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Annual Review of Ecology, Evolution, and Systematics

Volume 49, 2018

Variation and Evolution of Function-Valued Traits

Abstract

Function-valued traits—phenotypes whose expression depends on a continuous index (such as age, temperature, or space)—occur throughout biology and, like any trait, it is important to understand how they vary and evolve. Although methods for analyzing variation and evolution of function-valued traits are well developed, they have been underutilized by evolutionists, especially those who study natural populations. We seek to summarize advances in the study of function-valued traits and to make their analyses more approachable and accessible to biologists who could benefit greatly from their use. To that end, we explain how curve thinking benefits conceptual understanding and statistical analysis of functional data. We provide a detailed guide to the most flexible and statistically powerful methods and include worked examples (with R code) as supplemental material. We review ways to characterize variation in function-valued traits and analyze consequences for evolution, including constraint. We also discuss how selection on function-valued traits can be estimated and combined with estimates of heritable variation to project evolutionary dynamics.

Keyword(s): basis function expansion, curve thinking, evolutionary response, principal function, selection gradient, simple basis
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2018-11-02
2025-04-29
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Literature Cited

  1. Arnold SJ, Bürger R, Hohenlohe PA, Ajie BC, Jones AG. 2008. Understanding the evolution and stability of the g-matrix. Evolution 62:102451–61
     [Google Scholar]
  2. Arnold SJ, Wade MJ. 1984a. On the measurement of natural and sexual selection: applications. Evolution 38:4720–34
     [Google Scholar]
  3. Arnold SJ, Wade MJ. 1984b. On the measurement of selection in natural and laboratory populations: theory. Evolution 38:709–19
     [Google Scholar]
  4. Aston J, Buck D, Coleman J, Cotter C, Jones N et al. 2012. Functional phylogenies group: phylogenetic inference for function-valued traits. Trends Ecol. Evol. 27:160–66
     [Google Scholar]
  5. Beder JH, Gomulkiewicz R. 1998. Computing the selection gradient and evolutionary response of an infinite-dimensional trait. J. Math. Biol. 36:3299–319
     [Google Scholar]
  6. Beder JH, Gomulkiewicz R. 2007. Optimizing selection for function-valued traits. J. Math. Biol. 55:5861–82
     [Google Scholar]
  7. Blount ZD, Barrick JE, Davidson CJ, Lenski RE. 2012. Genomic analysis of a key innovation in an experimental Escherichia coli population. Nature 489:7417513–18
     [Google Scholar]
  8. Brumback LC, Lindstrom MJ. 2004. Self modeling with flexible, random time transformations. Biometrics 60:461–70
     [Google Scholar]
  9. Cabassi A, Pigoli D, Secchi P, Carter PA. 2017. Permutation tests for the equality of covariance operators of functional data with applications to evolutionary biology. Electron. J. Stat. 11:3815–40
     [Google Scholar]
  10. Calsbeek B, Goodnight CJ. 2009. Empirical comparison of G matrix test statistics: finding biologically relevant change. Evolution 63:102627–35
     [Google Scholar]
  11. Chakraborty A, Panaretos VM. 2017. Functional registration and local variations. arXiv:1702.03556 [stat.ME]
    [Google Scholar]
  12. Day T, Alizon S, Mideo N. 2011. Bridging scales in the evolution of infectious disease life histories: theory. Evolution 65:123448–61
     [Google Scholar]
  13. De Boor C. 2001. A Practical Guide to Splines New York: Springer
     [Google Scholar]
  14. Demidenko E. 2004. Mixed Models: Theory and Applications Hoboken, NJ: Wiley-Interscience
     [Google Scholar]
  15. Dingemanse NJ, Kazem AJ, Réale D, Wright J. 2010. Behavioural reaction norms: animal personality meets individual plasticity. Trends Ecol. Evol. 25:281–89
     [Google Scholar]
  16. Drown DM, Levri EP, Dybdahl MF. 2011. Invasive genotypes are opportunistic specialists not general purpose genotypes. Evol. Appl. 4:1132–43
     [Google Scholar]
  17. Duputié A, Massol F, Chuine I, Kirkpatrick M, Ronce O. 2012. How do genetic correlations affect species range shifts in a changing environment?. Ecol. Lett. 15:3251–59
     [Google Scholar]
  18. Efron B. 1994. Missing data, imputation, and the bootstrap. J. Am. Stat. Assoc. 89:426463–75
     [Google Scholar]
  19. Falconer DS, Mackay TFC. 1996. Introduction to Quantitative Genetics Harlow, UK: Pearson. 4th ed.
     [Google Scholar]
  20. Felsenstein J. 1985. Phylogenies and the comparative method. Am. Nat. 125:11–15
     [Google Scholar]
  21. Fisher RA. 1930. The Genetical Theory of Natural Selection Oxford, UK: Clarendon
     [Google Scholar]
  22. Fu E, Heckman N. 2017. Model-based curve registration via stochastic approximation EM algorithm. arXiv:1712.07265 [stat.ME]
    [Google Scholar]
  23. Gasser T, Kneip A. 1995. Searching for structure in curve samples. J. Am. Stat. Assoc. 90:4321179–88
     [Google Scholar]
  24. Gaydos T, Heckman N, Kirkpatrick M, Stinchcombe J, Schmitt J et al. 2013. Visualizing genetic constraints. Ann. Appl. Stat. 7:860–82
     [Google Scholar]
  25. Gervini D, Carter PA. 2014. Warped functional analysis of variance. Biometrics 70:3526–35
     [Google Scholar]
  26. Gilmour A, Gogel B, Cullis B, Thompson R. 2009. ASReml User Guide Release 3.0 Hemel Hempstead, UK: VSN Int.
     [Google Scholar]
  27. Goldsmith J, Bobb J, Crainiceanu CM, Caffo B, Reich D. 2011. Penalized functional regression. J. Comput. Gr. Stat. 20:4830–51
     [Google Scholar]
  28. Gomulkiewicz R, Beder JH. 1996. The selection gradient of an infinite-dimensional trait. SIAM J. Appl. Math. 56:2509–23
     [Google Scholar]
  29. Gomulkiewicz R, Houle D. 2009. Demographic and genetic constraints on evolution. Am. Nat. 174:6E218–29
     [Google Scholar]
  30. Gomulkiewicz R, Kirkpatrick M. 1992. Quantitative genetics and the evolution of reaction norms. Evolution 46:390–411
     [Google Scholar]
  31. Goolsby EW. 2015. Phylogenetic comparative methods for evaluating the evolutionary history of function-valued traits. Syst. Biol. 64:568–78
     [Google Scholar]
  32. Goolsby EW. 2017. Phylocurve: Phylogenetic comparative methods for high-dimensional traits. R package for studying the evolution of high-dimensional traits https://CRAN.R-project.org/package=phylocurve
    [Google Scholar]
  33. Griswold CK, Gomulkiewicz R, Heckman N. 2008. Hypothesis testing in comparative and experimental studies of function-valued traits. Evolution 62:51229–42
     [Google Scholar]
  34. Griswold CK, Logsdon B, Gomulkiewicz R. 2007. Neutral evolution of multiple quantitative characters: a genealogical approach. Genetics 176:1455–66
     [Google Scholar]
  35. Hadjipantelis J, Jones N, Moriarty J, Springate D, Knight C. 2013. Function-valued traits in evolution. J. R. Soc. Interface 10:20121032
     [Google Scholar]
  36. Hansen TF, Houle D. 2008. Measuring and comparing evolvability and constraint in multivariate characters. J. Evol. Biol. 21:51201–19
     [Google Scholar]
  37. Harvey PH, Pagel MD. 1991. The Comparative Method in Evolutionary Biology Oxford, UK: Oxford Univ. Press
     [Google Scholar]
  38. Houle D. 2001. Characters as the units of evolutionary change. The Character Concept in Evolutionary Biology GP Wagner109–40 San Diego, CA: Academic
     [Google Scholar]
  39. Huang C, Thompson P, Wang Y, Yu Y, Zhang J et al. 2017. FGWAS: Functional genome wide association analysis. NeuroImage 159:107–21
     [Google Scholar]
  40. Huey RB, Kingsolver JG. 1989. Evolution of thermal sensitivity of ectotherm performance. Trends Ecol. Evol. 4:5131–35
     [Google Scholar]
  41. Irwin K, Carter P. 2013. Constraints on the evolution of function-valued traits: a study of growth in Tribolium castaneum. J. Evol. Biol. 26:122633–43
     [Google Scholar]
  42. Irwin K, Carter P. 2014. Artificial selection on larval growth curves in Tribolium: correlated responses and constraints. J. Evol. Biol. 27:102069–79
     [Google Scholar]
  43. Izem R, Kingsolver JG. 2005. Variation in continuous reaction norms: quantifying directions of biological interest. Am. Nat. 166:2277–89
     [Google Scholar]
  44. Izem R, Marron JS. 2007. Analysis of nonlinear modes of variation for functional data. Electron. J. Stat. 1:641–76
     [Google Scholar]
  45. Jones AG, Arnold SJ, Bürger R. 2003. Stability of the G-matrix in a population experiencing pleiotropic mutation, stabilizing selection, and genetic drift. Evolution 57:81747–60
     [Google Scholar]
  46. Jones NS, Moriarty J. 2013. Evolutionary inference for function-valued traits: Gaussian process regression on phylogenies. J. R. Soc. Interface 10:7820120616
     [Google Scholar]
  47. Kingsolver JG, Diamond S, Gomulkiewicz R. 2015a. Curve-thinking: understanding reaction norms and developmental trajectories as traits. Integrative Organismal Biology LB Martin, CK Ghalambor, HA Woods39–53 New York: Wiley
     [Google Scholar]
  48. Kingsolver JG, Diamond SE, Siepielski AM, Carlson SM. 2012. Synthetic analyses of phenotypic selection in natural populations: lessons, limitations and future directions. Evol. Ecol. 26:51101–18
     [Google Scholar]
  49. Kingsolver JG, Gomulkiewicz R. 2003. Environmental variation and selection on performance curves. Integr. Comp. Biol. 43:3470–77
     [Google Scholar]
  50. Kingsolver JG, Heckman N, Zhang J, Carter PA, Knies JL et al. 2015b. Genetic variation, simplicity, and evolutionary constraints for function-valued traits. Am. Nat. 185:6E166–81
     [Google Scholar]
  51. Kingsolver JG, Hoekstra HE, Hoekstra JM, Berrigan D, Vignieri SN et al. 2001. The strength of phenotypic selection in natural populations. Am. Nat. 157:3245–61
     [Google Scholar]
  52. Kingsolver JG, Massie KR, Shlichta JG, Smith MH, Ragland GJ, Gomulkiewicz R. 2007. Relating environmental variation to selection on reaction norms: an experimental test. Am. Nat. 169:2163–74
     [Google Scholar]
  53. Kirkpatrick M. 1988. The evolution of size in size-structured populations. The Dynamics of Size-structured Populations B Ebenman, L Persson14–28 Berlin: Springer-Verlag
     [Google Scholar]
  54. Kirkpatrick M. 2009. Patterns of quantitative genetic variation in multiple dimensions. Genetica 136:2271–84
     [Google Scholar]
  55. Kirkpatrick M, Heckman N. 1989. A quantitative genetic model for growth, shape, reaction norms, and other infinite-dimensional characters. J. Math. Biol. 27:429–50
     [Google Scholar]
  56. Kirkpatrick M, Hill WG, Thompson R. 1994. Estimating the covariance structure of traits during growth and aging, illustrated with lactation in dairy cattle. Genet. Res. 64:57–69
     [Google Scholar]
  57. Kirkpatrick M, Lofsvold D. 1992. Measuring selection and constraint in the evolution of growth. Evolution 46:954–71
     [Google Scholar]
  58. Kirkpatrick M, Lofsvold D, Bulmer M. 1990. Analysis of inheritance, selection and evolution of growth trajectories. Genetics 124:979–93
     [Google Scholar]
  59. Kneip A, Gasser T. 1992. Statistical tools to analyze data representing a sample of curves. Ann. Stat. 20:1266–305
     [Google Scholar]
  60. Knies JL, Izem R, Supler KL, Kingsolver JG, Burch CL. 2006. The genetic basis of thermal reaction norm evolution in lab and natural phage populations. PLOS Biol. 4:7e201
     [Google Scholar]
  61. Kulbaba MW, Clocher IC, Harder LD. 2017. Inflorescence characteristics as function-valued traits: analysis of heritability and selection on architectural effects. J. Syst. Evol. 55:559–65
     [Google Scholar]
  62. Lande R. 1976. Natural selection and random genetic drift in phenotypic evolution. Evolution 30:2314–34
     [Google Scholar]
  63. Lande R. 1979. Quantitative genetic analysis of multivariate evolution, applied to brain: body size allometry. Evolution 33:402–16
     [Google Scholar]
  64. Lande R, Arnold SJ. 1983. The measurement of selection on correlated characters. Evolution 37:61210–26
     [Google Scholar]
  65. Levins R. 1968. Evolution in Changing Environments: Some Theoretical Explorations Princeton, NJ: Princeton Univ. Press
     [Google Scholar]
  66. Lewontin RC. 1974. The Genetic Basis of Evolutionary Change New York: Columbia Univ. Press
     [Google Scholar]
  67. Liefting M, Hoffmann AA, Ellers J. 2014. Measuring the plasticity of developmental rate across insect populations: comment on Rocha and Klaczko (2012). Evolution 68:51544–47
     [Google Scholar]
  68. Lynch M, Walsh B. 1998. Genetics and Analysis of Quantitative Traits Sunderland, MA: Sinauer
     [Google Scholar]
  69. Martin JGA, Nussey DH, Wilson AJ, Réale D. 2011. Measuring individual differences in reaction norms in field and experimental studies: a power analysis of random regression models. Methods Ecol. Evol. 2:4362–74
     [Google Scholar]
  70. Martins EP, Hansen TF. 1997. Phylogenies and the comparative method: a general approach to incorporating phylogenetic information into the analysis of interspecific data. Am. Nat. 149:4646–67
     [Google Scholar]
  71. Meyer K. 1998. Estimating covariance functions for longitudinal data using a random regression model. Genet. Sel. Evol. 30:3221
     [Google Scholar]
  72. Meyer K. 2005. Random regression analyses using B-splines to model growth of Australian Angus cattle. Genet. Sel. Evol. 37:5473–500
     [Google Scholar]
  73. Meyer K. 2007. WOMBAT: A tool for mixed model analyses in quantitative genetics by restricted maximum likelihood (REML). J. Zhejiang Univ. Sci. B 8:815–21
     [Google Scholar]
  74. Meyer K, Hill WG. 1997. Estimation of genetic and phenotypic covariance functions for longitudinal or ‘repeated’ records by restricted maximum likelihood. Livest. Prod. Sci. 47:3185–200
     [Google Scholar]
  75. Meyer K, Kirkpatrick M. 2005. Up hill, down dale: quantitative genetics of curvaceous traits. Philos. Trans. R. Soc. Lond. B. 360:14591443–55
     [Google Scholar]
  76. Mezey JG, Houle D. 2005. The dimensionality of genetic variation for wing shape in Drosophila melanogaster. Evolution 59:51027–38
     [Google Scholar]
  77. Mitchell-Olds T, Shaw RG. 1987. Regression analysis of natural selection: statistical inference and biological interpretation. Evolution 41:61149–61
     [Google Scholar]
  78. Morrissey MB, Liefting M. 2016. Variation in reaction norms: statistical considerations and biological interpretation. Evolution 70:91944–59
     [Google Scholar]
  79. Murren CJ, Auld JR, Callahan H, Ghalambor CK, Handelsman CA et al. 2015. Constraints on the evolution of phenotypic plasticity: limits and costs of phenotype and plasticity. Heredity 115:4293
     [Google Scholar]
  80. Pletcher SD, Geyer CJ. 1999. The genetic analysis of age-dependent traits: modeling the character process. Genetics 153:2825–35
     [Google Scholar]
  81. Price GR. 1970. Selection and covariance. Nature 227:520–21
     [Google Scholar]
  82. Ragland G, Carter P. 2004. Genetic covariance structure of growth in the salamander Ambystoma macrodactylum. Heredity 92:6569–78
     [Google Scholar]
  83. Raket LL, Sommer S, Markussen B. 2014. A nonlinear mixed-effects model for simultaneous smoothing and registration of functional data. Pattern Recognit. Lett. 38:1–7
     [Google Scholar]
  84. Ramsay JO, Li X. 1998. Curve registration. J. R. Stat. Soc. B 60:2351–63
     [Google Scholar]
  85. Ramsay JO, Silverman B. 1997. Functional Data Analysis New York: Springer-Verlag. 1st ed.
     [Google Scholar]
  86. Ramsay JO, Silverman B. 2005. Functional Data Analysis New York: Springer-Verlag. 2nd ed.
     [Google Scholar]
  87. Randolph TW, Harezlak J, Feng Z. 2012. Structured penalties for functional linear models—partially empirical eigenvectors for regression. Electron. J. Stat. 6:323
     [Google Scholar]
  88. Rausher MD, Delph LF. 2015. Commentary: When does understanding phenotypic evolution require identification of the underlying genes?. Evolution 69:71655–64
     [Google Scholar]
  89. Robertson A. 1966. A mathematical model of the culling process in dairy cattle. Anim. Sci. 8:195–108
     [Google Scholar]
  90. Rocha FB, Klaczko LB. 2012. Connecting the dots of nonlinear reaction norms unravels the threads of genotype–environment interaction in Drosophila. Evolution 66:113404–16
     [Google Scholar]
  91. Rocha FB, Klaczko LB. 2014. Undesirable consequences of neglecting nonlinearity: response to comments by Liefting et al. (2013) on Rocha & Klaczko (2012). Evolution 68:51548–51
     [Google Scholar]
  92. Rockman MV. 2012. The QTN program and the alleles that matter for evolution: all that's gold does not glitter. Evolution 66:11–17
     [Google Scholar]
  93. RStudio 2016. rmarkdown: dynamic documents for R. Software for creating documents with R https://github.com/rstudio/rmarkdown
    [Google Scholar]
  94. Sakoe H, Chiba S. 1978. Dynamic programming algorithm optimization for spoken word recognition. IEEE Trans. Acoust. Speech Signal Proc. 26:143–49
     [Google Scholar]
  95. Schluter D. 1988. Estimating the form of natural selection on a quantitative trait. Evolution 42:849–61
     [Google Scholar]
  96. Schluter D. 1996. Adaptive radiation along genetic lines of least resistance. Evolution 50:51766–74
     [Google Scholar]
  97. Schluter D, Nychka D. 1994. Exploring fitness surfaces. Am. Nat. 143:4597–616
     [Google Scholar]
  98. Segev O, Mangel M, Wolf N, Sadeh A, Kershenbaum A, Blaustein L. 2011. Spatiotemporal reproductive strategies in the fire salamander: a model and empirical test. Behav. Ecol. 22:3670–78
     [Google Scholar]
  99. Srivastava A, Wu W, Kurtek S, Klassen E, Marron J. 2011. Registration of functional data using Fisher-Rao metric. arXiv:1103.3817 [math.ST]
    [Google Scholar]
  100. Telesca D, Inoue LYT. 2008. Bayesian hierarchical curve registration. J. Am. Stat. Assoc. 103:481328–39
     [Google Scholar]
  101. Travisano M, Shaw RG. 2013. Lost in the map. Evolution 67:2305–14
     [Google Scholar]
  102. Via S, Lande R. 1985. Genotype-environment interaction and the evolution of phenotypic plasticity. Evolution 39:3505–22
     [Google Scholar]
  103. Wright S. 1931. Evolution in Mendelian populations. Genetics 16:97–159
     [Google Scholar]
  104. Wright S. 1932. The roles of mutation, inbreeding, crossbreeding and selection in evolution. Proceedings of the Sixth Annual Congress of Genetics 1 DF Jones356–66 Austin, Tex.: Genet. Soc. Am.
     [Google Scholar]
  105. Wu R, Lin M. 2006. Functional mapping—how to map and study the genetic architecture of dynamic complex traits. Nat. Rev. Genet. 7:3229–37
     [Google Scholar]
  106. Yamahira K, Kawajiri M, Takeshi K, Irie T. 2007. Inter- and intrapopulation variation in thermal reaction norms for growth rate: evolution of latitudinal compensation in ectotherms with a genetic constraint. Evolution 61:71577–89
     [Google Scholar]
  107. Yao F, Müller H-G, Wang J-L. 2005. Functional data analysis for sparse longitudinal data. J. Am. Stat. Assoc. 100:470577–90
     [Google Scholar]
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Variation and Evolution of Function-Valued Traits
Annual Review of Ecology, Evolution, and Systematics 49, 139 (2018); https://doi.org/10.1146/annurev-ecolsys-110316-022830
/content/journals/10.1146/annurev-ecolsys-110316-022830
/content/journals/10.1146/annurev-ecolsys-110316-022830
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