Advertisement

Theoretical and Applied Genetics

, Volume 131, Issue 2, pp 283–298 | Cite as

Bayesian estimation and use of high-throughput remote sensing indices for quantitative genetic analyses of leaf growth

  • Robert L. Baker
  • Wen Fung Leong
  • Nan An
  • Marcus T. Brock
  • Matthew J. Rubin
  • Stephen Welch
  • Cynthia Weinig
Original Article

Abstract

Key message

We develop Bayesian function-valued trait models that mathematically isolate genetic mechanisms underlying leaf growth trajectories by factoring out genotype-specific differences in photosynthesis. Remote sensing data can be used instead of leaf-level physiological measurements.

Abstract

Characterizing the genetic basis of traits that vary during ontogeny and affect plant performance is a major goal in evolutionary biology and agronomy. Describing genetic programs that specifically regulate morphological traits can be complicated by genotypic differences in physiological traits. We describe the growth trajectories of leaves using novel Bayesian function-valued trait (FVT) modeling approaches in Brassica rapa recombinant inbred lines raised in heterogeneous field settings. While frequentist approaches estimate parameter values by treating each experimental replicate discretely, Bayesian models can utilize information in the global dataset, potentially leading to more robust trait estimation. We illustrate this principle by estimating growth asymptotes in the face of missing data and comparing heritabilities of growth trajectory parameters estimated by Bayesian and frequentist approaches. Using pseudo-Bayes factors, we compare the performance of an initial Bayesian logistic growth model and a model that incorporates carbon assimilation (A max) as a cofactor, thus statistically accounting for genotypic differences in carbon resources. We further evaluate two remotely sensed spectroradiometric indices, photochemical reflectance (pri2) and MERIS Terrestrial Chlorophyll Index (mtci) as covariates in lieu of A max, because these two indices were genetically correlated with A max across years and treatments yet allow much higher throughput compared to direct leaf-level gas-exchange measurements. For leaf lengths in uncrowded settings, including A max improves model fit over the initial model. The mtci and pri2 indices also outperform direct A max measurements. Of particular importance for evolutionary biologists and plant breeders, hierarchical Bayesian models estimating FVT parameters improve heritabilities compared to frequentist approaches.

Notes

Acknowledgements

We thank two anonymous reviewers for insightful comments that greatly improved the manuscript. University of Wyoming undergraduates E. Gimpel, J. Whipps, K. Anderson, M. Pratt, J. Beckius, C. Blumenshine, S. Cheeney, M. Yorgason, W. Gardner, C. Planche, C. Gifford, L. Lucas, K. Riggs, D. Larimer, D. Nykodym, and L. Steinken assisted with data collection and entry. M. Knapp (Kansas State University) provided temperature data. C. Seals and R. Pendleton facilitated plant growth. The manuscript was enriched by helpful discussions with R. J. C. Markelz (University of California, Davis & Revgenomics, Oakland CA) and the insight of our editor, Dr. H. Iwata (University of Tokyo).

Compliance with ethical standards

Conflict of interest

This work was supported by National Science Foundation grants IOS-1306574 to RLB, IOS-0923752 to C.W and SW, and IOS-1025965 to C.W. The authors declare that they have no potential conflicts of interest.

Supplementary material

122_2017_3001_MOESM1_ESM.pdf (531 kb)
Supplementary material 1 Online Resource 1 An example of the experimental design. Each block (colored bars) consists of an entire RIL set. Treatments were applied to whole blocks: red blocks consist of crowded (CR) plants and blue blocks consist of uncrowded (UN) plants. The location of blocks (CR vs. UN) within the field is fully randomized as is the location of individual genotypes (RILs) within each block (PDF 530 kb)
122_2017_3001_MOESM2_ESM.pdf (1 mb)
Supplementary material 2 Online Resource 2 FVT parameters for Bayesian models including the A max cofactor (PDF 1057 kb)
122_2017_3001_MOESM3_ESM.pdf (703 kb)
Supplementary material 3 Online Resource 3 Spectroradiometric index and R:FR values (PDF 703 kb)
122_2017_3001_MOESM4_ESM.tif (817 kb)
Supplementary material 4 Online Resource 4 The kernel density function that quantifies the likelihood of measurement errors (mm) for leaf length. The histogram shows tabulated values and the dotted line is the smoothed curve that was used in both leaf length and leaf width parameter estimation (TIFF 816 kb)
122_2017_3001_MOESM5_ESM.pdf (755 kb)
Supplementary material 5 Online Resource 5 Patterns of correlations for genotypic means. All leaf FVT parameters from Bayesian models that include the A max cofactor from the uncrowded treatment are presented along with uncrowded spectroradiometric indices (and R:FR), and estimates of phenology, fitness, and physiology (PDF 754 kb)
122_2017_3001_MOESM6_ESM.pdf (495 kb)
Supplementary material 6 Online Resource 6 Patterns of correlations for genotypic means. All leaf FVT parameters from Bayesian models that include the A max cofactor from the crowded treatment are presented along with crowded spectroradiometric indices (and R:FR), and estimates of phenology, fitness, and physiology (PDF 494 kb)
122_2017_3001_MOESM7_ESM.pdf (66 kb)
Supplementary material 7 Online Resource 7 Heritabilities for spectroradiometric indices and R:FR (PDF 66 kb)

References

  1. An N, Goldsby AL, Price KP, Bremer DJ (2015) Using hyperspectral radiometry to predict the green leaf area index of turfgrass. Int J Remote Sens 36:1470–1483CrossRefGoogle Scholar
  2. Araus JL, Alegre L, Tapia L, Calafell R, Serret MD (1986) Relationships between photosynthetic capacity and leaf structure in several shade plants. Am J Bot 73:1760–1770CrossRefGoogle Scholar
  3. Baker RL, Leong WF, Brock MT, Markelz R, Covington MF, Devisetty UK, Edwards CE, Maloof J, Welch S, Weinig C (2015) Modeling development and quantitative trait mapping reveal independent genetic modules for leaf size and shape. New Phytol 208:257–268CrossRefPubMedGoogle Scholar
  4. Bates D, Maechler M, Bolker B, Walker S (2014) lmer: linear mixed-effects models using Eigen and S4. R package version 1, 1–7 ednGoogle Scholar
  5. Bayarri MJ, Berger JO (2004) The interplay of Bayesian and frequentist analysis. Stat Sci 19:58–80CrossRefGoogle Scholar
  6. Bradshaw AD (1965) Evolutionary significance of phenotypic plasticity in plants. Adv Genet 13:115–155Google Scholar
  7. Brock MT, Weinig C (2007) Plasticity and environment-specific covariances: an investigation of floral-vegetative and within flower correlations. Evolution 61:2913–2924CrossRefPubMedGoogle Scholar
  8. Bustos-Korts D, Malosetti M, Chapman S, van Eeuwijk F (2016) Modelling of genotype by environment interaction and prediction of complex traits across multiple environments as a synthesis of crop growth modelling, genetics and statistics. In: Yin X, Struik PC (eds) Crop systems biology: narrowing the gaps between crop modelling and genetics. Springer, Heidelberg, pp 55–82Google Scholar
  9. Celeux G, El Anbari M, Marin J-M, Robert CP (2012) Regularization in regression: comparing Bayesian and frequentist methods in a poorly informative situation. Bayesian anal 7(2):477–502CrossRefGoogle Scholar
  10. Chenu K, Chapman SC, Tardieu F, McLean G, Welcker C, Hammer GL (2009) Simulating the yield impacts of organ-level quantitative trait loci associated with drought response in maize: a “gene-to-phenotype” modeling approach. Genetics 183:1507–1523CrossRefPubMedPubMedCentralGoogle Scholar
  11. Chib S, Greenberg E (1995) Understanding the metropolis-hastings algorithm. Am Stat 49:327–335Google Scholar
  12. Christensen R, Johnson W, Branscum A, Hanson TE (2010) Bayesian ideas and data analysis: an introduction for scientists and statisticians. CRC Press, New YorkGoogle Scholar
  13. Cover TM, Thomas JA (2013) Elements of information theory, 2nd edn. Wiley, HobokenGoogle Scholar
  14. Dash J, Curran PJ (2004) The MERIS terrestrial chlorophyll index. Int J Remote Sens 25:5403–5413CrossRefGoogle Scholar
  15. de Villemereuil P, Gimenez O, Doligez B (2013) 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 Ecol Evol 4:260–275CrossRefGoogle Scholar
  16. Dordas CA, Sioulas C (2008) Safflower yield, chlorophyll content, photosynthesis, and water use efficiency response to nitrogen fertilization under rainfed conditions. Ind Crops Prod 27:75–85CrossRefGoogle Scholar
  17. Edwards CE, Ewers BE, Williams DG, Xie Q, Lou P, Xu X, McClung CR, Weinig C (2011) The genetic architecture of ecophysiological and Circadian traits in Brassica rapa. Genetics 189:375–390CrossRefPubMedPubMedCentralGoogle Scholar
  18. Edwards CE, Ewers BE, McClung CR, Lou P, Weinig C (2012) Quantitative variation in water-use efficiency across water regimes and its relationship with Circadian, vegetative, reproductive, and leaf gas-exchange traits. Mol Plant 5:653–668CrossRefPubMedGoogle Scholar
  19. Fellows RJ, Geiger DR (1974) Structural and physiological changes in sugar beet leaves during sink to source conversion. Plant Physiol 54:877–885CrossRefPubMedPubMedCentralGoogle Scholar
  20. Filella I, Amaro T, Araus JL, Peñuelas J (1996) Relationship between photosynthetic radiation-use efficiency of barley canopies and the photochemical reflectance index (PRI). Physiol Plant 96:211–216CrossRefGoogle Scholar
  21. Gahoonia TS, Ali O, Sarker A, Nielsen NE, Rahman MM (2006) Genetic variation in root traits and nutrient acquisition of lentil genotypes. J Plant Nutr 29:643–655CrossRefGoogle Scholar
  22. Gamon JA, Peñuelas J, Field CB (1992) A narrow-waveband spectral index that tracks diurnal changes in photosynthetic efficiency. Remote Sens Environ 41:35–44CrossRefGoogle Scholar
  23. Garbulsky MF, Peñuelas J, Gamon J, Inoue Y, Filella I (2011) The photochemical reflectance index (PRI) and the remote sensing of leaf, canopy and ecosystem radiation use efficiencies: a review and meta-analysis. Remote Sens Environ 115:281–297CrossRefGoogle Scholar
  24. Garn SM, Lewis AB, Kerewsky RS (1965) Genetic, nutritional, and maturational correlates of dental development. J Dent Res 44:228–242CrossRefGoogle Scholar
  25. Gelman A, Hill J (2007) Data analysis using regression and multilevel/hierarchical models. Cambridge University Press, CambridgeGoogle Scholar
  26. Gitelson AA, Merzlyak MN, Chivkunova OB (2001) Optical properties and nondestructive estimation of anthocyanin content in plant leaves. Photochem Photobiol 74:38–45CrossRefPubMedGoogle Scholar
  27. Gitelson AA, Zur Y, Chivkunova OB, Merzlyak MN (2002) Assessing carotenoid content in plant leaves with reflectance spectroscopy. Photochem Photobiol 75:272–281CrossRefPubMedGoogle Scholar
  28. Glenn EP, Huete AR, Nagler PL, Nelson SG (2008) Relationship between remotely-sensed vegetation indices, canopy attributes and plant physiological processes: what vegetation indices can and cannot tell us about the landscape. Sensors (Basel, Switzerland) 8:2136–2160CrossRefPubMedCentralGoogle Scholar
  29. Golan D, Rosset S (2011) Accurate estimation of heritability in genome wide studies using random effects models. Bioinformatics 27:i317–i323CrossRefPubMedPubMedCentralGoogle Scholar
  30. Goldberger AS (1962) Best linear unbiased prediction in the generalized linear regression model. J Am Stat Assoc 57:369–375CrossRefGoogle Scholar
  31. Haboudane D, Miller JR, Pattey E, Zarco-Tejada PJ, Strachan IB (2004) Hyperspectral vegetation indices and novel algorithms for predicting green LAI of crop canopies: modeling and validation in the context of precision agriculture. Remote Sens Environ 90:337–352CrossRefGoogle Scholar
  32. Hall FG, Huemmrich KF, Goetz SJ, Sellers PJ, Nickeson JE (1992) Satellite remote sensing of surface energy balance: success, failures, and unresolved issues in FIFE. J Geophys Res Atmos 97:19061–19089CrossRefGoogle Scholar
  33. Hammer GL, Kropff MJ, Sinclair TR, Porter JR (2002) Future contributions of crop modelling—from heuristics and supporting decision making to understanding genetic regulation and aiding crop improvement. Eur J Agron 18:15–31CrossRefGoogle Scholar
  34. Hammer GL, Chapman S, van Oosterom E, Podlich DW (2005) Trait physiology and crop modelling as a framework to link phenotypic complexity to underlying genetic systems. Aust J Agric Res 56:947–960CrossRefGoogle Scholar
  35. Haukoos JS, Lewis RJ (2005) Advanced statistics: bootstrapping confidence intervals for statistics with “difficult” distributions. Acad Emerg Med 12:360–365CrossRefPubMedGoogle Scholar
  36. Hinata K, Prakash S (1984) Ethnobotany and evolutionary origin of Indian oleiferous Brassicae. Indian J Genet Plant Breed 44:102–112Google Scholar
  37. Huete AR, Liu HQ, Batchily K, van Leeuwen W (1997) A comparison of vegetation indices over a global set of TM images for EOS-MODIS. Remote Sens Environ 59:440–451CrossRefGoogle Scholar
  38. Iniguez-Luy F, Lukens L, Farnham M, Amasino R, Osborn T (2009) Development of public immortal mapping populations, molecular markers and linkage maps for rapid cycling Brassica rapa and B. oleracea. Theor Appl Genet 120:31–43CrossRefPubMedGoogle Scholar
  39. Jaffrézic F, Pletcher SD (2000) Statistical models for estimating the genetic basis of repeated measures and other function-valued traits. Genetics 156:913–922PubMedPubMedCentralGoogle Scholar
  40. Jeffreys H (1961) Theory of probability, 3rd edn. The Clarendon Press, OxfordGoogle Scholar
  41. Ji T, Liu P, Nettleton D (2012) Borrowing information across genes and experiments for improved error variance estimation in microarray data analysis. Stat Appl Genet Mol Biol 11(3):Article 12Google Scholar
  42. Jiang L, Clavijo JA, Sun L, Zhu X, Bhakta MS, Gezan SA, Carvalho M, Vallejos CE, Wu R (2015) Plastic expression of heterochrony quantitative trait loci (hQTLs) for leaf growth in the common bean (Phaseolus vulgaris). New Phytol 207:872–882CrossRefPubMedGoogle Scholar
  43. Kass RE, Raftery AE (1995) Bayes factors. J Am Stat Assoc 90:773–795CrossRefGoogle Scholar
  44. Kingsolver J, Gomulkiewicz R, Carter PA (2001a) Variation, selection and evolution of function-valued traits. In: Hendry AP, Kinnison MT (eds) Microevolution rate, pattern, process. Springer, Dordrecht, pp 87–104CrossRefGoogle Scholar
  45. Kingsolver JG, Gomulkiewicz R, Carter PA (2001b) Variation, selection and evolution of function-valued traits. Genetica 112–113:87–104CrossRefPubMedGoogle Scholar
  46. Koch KE (1996) Carbohydrated-modulated gene expression in plants. Annu Rev Plant Physiol Plant Mol Biol 47:509–540CrossRefPubMedGoogle Scholar
  47. Kruschke JK (2015) Doing Bayesian data analysis: a tutorial with R, BUGS, and Stan, 2nd edn. Academic Press, San DiegoGoogle Scholar
  48. Kuznetsova A, Brockhoff PB, Bojesen CRH (2015) lmerTest: tests in linear mixed effects models. R package version 2.0-25. https://CRAN.R-project.org/package=lmerTest
  49. Li Z, Sillanpää MJ (2015) Dynamic quantitative trait locus analysis of plant phenomic data. Trends Plant Sci 20:822–833CrossRefPubMedGoogle Scholar
  50. Merzlyak MN, Gitelson AA, Chivkunova OB, Rakitin VYU (1999) Non-destructive optical detection of pigment changes during leaf senescence and fruit ripening. Physiol Plant 106:135–141CrossRefGoogle Scholar
  51. Moczek AP, Sears KE, Stollewerk A, Wittkopp PJ, Diggle P, Dworkin I, Ledon-Rettig C, Matus DQ, Roth S, Abouheif E, Brown FD, Chiu C-H, Cohen CS, Tomaso AWD, Gilbert SF, Hall B, Love AC, Lyons DC, Sanger TJ, Smith J, Specht C, Vallejo-Marin M, Extavour CG (2015) The significance and scope of evolutionary developmental biology: a vision for the 21st century. Evol Dev 17:198–219CrossRefPubMedGoogle Scholar
  52. Patil A, Huard D, Fonnesbeck CJ (2010) PyMC: Bayesian stochastic modelling in python. J Stat Softw 35:1–81CrossRefPubMedPubMedCentralGoogle Scholar
  53. Penuelas J, Pinol J, Ogaya R, Filella I (1997) Estimation of plant water concentration by the reflectance water index WI (R900/R970). Int J Remote Sens 18:2869–2875CrossRefGoogle Scholar
  54. Peñuelas J, Gamon JA, Fredeen AL, Merino J, Field CB (1994) Reflectance indices associated with physiological changes in nitrogen- and water-limited sunflower leaves. Remote Sens Environ 48:135–146CrossRefGoogle Scholar
  55. Peñuelas J, Baret F, Filella I (1995) Semi-empirical indices to assess carotenoids/chlorophyll a ratio from leaf spectral reflectance. Photosynthetica 31:221–230Google Scholar
  56. Pilson D (2000) The evolution of plant response to herbivory: simultaneously considering resistance and tolerance in Brassica rapa. Evol Ecol 14:457–489CrossRefGoogle Scholar
  57. R Core Team (2015) R: a language and environment for statistical computing, 3.2.3 edn. R Core Team, AustriaGoogle Scholar
  58. Raines C, Paul M (2006) Products of leaf primary carbon metabolism modulate the developmental programme determining plant morphology. J Exp Bot 57:1857–1862CrossRefPubMedGoogle Scholar
  59. Rajapakse NC, Pollock RK, McMahon MJ, Kelly JW, Young RE (1992) Interpretation of light quality measurements and plant response in spectral filter research. HortScience 27:1208–1211Google Scholar
  60. Rouder JN, Lu J (2005) An introduction to Bayesian hierarchical models with an application in the theory of signal detection. Psychon Bull Rev 12:573–604CrossRefPubMedGoogle Scholar
  61. Roux F, Gao L, Bergelson J (2010) Impact of initial pathogen density on resistance and tolerance in a polymorphic disease resistance gene system in Arabidopsis thaliana. Genetics 185:283–291CrossRefPubMedPubMedCentralGoogle Scholar
  62. Samaniego FJ (2010) A comparison of the Bayesian and frequentist approaches to estimation. Springer, New YorkCrossRefGoogle Scholar
  63. Schneidereit J, Häusler RE, Fiene G, Kaiser WM, Weber APM (2006) Antisense repression reveals a crucial role of the plastidic 2-oxoglutarate/malate translocator DiT1 at the interface between carbon and nitrogen metabolism. Plant J 45:206–224CrossRefPubMedGoogle Scholar
  64. Sellers PJ (1985) Canopy reflectance, photosynthesis and transpiration. Int J Remote Sens 6:1335–1372CrossRefGoogle Scholar
  65. Sillanpaa MJ, Pikkuhookana P, Abrahamsson S, Knurr T, Fries A, Lerceteau E, Waldmann P, Garcia-Gil MR (2012) Simultaneous estimation of multiple quantitative trait loci and growth curve parameters through hierarchical Bayesian modeling. Heredity 108:134–146CrossRefPubMedGoogle Scholar
  66. Sims DA, Gamon JA (2002) Relationships between leaf pigment content and spectral reflectance across a wide range of species, leaf structures and developmental stages. Remote Sens Environ 81:337–354CrossRefGoogle Scholar
  67. Stinchcombe JR, Kirkpatrick M (2012) Genetics and evolution of function-valued traits: understanding environmentally responsive phenotypes. Trends Ecol Evol 27:637–647CrossRefPubMedGoogle Scholar
  68. Stinchcombe JR, Izem R, Heschel MS, McGoey BV, Schmitt J (2010) Across-environment genetic correlations and the frequency of selective environments shape the evolutionary dynamics of growth rate in Impatiens capensis. Evolution 64:2887–2903PubMedGoogle Scholar
  69. Sultan SE (1987) Evolutionary implications of phenotypic plasticity in plants. In: Hecht MK, Wallace B, Prance GT (eds) Evolutionary biology, vol 21. Springer, Boston, pp 127–178CrossRefGoogle Scholar
  70. Tardieu F, Reymond M, Muller B, Granier C, Simonneau T, Sadok W, Welcker C (2005) Linking physiological and genetic analyses of the control of leaf growth under changing environmental conditions. Aust J Agric Res 56:937–946CrossRefGoogle Scholar
  71. Torrey JG (1986) Endogenous and exogenous influences on the regulation of lateral root formation. In: Jackson MB (ed) New root formation in plants and cuttings. Springer, Dordrecht, pp 31–66CrossRefGoogle Scholar
  72. van Eeuwijk FA, Bink MCAM, Chenu K, Chapman SC (2010) Detection and use of QTL for complex traits in multiple environments. Curr Opin Plant Biol 13:193–205CrossRefPubMedGoogle Scholar
  73. Vigil MF, Anderson RL, Beard WE (1997) Base temperature and growing-degree-hour requirements for the emergence of canola. Crop Sci 37:844–849CrossRefGoogle Scholar
  74. Wu R, Lin M (2006) Functional mapping—how to map and study the genetic architecture of dynamic complex traits. Nat Rev Genet 7:229–237CrossRefPubMedGoogle Scholar
  75. Wu W-R, Li W-M, Tang D-Z, Lu H-R, Worland AJ (1999) Time-related mapping of quantitative trait loci underlying tiller number in rice. Genetics 151:297–303PubMedPubMedCentralGoogle Scholar
  76. Xiong H, Goulding EH, Carlson EJ, Tecott LH, McCulloch CE, Sen Ś (2011) A flexible estimating equations approach for mapping function-valued traits. Genetics 189:305–316CrossRefPubMedPubMedCentralGoogle Scholar
  77. Xu M, Jiang L, Zhu S, Zhou C, Ye M, Mao K, Sun L, Su X, Pan H, Zhang S, Huang M, Wu R (2016) A computational framework for mapping the timing of vegetative phase change. New Phytol 211:750–760CrossRefPubMedGoogle Scholar
  78. Yin X, Chasalow SD, Dourleijn CJ, Stam P, Kropff MJ (2000) Coupling estimated effects of QTLs for physiological traits to a crop growth model: predicting yield variation among recombinant inbred lines in barley. Heredity 85:539–549CrossRefPubMedGoogle Scholar
  79. Zhang Z, Hamagami F, Lijuan Wang L, Nesselroade JR, Grimm KJ (2007) Bayesian analysis of longitudinal data using growth curve models. Int J Behav Dev 31:374–383CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of BotanyUniversity of WyomingLaramieUSA
  2. 2.Biology DepartmentMiami UniversityOxfordUSA
  3. 3.Department of AgronomyKansas State UniversityManhattanUSA
  4. 4.Department of Molecular BiologyUniversity of WyomingLaramieUSA

Personalised recommendations