Your PDF has successfully downloaded.

You may be interested in finding more content on these topics:


You are not currently logged in.

Access JSTOR through your library or other institution:


Log in through your institution.

Journal Article

Genetic Variation, Simplicity, and Evolutionary Constraints for Function-Valued Traits

Joel G. Kingsolver, Nancy Heckman, Jonathan Zhang, Patrick A. Carter, Jennifer L. Knies, John R. Stinchcombe and Karin Meyer
The American Naturalist
Vol. 185, No. 6 (June 2015), pp. E166-E181
DOI: 10.1086/681083
Stable URL:
Page Count: 16
Were these topics helpful?
See somethings inaccurate? Let us know!

Select the topics that are inaccurate.

  • Download PDF
  • Add to My Lists
  • Cite this Item
We're having trouble loading this content. Download PDF instead.


AbstractUnderstanding the patterns of genetic variation and constraint for continuous reaction norms, growth trajectories, and other function-valued traits is challenging. We describe and illustrate a recent analytical method, simple basis analysis (SBA), that uses the genetic variance-covariance (G) matrix to identify “simple” directions of genetic variation and genetic constraints that have straightforward biological interpretations. We discuss the parallels between the eigenvectors (principal components) identified by principal components analysis (PCA) and the simple basis (SB) vectors identified by SBA. We apply these methods to estimated G matrices obtained from 10 studies of thermal performance curves and growth curves. Our results suggest that variation in overall size across all ages represented most of the genetic variance in growth curves. In contrast, variation in overall performance across all temperatures represented less than one-third of the genetic variance in thermal performance curves in all cases, and genetic trade-offs between performance at higher versus lower temperatures were often important. The analyses also identify potential genetic constraints on patterns of early and later growth in growth curves. We suggest that SBA can be a useful complement or alternative to PCA for identifying biologically interpretable directions of genetic variation and constraint in function-valued traits.

Notes and References

This item contains 44 references.

Literature Cited
  • ['Aguirre, J. D., E. Hine, K. McGuigan, and M. W. Blows. 2014. Comparing G: multivariate analysis of genetic variation in multiple populations. Heredity 112:21–29.']
  • ['Angilletta, M. J. 2009. Thermal adaptation: a theoretical and empirical synthesis. Oxford University Press, Oxford.']
  • ['Berner, D. 2012. How much can the orientation of G’s eigenvectors tell us about genetic constraints? Ecology and Evolution 2:1834–1842.']
  • ['Biro, P. A., M. V. Abrahams, J. R. Post, and E. A. Parkinson. 2004. Predators select against high growth rates and risk-taking behaviour in domestic trout populations. Proceedings of the Royal Society B: Biological Sciences 1554:2233–2237.']
  • ['Blows, M. W. 2007. A tale of two matrices: multivariate approaches in evolutionary biology. Journal of Evolutionary Biology 20:1–8.']
  • ['Bronikowski, A. M., A. F. Bennett, and R. E. Lenski. 2001. Evolutionary adaptation to temperature. VII. Effects of temperature on growth rate in natural isolates of Escherichia coli and Salmonella enterica from different thermal environments. Evolution 55:33–40.']
  • ['Cubranic, D., J. Zhang, N. E. Heckman, T. L. Gaydos, and J. S. Marron. 2013. prinsimp: finding and plotting simple basis vectors for multivariate data. Comprehensive R Archive Network. Accessed November 2014.']
  • ['Gaydos, T. L., N. E. Heckman, M. Kirkpatrick, J. R. Stinchcombe, J. Schmitt, J. G. Kingsolver, and J. S. Marron. 2013. Visualizing genetic constraints. Annals of Applied Statistics 7:860–882.']
  • ['Gilchrist, G. W. 1996. A quantitative genetic analysis of thermal sensitivity in the locomotor performance curve of Aphidius ervi. Evolution 50:1560–1572.']
  • ['Gomulkiewicz, R., and D. Houle. 2009. Demographic and genetic constraints on evolution. American Naturalist 174:E218–E229.']
  • ['Green, P. J., and B. W. Silverman. 1994. Nonparametric regression and generalized linear models: a roughness penalty approach. Chapman & Hall, London.']
  • ['Gwaze, D. P., F. E. Bridgwater, and C. G. Williams. 2002. Genetic analysis of growth curves for a wood perennial species, Pinus taeda L. Theoretical and Applied Genetics 105:526–531.']
  • ['Hadfield, J. 2010. MCMC methods for multi-response generalized linear mixed models: the MCMCglmm R package. Journal of Statistical Software 33:1–22.']
  • ['Hansen, T. F., and D. Houle. 2008. Measuring and comparing evolvability and constraint in multivariate characters. Journal of Evolutionary Biology 21:1201–1219.']
  • ['Hine, E., K. McGuigan, and M. W. Blows. 2014. Evolutionary constraints in high-dimensional trait sets. American Naturalist 184:119–131.']
  • ['Huey, R. B., and J. G. Kingsolver. 1989. Evolution of thermal sensitivity of ectotherm performance. Trends in Ecology and Evolution 4:131–135.']
  • ['Irwin, K. K., and P. A. Carter. 2013. Constraints on the evolution of function-valued traits: a study of growth in Tribolium casteneum. Journal of Evolutionary Biology 26:2633–2643.']
  • ['Izem, R., and J. G. Kingsolver. 2005. Variation in continuous reaction norms: quantifying directions of biological interest. American Naturalist 166:277–289.']
  • ['Kingsolver, J. G., S. E. Diamond, and R. Gomulkiewicz. 2015a. Curve thinking: understanding reaction norms and developmental trajectories as traits. Pages 39–54 in L. B. Martin, C. K. Ghalambor, and H. A. Woods, eds. Integrative organismal biology. Wiley Scientific, New York.']
  • ['Kingsolver, J. G., R. Gomulkiewicz, and P. A. Carter. 2001. Variation, selection and evolution of function-valued traits. Genetica 112:87–104.']
  • ['Kingsolver, J. G., N. Heckman, J. Zhang, P. A. Carter, J. L. Knies, J. R. Stinchcombe, and K. Meyer. 2015b. Data from: Genetic variation, simplicity, and evolutionary constraints for function-valued traits. American Naturalist, Dryad Digital Repository,']
  • ['Kingsolver, J. G., and D. W. Pfennig. 2004. Individual-level selection as a cause of Cope’s rule of phyletic size increase. Evolution 58:1608–1612.']
  • ['Kingsolver, J. G., G. J. Ragland, and J. G. Shlichta. 2004. Quantitative genetics of continuous reaction norms: thermal sensitivity of caterpillar growth rates. Evolution 58:1521–1529.']
  • ['Kirkpatrick, M., and N. Heckman. 1989. A quantitative genetic model for growth, shape, reaction norms, and other infinite-dimensional characters. Journal of Mathematical Biology 27:429–450.']
  • ['Kirkpatrick, M., and D. Lofsvold. 1992. Measuring selection and constraint in the evolution of growth. Evolution 46:954–971.']
  • ['Kirkpatrick, M., D. Lofsvold, and M. Bulmer. 1990. Analysis of the inheritance, selection and evolution of growth trajectories. Genetics 124:979–993.']
  • ['Knies, J. L., R. Izem, K. L. Supler, J. G. Kingsolver, and C. L. Burch. 2006. The genetic basis of thermal reaction norm evolution in lab and natural phage populations. PLoS Biology 4:1–8.']
  • ['Knies, J. L., J. G. Kingsolver, and C. L. Burch. 2009. Hotter is better and broader: thermal sensitivity of fitness in a population of bacteriophages. American Naturalist 173:419–430.']
  • ['Lande, R. 1979. Quantitative genetic analysis of multivariate evolution, applied to brain:body size allometry. Evolution 33:402–416.']
  • ['Lande, R., and S. J. Arnold. 1983. The measurement of selection on correlated characters. Evolution 37:1210–1226.']
  • ['Mangel, M., and J. Stamps. 2001. Trade-offs between growth and mortality and the maintenance of individual variation in growth. Evolutionary Ecology Research 3:583–593.']
  • ['Meyer, K., and D. Houle. 2013. Sampling based approximation of confidence intervals for functions of genetic covariance matrices. Proceedings of the Association for the Advancement of Animal Breeding and Genetics 20:523–526.']
  • ['Mezey, J. G., and D. Houle. 2005. The dimensionality of genetic variation for wing shape in Drosophila melanogaster. Evolution 59:1027–1038.']
  • ['Morgan, T. J., T. J. Garland, and P. A. Carter. 2003. Ontogenetic trajectories in mice selected for high wheel-running activity. I. Mean ontogenetic trajectories. Evolution 57:646–657.']
  • ['Morrissey, M. B., C. A. Walling, A. J. Wilson, J. M. Pembreton, T. H. Clutton-Brock, and L. E. B. Kruuk. 2012. Genetic analysis of life-history constraint and evolution in a wild ungulate population. American Naturalist 179:E97–E114.']
  • ['Ragland, G. J., and P. A. Carter. 2004. Genetic constraints on the evolution of growth and life history traits in the salamander Ambystoma macrodactylum. Heredity 92:569–578.']
  • ['Reinbold, D., G. H. Thorgaard, and P. A. Carter. 2009. Reduced swimming performance and increased growth in domesticated rainbow trout. Canadian Journal of Fisheries and Aquatic Sciences 66:1025–1032.']
  • ['Roff, D. A. 2002. Life history evolution. Sinauer, Sunderland, MA.']
  • ['Schluter, D. 2000. The ecology of adaptive radiation. Oxford University Press, Oxford.']
  • ['Stinchcombe, J. R., F.-V. T. W. Group, and M. Kirkpatrick. 2012. Genetics and evolution of function-valued traits: understanding environmentally responsive phenotypes. Trends in Ecology and Evolution 27:637–647.']
  • ['Stinchcombe, J. R., R. Izem, M. S. Herschel, B. V. McGoey, and J. Schmitt. 2010. Across-environment genetic correlations and the frequency of selective environments shape the evolutionary dynamics of growth rate in Impatiens capensis. Evolution 64:2887–2903.']
  • ['Stinchcombe, J. R., A. K. Simonsen, and M. W. Blows. 2014. Estimating uncertainty in multivariate responses to selection. Evolution 68:1188–1196.']
  • ['Via, S., and R. Lande. 1985. Genotype-environment interaction and the evolution of phenotypic plasticity. Evolution 39:505–522.']
  • ['Zhang, J., N. E. Heckman, D. Cubranic, J. G. Kingsolver, T. L. Gaydos, and J. S. Marron. 2014. Prinsimp. R Journal 6:27–42.']