.J. & Promislow, D.E. (2007) First evidence for heritable variation in cooperative breeding behaviour. Proceedings of the Royal Society B: Biological Sciences, 274(1619), 1757-1761.
12. Charmantier, A., Buoro, M., Gimenez, O. & Weimerskirch, H. (2011) Heritability of short-scale natal dispersal in a large-scale foraging bird, the wandering albatross. Journal of Evolutionary Biology, 24, 1487-1496.
13. Damgaard, L.H. (2007) Technical note: how to use winbugs to draw inferences in animal models. Journal of Animal Science, 85(6), 1363-1368.
14. Day, T. & Bonduriansky, R. (2011) A unified approach to the evolutionary consequences of genetic and nongenetic inheritance. The American Naturalist, 178(2), E18-E36.
15. Dempster, E.R. & Lerner, I.M. (1950) Heritability of threshold characters. Genetics, 35(2), 212-236.
16. Doligez, B., Daniel, G., Warin, P., Pärt, T., Gustafsson, L. & Réale, D. (2012) Estimation and comparison of heritability and parent-offspring resemblance in dispersal probability from capture-recapture data using different methods: the collared flycatcher as a case study. Journal of Ornithology, 152, Issue 2 supplement, 539-554.
17. Doligez, B., Gustafsson, L. & Pärt, T. (2009) 'Heritability' of dispersal propensity in a patchy population. Proceedings of the Royal Society B: Biological Sciences 276(1668), 2829-2836.
18. Ellegren, H. & Sheldon, B.C. (2008) Genetic basis of fitness differences in natural populations. Nature, 452(7184), 169-175.
19. Elston, R.C., Hill, W.G. & Smith, C. (1977) Query: Estimating Heritability of a dichotomous trait. Biometrics, 33(1), 231-236.
20. Engel, B. & Buist, W. (1998) Bias reduction of approximate maximum likelihood estimates for heritability in threshold models. Biometrics, 54(3), 1155-1164.
21. Falconer, D.S. & Mackay, T.F. (1996) Introduction to Quantitative Genetics. 4th edn, Benjamin Cummings, Harlow, Essex, UK.
22. Fischer, T.M., Gilmour, A.R. & Werf, J. (2004) Computing approximate standard errors for genetic parameters derived from random regression models fitted by average information REML. Genetics Selection Evolution, 36(3), 363-369.
23. Gelman, A. (2006) Prior distributions for variance parameters in hierarchical models. Bayesian Analysis, 1(3), 515-533.
24. Gelman, A., Carlin, J.B., Stern, H.S. & Rubin, D.B. (2004) Bayesian Data Analysis. Text in Statisctical Science. 2nd edn, Chapman & Hall/CRC Press, Boca Raton, Florida, USA.
25. Gianola, D. (1982) Theory and analysis of threshold characters. Journal of Animal Science, 54(5), 1079-1096.
26. Gilmour, A.R., Gogel, B.J., Cullis, B.R. & Thompson, R. (2006) ASReml user guide release 2.0. URL: http://www.vsni.co.uk/software/asreml/.
27. Gorjanc, G., Henderson, D.A., Kinghorn, B. & Percy, A. (2007) GeneticsPed: pedigree and genetic relationship functions. R package version 1.13.0. URL: http://www.bioconductor.org/packages/2.0/bioc/html/GeneticsPed.html.
28. Hadfield, J.D. (2010a) MCMC methods for multi-response generalised linear mixed models: the MCMCglmm R package. Journal of Statistical Software, 33(2), 1-22.
29. Hadfield, J.D. (2010b) MCMCglmm course notes. URL: http://cran.r-project.org/web/packages/MCMCglmm/index.html.
30. Hadfield, J.D., Burgess, M.D., Lord, A., Phillimore, A.B., Clegg, S.M. & Owens, I.P.F. (2006) Direct versus indirect sexual selection: Genetic basis of colour, size and recruitment in a wild bird. Proceedings of the Royal Society B: Biological Sciences, 273(1592), 1347-1353.
31. Hansson, B., Bensch, S. & Hasselquist, D. (2003) Heritability of dispersal in the great reed warbler. Ecology Letters, 6(4), 290-294.
32. Henderson, C.R. (1950) Estimation of genetic parameters. Annals of Mathematical Statistics, 21, 309-310.
33. Henderson, C.R. (1976) A simple method for computing the inverse of a numerator relationship matrix used in prediction of breeding values. Biometrics, 32(1), 69-83.
34. Hill, W.G. & Kirkpatrick, M. (2010) What animal breeding has taught us about evolution. Annual Review of Ecology, Evolution, and Systematics, 41, 1-19.
35. Holand, A.M., Steinsland, I., Martino, S. & Jensen, H. (2011) Animal models and integrated nested laplace approximations. Statistics. Preprints (4/2011).
36. Kirkpatrick, M. & Lande, R. (1989) The evolution of maternal characters. Evolution, 43(3), 485-503.
37. Knott, S.A., Sibly, R.M., Smith, R.H. & Moller, H. (1995) Maximum likelihood estimation of genetic parameters in life-history studies using the 'Animal model'. Functional Ecology, 9(1), 122-126.
38. Kruuk, L.E., Merilä, J. & Sheldon, B.C. (2001) Phenotypic selection on a heritable size trait revisited. The American Naturalist, 158(6), 557-571.
39. Kruuk, L.E.B. (2004) Estimating genetic parameters in natural populations using the 'animal model'. Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences, 359(1446), 873-890.
40. Kruuk, L.E.B. & Hadfield, J.D. (2007) How to separate genetic and environmental causes of similarity between relatives. Journal of Evolutionary Biology, 20(5), 1890-1903.
41. Kruuk, L.E., Slate, J. & Wilson, A.J. (2008) New answers for old questions: The evolutionary quantitative genetics of wild animal populations. Annual Review of Ecology, Evolution, and Systematics, 39(1), 525-548.
42. Kruuk, L.E.B., Slate, J., Pemberton, J.M., Brotherstone, S., Guinness, F. & Clutton-Brock, T. (2002) Antler size in red deer: Heritability and selection but no evolution. Evolution, 56(8), 1683-1695.
43. Lane, J.E., Kruuk, L.E.B., Charmantier, A., Murie, J.O., Coltman, D.W., Buoro, M., Raveh, S. & Dobson, F.S. (2011) A quantitative genetic analysis of hibernation emergence date in a wild population of columbian ground squirrels. Journal of Evolutionary Biology, 24(9), 1949-1959.
44. Lynch, M. & Walsh, B. (1998) Genetics and analysis of quantitative traits. Sinauer Associates, Sunderland, Massachussets, USA.
45. MacColl, A.D.C. & Hatchwell, B.J. (2003) Heritability of parental effort in a passerine bird. Evolution, 57(9), 2191-2195.
46. McCleery, R.H., Pettifor, R.A., Armbruster, P., Meyer, K., Sheldon, B.C. & Perrins, C.M. (2004) Components of variance underlying fitness in a natural population of the great tit parus major. The American Naturalist, 164(3), E62-E72.
47. Merilä, J., Kruuk, L.E.B. & Sheldon, B.C. (2001) Natural selection on the genetical component of variance in body condition in a wild bird population. Journal of Evolutionary Biology, 14(6), 918-929.
48. Meyer, K. (2007) WOMBAT-A tool for mixed model analyses in quantitative genetics by restricted maximum likelihood (REML). Journal of Zhejiang University. Science. B, 8(11), 815-821.
49. Milner, J.M., Pemberton, J.M., Brotherstone, S. & Albon, S.D., (2000) Estimating variance components and heritabilities in the wild: a case study using the 'animal model' approach. Journal of Evolutionary Biology, 13(5), 804-813.
50. Morales, J., Kim, S., Lobato, E., Merino, S., Tomás, G., Martínez de la Puente, J. & Moreno, J. (2010) On the heritability of blue-green eggshell colouration. Journal of Evolutionary Biology, 23(8), 1783-1791.
51. Morrissey, M.B. & Wilson, A.J. (2009) Pedantics: an R package for pedigree-based genetic simulation and pedigree manipulation, characterization and viewing. Molecular Ecology Resources, 10(4), 711-719.
52. Morrissey, M.B., Wilson, A.J., Pemberton, J.M. & Ferguson, M.M. (2007) A framework for power and sensitivity analyses for quantitative genetic studies of natural populations, and case studies in soay sheep (Ovis aries). Journal of Evolutionary Biology, 20(6), 2309-2321.
53. Mousseau, T.A. & Roff, D.A. (1987) Natural selection and the heritability of fitness components. Heredity, 59(2), 181-197.
54. Nakagawa, S. & Schielzeth, H. (2010) Repeatability for gaussian and non gaussian data: a practical guide for biologists. Biological Reviews, 85(4), 935-956.
55. Nilsson, J.A., Åkesson, M. Nilsson, J.F. (2009) Heritability of resting metabolic rate in a wild population of blue tits. Journal of Evolutionary Biology, 22(9), 1867-1874.
56. O'Hara, R.B., Cano, J.M., Ovaskainen, O., Teplitsky, C. & Alho, J.S. (2008) Bayesian approaches in evolutionary quantitative genetics. Journal of Evolutionary Biology, 21(4), 949-957.
57. Papaïx, J., Cubaynes, S., Buoro, M., Charmantier, A., Perret, P. & Gimenez, O. (2010) Combining capture-recapture data and pedigree information to assess heritability of demographic parameters in the wild. Journal of Evolutionary Biology, 23(10), 2176-2184.
58. Patterson, H.D. & Thompson, R. (1971) Recovery of inter-block information when block sizes are unequal. Biometrika, 58(3), 545-554.
59. Plummer, M., Best, N., Cowles, K. & Vines, K. (2006) CODA: convergence diagnosis and output analysis for MCMC. R News, 6 (1), 7-11.
60. Postma, E. & Charmantier, A. (2007) What 'animal models' can and cannot tell ornithologists about the genetics of wild populations. Journal of Ornithology, 148(S2), 633-642.
61. Quinn, J.L., Charmantier, A., Garant, D. & Sheldon, B.C. (2006) Data depth, data completeness, and their influence on quantitative genetic estimation in two contrasting bird populations. Journal of Evolutionary Biology, 19(3), 994-1002.
62. R Development Core Team (2011) R: a language and environment for statistical computing. URL: http://www.R-project.org/.
63. Reid, J.M., Arcese, P., Sardell, R.J. & Keller, L.F. (2011a) Additive genetic variance, heritability and inbreeding depression in male extra-pair reproductive success. The American Naturalist, 177, 177-187.
64. Reid, J.M., Arcese, P., Sardell, R.J. & Keller, L.F. (2011b) Heritability of female extra-pair paternity rate in song sparrows (Melospiza melodia). Proceedings of the Royal Society B: Biological Sciences, 278(1708), 1114-1120.
65. Ridley, M. (2003) Evolution. 3rd edn. Wiley-Blackwell, Hoboken, New-Jersey, USA.
66. Rodriguez, G. & Goldman, N. (2001) Improved estimation procedures for multilevel models with binary response: a case-study. Journal of the Royal Statistical Society. Series A (Statistics in Society), 164(2), 339-355.
67. Roff, D.A. (1997) Evolutionary quantitative genetics. Chapman & Hall, New York, USA.
68. Roff, D.A. (2007) A centennial celebration for quantitative genetics. Evolution, 61(5), 1017-1032.
69. Rossiter, M. (1996) Incidence and consequences of inherited environmental effects. Annual Review of Ecology and Systematics, 27, 451-476.
70. Räsänen, K. & Kruuk, L.E.B. (2007) Maternal effects and evolution at ecological time-scales. Functional Ecology, 21(3), 408-421.
71. Réale, D., Festa-Bianchet, M. & Jorgenson, J.T. (1999) Heritability of body mass varies with age and season in wild bighorn sheep. Heredity, 83(5), 526-532.
72. Sheldon, B.C., Kruuk, L.E.B. & Merilä, J. (2003) Natural selection and inheritance of breeding time and clutch size in the collared flycatcher. Evolution, 57(2), 406-420.
73. Sillanpää, M.J. (2011) On statistical methods for estimating heritability in wild populations. Molecular Ecology, 20(7), 1324-1332.
74. Slate, J., Santure, A.W., Feulner, P.G., Brown, E.A., Ball, A.D., Johnston, S.E. & Gratten, J. (2010) Genome mapping in intensively studied wild vertebrate populations. Trends in Genetics, 26(6), 275-284.
75. Sorensen, D. & Gianola, D. (2002) Likelihood, Bayesian and MCMC Methods in Quantitative Genetics. Statistics for Biology and Health, Springer, New York, USA.
76. Sorensen, D.A. & Kennedy, B.W. (1984) Estimation of genetic variances from unselected and selected populations. Journal of Animal Science, 59(5), 1213-1223.
77. Thompson, R. (1976) The estimation of maternal genetic variances. Biometrics, 32(4), 903-917.
78. Thériault, V., Garant, D., Bernatchez, L. & Dodson, J.J. (2007) Heritability of life-history tactics and genetic correlation with body size in a natural population of brook charr (Salvelinus fontinalis). Journal of Evolutionary Biology, 20(6), 2266-2277.
79. Vazquez, A.I., Bates, D.M., Rosa, G.J.M., Gianola, D. & Weigel, K.A. (2010) Technical note: an r package for fitting generalized linear mixed models in animal breeding1. Journal of Animal Science, 88(2), 497-504.
80. Visscher, P.M., Hill, W.G. & Wray, N.R. (2008) Heritability in the genomics era-concepts and misconceptions. Nature Reviews Genetics, 9(4), 255-266.
81. van Vleck, L. (1972) Estimation of heritability of threshold characters. Journal of Dairy Science, 55(2), 218-225.
82. Waldmann, P. (2009) Easy and flexible Bayesian inference of quantitative genetic parameters. Evolution, 63(6), 1640-1643.
83. van der Werf, J.H. & de Boer, I.J. (1990) Estimation of additive genetic variance when base populations are selected. Journal of Animal Science, 68(10), 3124-3132.
84. Willham, R.L. (1963) The covariance between relatives for characters composed of components contributed by related individuals. Biometrics, 19(1), 18.
85. Willham, R.L. (1972) The role of maternal effects in animal breeding: III. Biometrical aspects of maternal effects in animals. Journal of Animal Science, 35(6), 1288-1293.
86. Wilson, A.J., Coltman, D.W., Pemberton, J.M., Overall, A.D.J., Byrne, K.A. & Kruuk, L.E.B. (2004) Maternal genetic effects set the potential for evolution in a free-living vertebrate population. Journal of Evolutionary Biology, 18(2), 405-414.
87. Wilson, A.J., Morrissey, M.B., Adams, M.J., Walling, C.A., Guinness, F.E., Pemberton, J.M., Clutton-Brock, T.H. & Kruuk, L.E.B. (2011) Indirect genetics effects and evolutionary constraint: an analysis of social dominance in red deer, cervus elaphus. Journal of Evolutionary Biology, 24(4), 772-783.
88. Wilson, A.J., Réale, D., Clements, M.N., Morrissey, M.M., Postma, E., Walling, C.A., Kruuk, L.E.B. & Nussey, D.H. (2010) An ecologist's guide to the animal model. Journal of Animal Ecology, 79(1), 13-26.
89. Wright, S. (1934) An analysis of variability in number of digits in an inbred strain of guinea pigs. Genetics, 19(6), 506-536.
90. Zuur, A.F., Ieno, E.N., Walker, N.J., Saveliev, A.A. & Smith, G.M. (2009) Mixed effects models and extensions in ecology with R. Statistics for Biology and Health, Springer, New York, USA.
91. Åkesson, M., Bensch, S., Hasselquist, D., Tarka, M. & Hansson, B. (2008) Estimating heritabilities and genetic correlations: comparing the 'Animal model' with parent-offspring regression using data from a natural population. PLoS ONE, 3(3), e1739.