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


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.


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.

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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).

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Correspondence to Robert L. Baker.

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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.

Additional information

Communicated by Hiroyoshi Iwata.

Electronic supplementary material

Below is the link to the electronic supplementary material.

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)

Supplementary material 2 Online Resource 2 FVT parameters for Bayesian models including the A max cofactor (PDF 1057 kb)

Supplementary material 3 Online Resource 3 Spectroradiometric index and R:FR values (PDF 703 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)

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)

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)

Supplementary material 7 Online Resource 7 Heritabilities for spectroradiometric indices and R:FR (PDF 66 kb)

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Baker, R.L., Leong, W.F., An, N. et al. Bayesian estimation and use of high-throughput remote sensing indices for quantitative genetic analyses of leaf growth. Theor Appl Genet 131, 283–298 (2018). https://doi.org/10.1007/s00122-017-3001-6

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