short title: fpca-based gwas for time-series data in sorghummay 27, 2020 · 1 short title:...
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Short title: FPCA-based GWAS for time-series data in sorghum 1
2
Increased power and accuracy of causal locus identification in time-series 3
genome-wide association in sorghum 4
5
Chenyong Miao1, Yuhang Xu
2, Sanzhen Liu
3, Patrick S. Schnable
4, and James 6
C. Schnable1*
7
1Quantitative Life Science Initiative, Center for Plant Science Innovation, 8
Department of Agronomy and Horticulture, University of Nebraska-Lincoln, 9
Lincoln, NE USA 10 2Department of Applied Statistics and Operations Research, Bowling Green State 11
University, Bowling Green, OH USA 12 3Department of Plant Pathology, Kansas State University, Manhattan, KS USA 13
4Department of Agronomy, Iowa State University, Ames, IA USA 14
*Corresponding author: James C. Schnable ([email protected]) 15
Author contributions: 16
CM and JCS designed the study. CM, SL, PSS, and JCS contributed methodology 17
and provided datasets. CM and YX analyzed the data. CM and JCS wrote the 18
paper. All authors reviewed and approved the manuscript. 19
One-sentence summary: Applying functional principal component analyses to 20
time-series genome-wide association studies increases the power and accuracy of 21
gene identification in a sorghum association panel. 22
23
Abstract 24
The phenotypes of plants develop over time and change in response to the 25
environment. New engineering and computer vision technologies track these 26
phenotypic changes. Identifying the genetic loci regulating differences in the 27
pattern of phenotypic change remains challenging. This study used functional 28
principal component analysis (FPCA) to achieve this aim. Time-series phenotype 29
data was collected from a sorghum (Sorghum bicolor) diversity panel using a 30
Plant Physiology Preview. Published on May 27, 2020, as DOI:10.1104/pp.20.00277
Copyright 2020 by the American Society of Plant Biologists
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number of technologies including RGB and hyperspectral imaging. This imaging 31
lasted for thirty-seven days and centered on reproductive transition. A new higher 32
density marker set was generated for the same population. Several genes known 33
to control trait variation in sorghum have been previously cloned and 34
characterized. These genes were not confidently identified in genome-wide 35
association analyses at single time points. However, FPCA successfully identified 36
the same known and characterized genes. FPCA analyses partitioned the role 37
these genes play in controlling phenotypes. Partitioning was consistent with the 38
known molecular function of the individual cloned genes. These data demonstrate 39
that FPCA-based genome-wide association studies can enable robust time-series 40
mapping analyses in a wide range of contexts. Moreover, time-series analysis can 41
increase the accuracy and power of quantitative genetic analyses. 42
Introduction 43
Quantitative genetic approaches are widely used across all domains of biology to 44
identify genetic loci controlling variation in target traits. Many genes where 45
naturally occurring functionally variable alleles control variation in agronomically 46
relevant traits have been identified. Both quantitative trait locus (QTL) mapping 47
(structured populations) or genome-wide association studies (association panels) 48
have been used to identify these loci (Chen et al., 2016; Navarro et al., 2017; 49
Huang et al., 2010). Collecting phenotypic data from the hundreds to thousands of 50
accessions required for QTL mapping or genome-wide association study (GWAS) 51
has historically been a time- and resource-intensive undertaking. Hence, most 52
attempts to identify genes controlling variation in a target trait employ data from a 53
single time point, usually either at maturity or after a fixed number of days from 54
planting. However, recent engineering advances, such as wearable devices, 55
automated phenotyping greenhouses, field phenotyping robots, unmanned aerial 56
vehicles, and computer vision advances, are lowering the barriers and activation 57
energy required to score traits from multiple points throughout development 58
(Moore et al., 2013; Oren et al., 2017; Furbank and Tester, 2011; Honsdorf et al., 59
2014; Fernandez et al., 2017; Holman et al., 2016; Feldman et al., 2017, 2018). 60
Plant growth and development is a dynamic process, responding to environmental 61
perturbations. It is regulated by different suites of genes at different times and in 62
different environments (Yan et al., 1998; Wu and Lin, 2006; Moore et al., 2013; 63
Würschum et al., 2014; Muraya et al., 2017; Feldman et al., 2017, 2018). The 64
availability and use of time-series trait data from mapping and association 65
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populations has the potential to increase the accuracy and power of gene mapping 66
studies (Moore et al., 2013; Sang et al., 2019). It may also provide greater insight 67
into the biologically distinct roles different loci play in determining final 68
phenotypes. However, integrating time-series data into statistical frameworks 69
originally envisioned for single-trait measurements across large populations is not 70
straightforward. A range of approaches are currently being explored by the 71
research community. 72
There are several approaches to the use of time-series phenotypic data in 73
mapping studies. The most straightforward is to conduct QTL mapping or GWAS 74
separately at each time point and then summarize the mapping results (Yan et al., 75
1998; Wu et al., 2010; Osman et al., 2013). However, this approach is not robust 76
when faced with missing data, or when subsets of the population are scored on 77
alternating time points. This procedure also requires complex approaches to 78
multiple testing correction given the partially correlated nature of both linked 79
genetic markers and measurements of the same trait in the same individuals at 80
multiple time points. A second widely employed method is to summarize patterns 81
of change over time using predefined functions with discrete numbers of variables 82
(Ma et al., 2002; Wu et al., 2004; Paine et al., 2012). QTL mapping or GWAS can 83
then be conducted for the values of the different variables within the equation as 84
that function is fit to data from different individuals. This approach can be 85
powerful and is able to impute missing data points in individuals. However, this 86
approach can fail when the pattern of phenotypic change over time follows an 87
unknown function, is too complex to fit, or does not conform to the expected 88
function (Feldman et al., 2018). Functional principal component analysis (FPCA), 89
as a more general method, provides some of the strengths of fitting parametric 90
functions sharing data across time points. This includes the ability to impute 91
missing values without requiring that patterns of phenotypic change over time fit 92
any particular function (Kwak et al., 2016; Xu et al., 2018a,b). A variation of 93
nonparametric functional principal component-based mapping has been 94
successfully employed to identify loci controlling the gravitropism response in A. 95
thaliana seedlings (Moore et al., 2013; Kwak et al., 2016). Kwak et al. (2016) 96
concluded that dimensional reduction via FPCA may increase the power to detect 97
QTL in recombinant inbred populations relative to prior approaches that include 98
trait data from each time point. Muraya et al. (2017) employed an FPCA method 99
adapted from Kwak et al. (2016) to identify several trait-associated SNPs for maize 100
(Zea mays) biomass accumulation in vegetative development. This represented an 101
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advancement over parametric regression, which had not been able to identify any 102
trait-associated SNPs using the same trait and marker dataset. However, none of 103
the identified loci coincided either with markers identified in single time point 104
analyses, or with known loci controlling the trait of interest. 105
Three cloned sorghum (Sorghum bicolor) genes controlling height–dwarf1, 106
dwarf2, and dwarf3–are segregating in the Sorghum Association Panel (SAP). 107
Dwarf1 (Dw1, Sobic.009G229800) was cloned by two independent fine mapping 108
studies (Hilley et al., 2016; Yamaguchi et al., 2016). The function of the Dw1 gene 109
appears to act in the brassinosteroid signaling pathway to influence sorghum plant 110
height by reducing cell proliferation activity in the internodes (Hirano et al., 2017). 111
Dwarf2 (Dw2, Sobic.006G067700) on chromosome 6 is in tight linkage with 112
maturity1 (Ma1, Sobic.006G057866), a gene with a large effect on sorghum 113
flowering time. In many cases, both loci are introgressed together during the 114
backcrossing and conversion process of adapting tropical sorghum germplasm to 115
grow in temperate latitudes (Quinby, 1974; Higgins et al., 2014). The Dw2 gene 116
encodes a protein kinase which is homologous to KIPK in Arabidopsis and 117
influences sorghum plant height by reducing the length of internodes (Hilley et al., 118
2017). Maturity1 gene has the largest impact on flowering time through encoding 119
the pseudoresponse regulator protein 37 (PRR37) to modulate flowering time in 120
sorghum (Murphy et al., 2011). Dwarf3 (Dw3, Sobic.007G163800) encodes a 121
MDR transporter orthologous to brachytic2 in maize, and appears to influence cell 122
elongation through a role in polar auxin transport (Multani et al., 2003). Previous 123
sorghum height mapping studies identified epistatic interactions between Dw1 and 124
Dw3, but no significant epistatic interactions have been reported between Dw2 and 125
either Dw1 or Dw3 (Brown et al., 2008; Hilley et al., 2016; Yamaguchi et al., 126
2016). 127
In this study, we employed a new approach to functional principal 128
component analysis of non-parametric regression data (Xu et al., 2018a). The 129
procedure’s effectiveness at both controlling false positives and identifying known 130
true positives in sorghum was evaluated. A phenotypically constrained subset of 131
the SAP was utilized (Casa et al., 2008). This population was grown and imaged 132
through vegetative and reproductive development in a high-throughput 133
phenotyping facility. Organ-level semantic segmentation from hyperspectral 134
images was employed to extract phenotypic values (Miao et al., 2020). Genome-135
wide association using the functional principal component scores derived from the 136
FPCA approach described by Xu et al. (2018a) could be used to successfully 137
identify all three known dwarf genes. Three novel signals were also detected. The 138
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signal on chromosome 3 was independently validated in data from a previous 139
study of a different sorghum population. These results favorably contrasted with 140
terminal phenotyping or time point by time point analyses in the same population, 141
and provide additional insight into the distinct biological roles of three known 142
dwarf genes in determining sorghum height. 143
144
Results 145
Loss of association power in phenotypically constrained populations 146
The classical sorghum dwarfing genes have large effects on plant height and are 147
segregating within the SAP (Morris et al., 2013; Li et al., 2015). Field-collected 148
plant height data for 357 lines from the SAP correctly identified both Dw1 and 149
Dw2 [Figure 1A] as well as a third previously reported locus known to influence 150
variation in height in this population (Li et al., 2015). Thirty-eight lines from the 151
field study exceeded the physical limit on maximum height for the imaging facility 152
employed in this study [Figure 1B]. After the exclusion of these 38 lines as well as 153
an additional 27 lines which failed to germinate or thrive in the greenhouse, field-154
measured height data for the remaining 292 lines was still sufficient to identify 155
Dw1, albeit with substantially reduced statistical significance. However, after the 156
removal of these phenotypically extreme lines, signals from Dw2 and the other 157
previously reported height-controlling loci were no longer statistically significant 158
[Figure 1C]. Dw3, located on the long arm of chromosome 7, was not identified in 159
association analyses using either field data on terminal plant heights from the 160
complete set of 357 SAP lines, or in analyses of data only from the phenotypically 161
constrained subset of SAP lines employed for greenhouse experiments. Excluding 162
lines in the mapping population not only decreased the total population size, but 163
also reduced the minor allele frequency of SNPs near genes known to control 164
variation in sorghum height [Figure S1]. 165
Genetic associations with sorghum height at different time points 166
The phenotypically constrained subset of 292 SAP lines was imaged at the 167
University of Nebraska’s Greenhouse Innovation Center (UNGIC). Imaging lasted 168
approximately one month, and centered on reproductive development. Each plant 169
was imaged using a set of five cameras, including top views and side views from 170
multiple angles, and hyperspectral imaging from a single side view perspective 171
(Ge et al., 2016; Liang et al., 2017; Miao et al., 2020). Two methods were 172
employed to extract plant height at individual time points. The first was whole-173
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plant segmentation, an approach widely used in plant image analysis (Gehan et al., 174
2017): segmentation of an image into plant pixels and not plant pixels, and 175
measuring height by the difference between the minimum and maximum y-axis 176
values for plant pixels [Figure 2A]. The second approach was a recently described 177
method (Miao et al., 2020) to semantically segment "plant pixels" of sorghum 178
plants into separate stalk, leaf, and panicle classes [Figure 2B, S2]. There are many 179
different ways to measure the plant height (Brown et al., 2008; Miao et al., 2020). 180
Generally, researchers in the field have preferred to benchmark on the height of 181
stalk, height to the uppermost leaf collar, or the height to the tip of the 182
inflorescence rather than the height to the highest leaf tip. An advantage of the 183
latter method, semantic segmentation, is that it can be used to measure a version of 184
plant height which more closely approximates how height is measured in the field 185
(Miao et al., 2020). Sorghum plant height measured by whole-plant segmentation 186
tended to oscillate over time as new leaves emerged, whereas sorghum plant height 187
measured via the semantic segmentation method tended to be monotonically 188
increasing [Figure 2C]. Generally, researchers in the field have preferred to 189
measure the height of stalk or the height of inflorescence rather than the height to 190
the highest point on the plant, which is often a leaf tip. The semantic segmentation 191
approach makes it possible to measure height using a definition for plant height 192
that corresponds to the definition of plant height used by sorghum geneticists in the 193
field (Miao et al., 2020). 194
A second challenge faced by many time-series imaging studies is the maximum 195
daily throughput provided by fixed imaging infrastructure. In this particular study, 196
individual plants were divided into two groups imaged on alternating days. 197
Therefore, there was no single time point at which image or height data was 198
available for all individual plants [Figure S3A]. In order to estimate the height of 199
each individual plant at each individual time point, nonparametric regression was 200
employed to impute all missing data points [Figure S3B]. To assess the accuracy of 201
this imputation, the percent of variance in height explained by genetic factors was 202
assessed at individual time points for subsets of the population using either height 203
measured directly from images or height imputed from nonparametric curves. In 204
most cases, the proportion of variance in imputed height which could be explained 205
by genetic factors matched or exceeded the equivalent value for directly measured 206
height [Figure S4]. This is consistent with previous work which found that missing 207
values in time-series plant phenomics data can be imputed accurately from 208
nonparametric curves (Xu et al., 2018b). 209
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Independent genome-wide association analyses were conducted for imputed 210
sorghum height as measured via semantic segmentation on each day from 41 to 76 211
days after planting (DAP). Consistent with observations from field-collected plant 212
height data, almost no significant trait/marker associations were observed in the 213
analyses for DAP 65–76 [Figure S5; Supplementary file S1]. In the early days of 214
the experiment, statistically significant signals were identified all over the genome, 215
likely as a result of extreme height values for a small number of lines. Those lines 216
experienced reproductive transition and panicle emergence prior to the start of 217
imaging [Figure S6]. Excluding extreme lines led to the identification of signals 218
near Dw1, Dw3, and Ma3 in data from some early time points mixed in among 219
approximately a dozen other repeatedly identified loci across the genome. A loss 220
of detectable genetic associations between 54 and 66 DAP corresponded roughly 221
to booting and panicle exertion in many sorghum accessions. The peduncle length 222
is under the control of a distinct set of genetic factors from plant height below the 223
flag leaf (Li et al., 2015), and the timing of panicle exertion is under the control of 224
a third distinct set of factors, namely maturity genes (Quinby and Karper, 1945; 225
Quinby, 1967). We speculate that, once a large proportion of lines advanced to the 226
booting stage or beyond, the role these three sets of genetic factors played in 227
determining plant height diluted the total variance attributable to any one single 228
genetic locus, reducing power to identify statistically significant associations. 229
A second set of analyses were conducted where nonparametric curves calculated 230
for individual plants were aligned based on time relative to panicle emergence (e.g. 231
Days After Panicle Emergence or DAPE) rather than time relative to planting 232
(DAP) [Figure 3; Supplementary file S1]. Given variation in the date of panicle 233
emergence, and the dangers of extrapolating nonparametric curves beyond the 234
range of observed data points, it must be noted that this approach meant that data 235
was available only for distinct subsets of the original 292 phenotyped sorghum 236
lines at any given time point. Day-by-day genome-wide association studies were 237
conducted from 14 days prior to panicle emergence to 10 days after panicle 238
emergence, as described above [Figure 4]. No known sorghum flowering-time loci 239
were identified using this approach, with the exception of Ma1. However, due to 240
the strong linkage between Ma1 and Dw2 genes based on previous studies it is not 241
possible to exclude the possibility that the significantly associated markers near 242
Ma1 reflect the effect of Dw2 on plant height (Quinby, 1974; Higgins et al., 2014). 243
The signal corresponding to Dw2 was identified in the DAPE GWAS analysis for 244
six days between -14 to -5 DAPE with the signal 323 kilobases from the known 245
locus. The signal corresponding to Dw1 was identified from -14 to +1 DAPE and 246
was located only 15 kilobases away from the known location of Dw1 on sorghum 247
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chromosome 9. This was closer than the 114 kilobase distance between the gene 248
and the closest significant SNP identified in DAP GWAS results [Figure S6]. Dw3 249
did not show any statistically significant signal in the DAPE based analysis but 250
was identified in some time points when plant data was compared using DAP. 251
Hence, whereas it was possible to identify all three known true-positive genes 252
controlling sorghum plant height through genome-wide association analyses at 253
individual time points, in no case were all three identified in a single analysis 254
across the approximately 60 total genome-wide association studies either 255
conducted at different time points or using different developmental landmarks. 256
Many other confounding associations were also identified. In many cases, both the 257
single most significantly associated SNP, and the "hot zone" of SNPs all showing 258
strong significant association with trait variation, were quite distant from the 259
known causal locus. However, they were still within the range expected given 260
observed LD decay rates in sorghum (Morris et al., 2013; Miao et al., 2019). 261
Mapping genes controlling variation in growth curves 262
All three known true positive height genes were identified by sequential time 263
point–based GWAS. However, there was no single time point, nor any single 264
treatment of the data (DAP or DAPE), where all three of said genes were 265
identified. Many other loci not previously reported to be linked to height were also 266
identified with equal or greater statistical support to known true positive genes 267
across many time points. In order to conduct the individual time point analyses, it 268
was necessary to fit nonparametric curves to each individual plant to impute 269
unobserved values. Functional principal component analyses [Figure 5A] was 270
employed to decompose variation among the curves into four functional principal 271
components that combined to explain >99% of the total variance in curve shape 272
among the plants in the population. The first two functional principal components 273
were able to explain >97% of total variation [Figure 5B & C]. 274
As the first two functional principal components described the vast majority of 275
the variation in patterns of change in plant growth over time, genome-wide 276
association analyses were conducted to identify genes controlling variation in these 277
two phenotypic descriptors [Figure 6; Supplementary file S1]. Sorghum lines with 278
negative scores of the first functional principal component tended to be taller 279
overall and exhibited greater increases in height during panicle emergence than 280
lines with positive scores of the second functional principal component [Figure 6A 281
& B]. Both Dw1 and Dw2 showed statistically significant associations with 282
variation in the first functional principal component, as did a single locus on the 283
short arm of chromosome 3 [Figure 6E]. Sorghum lines with negative functional 284
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principal component two scores tended to be taller prior to panicle emergence, but 285
exhibited limited additional increases in height during panicle emergence. 286
Moreover, lines with positive functional principal component two scores started 287
out shorter, but exhibited big increases in height during panicle emergence. This 288
second set of lines was taller at the end of the experiment [Figure 6C & D]. Dw3 289
showed a statistically significant association with variation in the second 290
functional principal component, as did two other regions of the genome close to 291
the centromeres of sorghum chromosomes 5 and 9 [Figure 6F]. As was seen in 292
Figure 3, none of the hits identified here overlapped with known sorghum maturity 293
genes with the exception of Ma1. However, another potential explanation was that 294
previously uncharacterized loci were controlling flowering time in the 295
environmental conditions used to conduct this study. A genome-wide association 296
analysis for days to panicle emergence identified three well-supported loci: Ma1 297
on chromosome 6 and two loci on sorghum chromosomes 1 and 10. These loci do 298
not correspond to known sorghum maturity genes [Figure S7]. However, with the 299
exception of Ma1, these loci did not overlap with regions of the genome associated 300
with height or patterns of change in height when using panicle emergence as a 301
developmental landmark [Figure 3; Figure 6]. 302
The distance between the nearest SNP significantly associated with functional 303
principal component one and Dw1 (Sobic.009G229800) is approximately 35 304
kilobases. The hot region of SNPs on chromosome 6 which are significantly 305
associated with functional principal component one spans both Dw2 306
(Sobic.006G067700) and Ma1 (Sobic.006G057866). The novel hit for functional 307
principal component one on chromosome 3 was also identified in sequential DAPE 308
GWAS analysis [Figure 4]. The same small interval on chromosome 3 where this 309
novel hit was identified was previously linked to variation in sorghum height in an 310
independent QTL mapping population (Brown et al., 2006). This hit is associated 311
with a large–17 complete genes or gene fragments–tandem array of wall-312
associated kinase (WAK) genes. WAKs play a role in cell elongation and 313
expansion and previous antisense experiments targeting genes in this family in 314
Arabidopsis produced dwarf phenotypes (Wagner and Kohorn, 2001; Lally et al., 315
2001). The distance between the nearest SNP significantly associated with 316
functional principal component two and Dw3 (Sobic.007G163800) is 317
approximately 39 kilobases. The other two significant signals for functional 318
principal component two on chromosome 5 and chromosome 9 were not associated 319
with any immediately obvious candidate genes. This may reflect the location of 320
these hits in low-recombination/high linkage-disequilibrium regions of the 321
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genome, expanding the potential distance between a trait-associated genetic 322
marker and the causal locus. 323
Discussion 324
Engineering and computational advances are making it increasingly practical to 325
dynamically monitor the trait values for organisms across time and development. 326
Time-series data provides opportunities to understand the role individual genetic 327
loci play in shaping phenotype. At the same time, extracting the greatest possible 328
insight from time-series data requires modifications to quantitative genetic 329
approaches traditionally employed for linking genotypic variation to phenotypic 330
variation across an entire population at a single point in time. Time-series data 331
from a phenotypically constrained diversity population in sorghum was used to 332
evaluate a number of approaches for leveraging time-series data to identify and 333
characterize how different loci play different roles in determining phenotype at 334
different stages of development. A key feature which enabled the analyses was that 335
three known large-effect loci controlling height were segregating in the population 336
of plants analyzed. However, these loci were not consistently identified in 337
conventional single point GWAS given the phenotypically constrained set of the 338
plants employed in the study [Figure 1]. In field studies, it is often necessary to 339
restrict the range of phenotypic diversity exhibited by an association population 340
key trait in order to obtain meaningful and comparable trait data in a single 341
environment (Hansey et al., 2011). Artificial selection also tends to reduce the 342
range of phenotypic variation present within elite populations used for crop 343
improvement (Yamasaki et al., 2007). 344
Different plants proceed through different stages of their life cycle at different 345
rates. Comparisons across varieties must, explicitly or implicitly, employ life-cycle 346
landmarks to enable comparisons across individuals. In many field studies, traits 347
are collected from terminal-stage plants, using physiological maturity as the life-348
cycle landmark for comparisons across individuals. In several other studies, 349
including many greenhouse- or growth chamber–based ones, comparisons are 350
performed at a fixed number of days after planting or days after germination, i.e., 351
using planting or germination as the life-cycle landmark. The SAP employed in 352
this study is sampled primarily from sorghum conversion lines collected from 353
around the world (Casa et al., 2008). Despite the introgression of photoperiod 354
insensitivity loci as part of the conversion process, lines vary significantly in total 355
days spent in vegetative development before transitioning to reproductive 356
development. We experimented with using either time of planting or time of 357
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panicle emergence as the life-cycle landmark for phenotypic comparisons. For 358
these particular analyses, using panicle emergence as a landmark provided 359
significantly cleaner results with identification of known height-related loci [Figure 360
4]. In general, time-series trait data enable researchers to experiment with using 361
different landmarks for comparisons across individuals in a population. The correct 362
choice in any given case will depend on the specific goal of the analyses. 363
Plant heights at different time points were extracted from hyperspectral images 364
using a semantic segmentation approach (Miao et al., 2020). Compared to widely 365
used thresholding-based whole plant segmentation approaches in RGB images, 366
semantic segmentation is able to classify each plant pixel to the corresponding 367
organ, which provides more plant height estimations at different stages of 368
development. These estimations are more comparable to measurements made by 369
hand by biologists. The approach shows generalizability within sorghum between 370
mature plants and plants at the late vegetative stage, prior to visible reproductive 371
development but after clear leaf and stalk separations (Miao et al., 2020). 372
However, one source of error with the current classification approach is a tendency 373
to misclassify leaf midribs as stem pixels, particularly early in development. In 374
early vegetative development of sorghum, the shoot apical meristem remains 375
below the soil surface, and the apparent stem is simply a whorl of multiple leaf 376
sheaths. As the dataset evaluated here consists of plants from 40 DAP onwards, it 377
is not possible to draw strong conclusions about how this approach would perform 378
for sorghum seedlings. 379
Simulation studies based on fitting parametric models have demonstrated that 380
integrating longitudinal measures of phenotypes in a single population can provide 381
increased resolution and power to identify QTLs (Sang et al., 2019). Here we 382
employed nonparametric models which required fewer initial assumptions about 383
the pattern of how phenotypes change over time (Yang et al., 2009). Like 384
parametric models, nonparametric models can be used to accurately impute trait 385
values at unobserved time points (Xu et al., 2018b). This enables the combined 386
analyses of time data from larger populations given a fixed capacity in terms of 387
number of individuals phenotyped per day. Relative to previously published 388
functional principal component analyses, the statistical approach employed here is 389
robust to small with uneven numbers of time point observations per sample. 390
Genome-wide association studies based on functional principal component 391
weightings assigned to the time-series data from individual plants, collected on 392
separate days, successfully identified all three known true positive genes 393
controlling height in sorghum. Both Dw1 and Dw2 were associated with variation 394
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in the first functional principal component of sorghum height, which exhibited a 395
consistent effect on height both before and after panicle emergence and exertion 396
[Figure 6A, B & E]. Dw3 was instead associated with the second functional 397
principal component of sorghum height, which exhibited opposite directions of 398
effect on height before and after panicle emergence and exertion [Figure 6C, D & 399
F]. Previous studies suggest that epistasis exists between Dw1 and Dw3, but they 400
are thought to act through different mechanisms or pathways to influence sorghum 401
plant height (Yamaguchi et al., 2016; Hirano et al., 2017). Dw1 influences plant 402
height through the brassinosteroid signaling pathway (Hirano et al., 2017). It 403
reduces the length of all internodes by reducing the number of cells in each 404
internode (Yamaguchi et al., 2016; Hilley et al., 2016). However, Dw3 and its 405
maize ortholog brachytic2 appear to influence plant height through auxin transport. 406
Dw3 primarily reduces the lengths of lower internodes rather than all the 407
internodes, and acts by decreasing the length of cells rather than decreasing the 408
total cell number (Multani et al., 2003; Yamaguchi et al., 2016). The molecular 409
function of Dw2 (Sobic.006G067700) is still not clear but the Sobic.006G067700 410
loss of function phenotype includes reductions in the length of all internodes, 411
which is similar to the loss of function phenotype of Dw1(Sobic.009G229800) and 412
dissimilar to the loss of function phenotype of Dw3 (Sobic.007G163800) (Hilley et 413
al., 2017). These known phenotypes and molecular functions of the three sorghum 414
dwarfing genes are consistent with the pattern observed in the FPCA-based GWAS 415
analyses where Dw1 and Dw2 are associated with a consistent effect before and 416
after panicle emergence. At the same time, Dw3 is associated with a functional 417
principle component which switches the direction of effect before and after panicle 418
emergence. 419
In addition to successfully identifying all three known true positive height genes 420
in sorghum, functional principal component–based mapping for plant height 421
exhibited much greater enrichment for these genes. Three statistically significant 422
loci were identified outside of the predefined known true positive set: the signal on 423
the short arm of chromosome three for the first functional principal component, 424
and two signals in the pericentromeric regions of chromosomes five and nine for 425
the second functional principal component. Given the broader mapping intervals 426
and slower LD decay in pericentromeric regions, it was not possible to confidently 427
conclude whether the signals on chromosomes five and nine correspond to specific 428
previous reports from QTL mapping or genome-wide association in sorghum. 429
However, the chromosome three signal associated with WAK genes was also 430
identified in the DAPE-based sequential GWAS results around panicle emergence 431
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[Figure 4]. This indicates it may play an important role in a shift in the speed that 432
booting stage occurs. This signal was also validated as corresponding to a tightly 433
mapped sorghum plant height QTL identified in a separate recombinant inbred line 434
population (Brown et al., 2006). 435
Compared to the GWAS results on terminal height collected from the field in 436
the phenotypically constrained population [Figure1C], FPCA-based GWAS 437
analyses recovered Dw1 and Dw2 identified using the whole population and also 438
identified Dw3 as well as several additional loci [Figure 6E,F; Figure1A]. 439
However, the known height locus on chromosome 6, which was identified in the 440
field-based data presented in this paper as well as in previous GWAS for sorghum 441
height, was not recovered (Li et al., 2015). Mapping genes controlling height, or 442
most other highly polygenic traits in different field seasons or locations, will tend 443
to identify only partially overlapping sets of loci. This can be a result of genotype 444
by environment interactions, where certain loci influence variation in a given trait 445
in some environments but not others. It can also be a result of stochastic noise in 446
phenotypic measurements. The statistical approaches used for GWAS are designed 447
to minimize false positives and accept a very high false negative rate. As a result, 448
modest-effect loci will rise above the noise in some experimental replications but 449
not others. Consistent with either of these explanations, the known height locus on 450
chromosome 6 was not statistically significant in a GWAS analysis for genes 451
controlling sorghum height conducted by Morris et al. (2013), but was statistically 452
significant in a separate analysis conducted for the same trait by Li et al. (2015). 453
Time-series trait data is rapidly becoming more widely available and collected 454
in a broad range of contexts: model organisms, crops, livestock, humans, etc. 455
Integrating functional principal component analyses into genome-wide association 456
studies allows the identification of known true positive genes controlling 457
phenotypic variation in populations where these genes cannot be confidently 458
identified from data at any single time point. In addition, this study demonstrates 459
that the associations of different known true positive genes with different 460
functional principal components describing variation in the target trait are 461
consistent with the known biological roles and previous quantitative genetic 462
associations of those genes. This in turn suggests that functional principal 463
component-based genome-wide association studies of time-series data can provide 464
greater insight into the distinct roles different trait-associated loci play in 465
determining variation in a single phenotype. A statistical approach to decomposing 466
patterns of phenotypic variation over time into functional principal components 467
was employed that is robust to incomplete and used uneven observations of 468
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different subsets of the population at different time points. This robust approach 469
should aid the broader adoption of functional principal component-based genome-470
wide association in a wider range of quantitative genetics contexts. 471
Materials and Methods 472
Plant materials and growth conditions 473
357 sorghum (Sorghum bicolor) lines from the SAP were planted, grown, and 474
phenotyped at (Latitude: 41.162, Longitude: -96.407) part of the University of 475
Nebraska-Lincoln’s Eastern Nebraska Research and Extension Center in 2016. 476
Plant height, defined as the distance from emergence from the soil to the top of the 477
uppermost panicle, was manually scored at maturity. Due to the height limitation 478
of the imaging chamber equipped in the high-throughput phenotyping facility in 479
the University of Nebraska-Lincoln’s Greenhouse Innovation Center (UNL-GIC) 480
(Latitude: 40.83, Longitude: -96.69), 38 lines with heights in the field >2 meters 481
were excluded from subsequent greenhouse experiments. Seeds from the 482
remaining 319 sorghum SAP lines were sown in the greenhouse of UNL-GIC on 483
June 15, 2016. Sorghum seeds were sown in 9.46-liter pots with Fafard 484
germination mix supplemented with 8.8 kg 3–4 month Osmocote and 8.8 kg 5–6 485
month Osmocote, 1 tablespoon (15 mL) of Micromax Micronutrients, and 1,800 g 486
lime per 764.5 liter (1 cubic yard) of soil. Twenty-seven sorghum lines failed to 487
germinate or failed to grow healthily under greenhouse conditions. These sorghum 488
lines were omitted from downstream analyses, leaving a total of 292 lines for 489
phenotyping. Phenotyped plants were grown under a target photoperiod of 14:10 490
day:night with supplementary light provided by light-emitting diode (LED) growth 491
lamps from 07:00 to 21:00 each day. The target temperature of the growth facility 492
was between 20–28.3°C. After growing in the greenhouse for 40 days, all the 493
plants were moved on to the conveyor belt, which transferred each pot to the 494
imaging chamber every two days and to the watering station each day to keep all 495
the plants growing under a good condition. At the watering station, plants were 496
weighed once per day and watered back to a target weight, including pot, soil, 497
carrier, and plant of 6,300 g from July 25th to August 9th, 7,000 g from August 9th 498
until the termination of the experiment August 31st–76 days after planting (DAP). 499
500
Image data acquisition 501
The imaging of all phenotyped sorghum lines commenced on July 26th and 502
continued until August 31st, 41–76 DAP. Image data was collected using the high-503
throughput phenotyping facility in UNL-GIC previously described (Ge et al., 504
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2016). Each plant was imaged every other day by a visible camera (piA2400-505
17gm, BASLER, Germany with PENTAX lens) and a hyperspectral camera 506
(Headwall Photonics, Fitchburg, MA, USA). The visible camera was used to 507
capture RGB images with the resolution 2,354 × 2,056 including two different 508
zoom levels. The first zoom level was applied at 41–53 DAP. Each pixel 509
represented an area of approximately .45mm2 for objects in the range between the 510
camera and the pot containing the plant. The second zoom level with each pixel 511
representing an area of approximately 1.8mm2 was applied after 54 DAP until the 512
termination of the experiment (76 DAP). The hyperspectral camera has a spectral 513
range of 546–1,700 nm and 243 image bands. Plants were arranged so that most 514
leaves perpendicularly face to the hyperspectral camera. A hyperspectral cube for 515
each plant were captured at a resolution of 320 × 560 pixels. For each 516
hyperspectral cube, a total of 243 separate intensity values were captured for each 517
pixel spanning the range of light wavelengths between 546–1,700 nm. A constant 518
zoom level was applied for all the hyperspectral images throughout the whole 519
experiment with each pixel representing an area of approximately 8.8 mm2. 520
Height extraction from RGB and hyperspectral images 521
The estimate of plant height in RGB images uses the green index threshold method 522
based on the equation 2×Green/(Red + Blue) (Ge et al., 2016). In this study, the 523
green index threshold 1.12 was applied to separate plant pixels from background 524
pixels. After the whole-plant segmentation was done, the number of pixels from 525
the lowermost to the uppermost of the plant in the vertical direction were counted 526
to represent the plant height in the pixel unit. The stalk plus panicle height from 527
hyperspectral images were estimated using a semantic segmentation method based 528
on the hyperspectral signatures of different sorghum organs (Miao et al., 2020). A 529
Linear Discriminant Analysis (LDA) model was adopted from the previous 530
sorghum semantic segmentation project to classify each pixel to background, leaf, 531
stalk, or panicle (Miao et al., 2020). After the semantic segmentation, the stalk plus 532
panicle plant height in the pixel unit was estimated by counting the number of stalk 533
and panicle pixels on the vertical direction. Manual proofing of growth curves was 534
used to identify and correct a modest number of cases in early time points where 535
leaf midrib pixels were misclassified as stalk pixels, resulting in incorrect 536
estimation of plant heights. These cases could also be identified as poor fits of 537
nonparametric regression curves to the problematic data point relative to its 538
neighbors. The real plant heights from RGB and hyperspectral images were 539
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obtained by using the pixel height multiplied by the ratio of the real size and pixel 540
size based on the corresponding zoom level. 541
Nonparametric fitting of growth curves and missing heights imputation 542
The growth curve of each sorghum line was obtained by fitting the heights at 543
different time points using the nonparametric regression. The missing heights were 544
also imputed. Let Yij be the jth observed phenotype of the ith plant, made at day tij, i 545
= 1, 2, ..., n, j = 1, 2, ..., mi, where mi is the total number of days observed for the 546
ith plant. To model the plant growth, the following non-parametric model was 547
employed: 548
Yij =µ(tij)+e(tij) (1) 549
where µ(·) is a mean function of the phenotype development and e(tij) is a zero-550
mean process associated with ith plant observed at tij. Let B(t) = (B1, ..., BK)T
(t) be 551
a vector of B-spline basis functions, where K is the number of basis functions. The 552
estimated mean function can be expressed as µ^ 𝑡 = 𝐵𝑇 𝑡 𝑐 = 𝐵𝑘
𝐾𝑘=1 𝑡 𝑐𝑘 , 553
where c is a vector of coefficients of length K obtained using penalized least 554
squares approach (Ramsay and Silverman, 2005; Xu et al., 2018b). 555
Functional principal component analysis (FPCA) 556
The plant growth curves over time were summarized using functional principle 557
component scores. In FPCA, the process e(tij) in (1) is decomposed into two parts: 558
𝑒 𝑡𝑖𝑗 = 𝜉𝑖,𝑙
𝐿
𝑙=1
∅𝑙 𝑡𝑖𝑗 + 𝜀𝑖𝑗
559
where ξi,l are zero-mean principal components scores with variance λl, ∅𝑙 𝑡𝑖𝑗 are 560
eigenfunctions corresponding to principal components scores, and εij are zero-mean 561
measurement errors with constant variance. In FPCA, eigenfunctions are 562
orthonormal, namely ∫∅𝑙1(t)∅𝑙2(t)dt = 0, for all 𝑙1≠ 𝑙2 and ∫ ∅𝑙2 𝑡 𝑑𝑡 = 1, so the 563
characteristics of phenotype development for the ith genotype can be represented 564
by its principal components scores ξi,l, 𝑙 = 1, 2, ..., L. The variance of the principal 565
components scores, λl,𝑙 = 1, 2, ..., L, are sorted in decreasing order, so the first few 566
principal components scores usually capture the majority of variation in the 567
phenotype data. B-spline bases were employed for the approximation of 568
eigenfunctions. The variance λl and eigenfunctions ∅𝑙 (·) are estimated by 569
eigenvalue decomposition and the principal components scores ξi,l, 𝑙 = 1, 2, ..., L 570
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are estimated using best linear unbiased prediction (Ramsay and Silverman, 2005; 571
Xu et al., 2018a). 572
Genotyping the SAP 573
DNA was extracted from seedling stage plants grown in the Beadle Center 574
Greenhouse complex at University of Nebraska-Lincoln using the same seed 575
employed for phenotyping. Sequencing libraries generated using a modified tGBS 576
protocol (Ott et al., 2017) were constructed and paired-end (151-bp read length) 577
sequenced in 8 lanes of an Illumina HiSeqX instrument. This produced an average 578
of 4 million paired-end reads per sample. The quality of raw reads was controlled 579
using the Trimmomatic/0.33 software with the parameters ’TRAILING:20’, 580
’SLIDINGWINDOW:4:20’, and ’MINLEN:40’ (Bolger et al., 2014). High-quality 581
reads were mapped to the sorghum reference genome (V4) (McCormick et al., 582
2017) using the BWA/0.7.17 MEM algorithm with default parameters (Li and 583
Durbin, 2009). After the alignment, the GATK/4.1 HaplotypeCaller function was 584
used to perform SNP calling with default parameters (McKenna et al., 2010) and 585
the raw VCF file including 358 samples was generated. Quality controls of the raw 586
VCF including missing data rate (<0.7), minor allele frequency (>0.01), and 587
heterozygous rate (<0.05) were applied using customized python scripts 588
(https://github.com/freemao/schnablelab). Missing data was then imputed using 589
Beagle/4.1 with parameters ’window=6600, overlap=1320’ (Browning and 590
Browning, 2016). The sizes of sliding windows and the overlap windows were set 591
to capture 10% of all SNPs on a given chromosome and 2% of all SNPs on a given 592
chromosome, respectively. A final set of 569,305 high-confidence SNPs was 593
generated and employed in all downstream analyses. 594
Genome-wide association study analyses 595
Three kinds of GWAS were conducted in this study: 1. Sequential GWAS of plant 596
height based on days after planting (DAP sequential GWAS); 2. Sequential GWAS 597
of plant height based on days after panicle emergence (DAPE sequential GWAS); 598
3. GWAS of the dynamic trait of the plant growth curve (FPCA GWAS). 599
For DAP sequential GWAS, the plant heights of 292 lines at each time point 600
were used as the phenotypes. As different subsets of the population were 601
phenotyped on alternating dates, height values for all plants on individual data 602
were drawn from the values for the nonparametrically fit curves for that genotype, 603
as described above. Genotype data of the 292 lines was drawn the original 604
genotype data including 358 lines from SAP. After subsetting to the data from the 605
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292 phenotyped SAP lines, any SNPs which now fell below the previous criteria 606
used to filter SNPs for the full set of 358 lines–minor allele frequency (>0.01) and 607
the heterozygous rate (<0.05)–were excluded. A total of 36 GWAS were 608
conducted from 41 DAP to 75 DAP using the same genotype data. For the DAPE 609
sequential GWAS, X-axis (time) values for individual plant growth curves were 610
recentered based on the date of panicle emergence. The panicle emergence was 611
defined when the tip of the panicle is visible from the sorghum flag leaf sheath in 612
the image. In all but thirteen cases, panicle emergence occurred within the window 613
in which image data was collected. In one case, panicle emergence occurred prior 614
to the first day of imaging; and in twelve cases, panicle emergence occurred 615
subsequent to the last day of imaging. As a result, the number of lines with 616
observed data was inconsistent across individual time points. Analyses were 617
conducted between -14 and 10 DAPE. Within this interval, observed height values 618
were present for at least 235 lines at each time point. For each time point, genotype 619
information was subset and refiltered based on the set of lines with available trait 620
data, as described above. A total of 25 GWAS were conducted from -14 to 10 621
DAPE using the corresponding customized marker datasets generated for 622
phenotyped lines at each individual time point. For the FPCA GWAS, the first and 623
second principal component (PC) scores of each sorghum line were used as trait 624
values. The genotype data used was identical to that employed for the DAP 625
sequential GWAS analyses. 626
All the GWAS were conducted using mixed linear models (MLM) implemented 627
by GEMMA/0.95 (Zhou and Stephens, 2012). The first five principal components 628
derived from the genotype data using Tassel/5.0 (Bradbury et al., 2007) were fitted 629
to MLM as the fixed effect. Meanwhile, the kinship matrix calculated using 630
“gemma -gk 1” command was fitted to MLM as the random effect. All 63 GWAS 631
jobs were run on the Holland Computing Center’s Crane cluster at the University 632
of Nebraska-Lincoln. The number of independent SNPs in each genotype data was 633
determined using the GEC/0.2 software (Li et al., 2012). A Bonferroni corrected p-634
value of 0.05 calculated based on the number of independent SNPs in each specific 635
analysis was applied as the cutoff for statistical significance in each separate 636
GWAS analysis (Yang et al., 2014). 637
638
Data and code availability 639
Both imputed and unimputed genotype datasets used in this study have been 640
deposited on Figshare (Miao and Schnable, 2019). Raw image data, including 641
RGB and hyperspectral collected from each plant at each time point are being 642
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19/30
deposited and disseminated through CyVerse (https://doi.org/10.25739/p39b-643
dz61). The R code implementing the nonparametric regression and FPCA used in 644
this study has been deposited on GitHub 645
(https://github.com/freemao/FPCA_GWAS). 646
Accession Numbers 647
Sequences for the four major genes/proteins mentioned in this paper Dwarf1 (Dw1, 648
Sobic.009G229800), Dwarf2 (Dw2, Sobic.006G067700), maturity1 (Ma1, 649
Sobic.006G057866), Dwarf3 (Dw3, Sobic.007G163800) were retrieved from v3.1.1 650
of the sorghum genome as provided in Phytozome v12.1. 651
Sequence data from this article can be found in the GenBank/EMBL data libraries 652
under accession numbers_. 653
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654
Supplemental Data 655
656
Supplemental Figure S1. The distributions of minor allele frequency (MAF) of 657
SNPs around dwarf genes. 658
in unconstrained (blue) and constrained (yellow) populations. 659
Supplemental Figure S2. Semantic segmentation of an example sorghum plant 660
using a hyperspectral image. 661
Supplemental Figure S3. Imputing unobserved height values for sorghum 662
genotypes through nonparametric regression. 663
Supplemental Figure S4. Proportion of variance explained for observed and 664
imputed plant heights. 665
Supplemental Figure S5. Summary of significant SNPs identified in independent 666
GWAS for each time point anchoring on days after planting rather than days after 667
panicle emergence. 668
Supplemental Figure S6. Manhattan plots for GWAS on height. 669
measured at 41 days after planting (Panel A) and 72 days after planting (Panel B). 670
Supplemental Figure S7. Manhattan plot for GWAS on the date of panicle. 671
emergence. 672
Supplemental Table S1. Significant SNPs identified by DAP Sequential GWAS. 673
674
675
Acknowledgements 676
This work was supported by a University of Nebraska Agricultural Research 677
Division seed grant to JCS and a National Science Foundation Award (OIA-678
1557417) to JCS. This project was completed utilizing the Holland Computing 679
Center of the University of Nebraska, which receives support from the Nebraska 680
Research Initiative. 681
Conflicts of Interest 682
JCS, PSS, and SL have equity interests in Data2Bio, a company which provides 683
genotyping services using the same protocol employed for genotyping in this 684
study. The authors affirm that they have no other conflicts of interest. 685
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Figure Legends 686
Figure 1. Reduced power to identify causal loci in phenotypically constrained 687
populations. (A) A genome wide association analyses for plant height, defined as 688
the distance between the soil surface and the top of the panicle at maturity, 689
using field collected data for 357 lines from sorghum association panel and the 690
set of genotype call data used in this study. The location of Dw1, Dw2 and Ma1 691
are indicated with dashed lines, as is an additional known height locus (KHL) 692
identified in multiple prior GWAS conducted on height in this population using 693
different genetic marker data. (B) Distribution of observed heights for the 357 694
lines employed for association analysis in panel A. The set of thirty eight lines 695
above two meters in height are marked in red. (C) An genome wide association 696
analysis identical to that shown in panel A but with the exclusion of lines with the 697
field heights >2 meters (38 lines) and those which we were not able to 698
successfully germinate and phenotype in this study (27 lines). 699
700
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22/30
Figure 2. Different methods to define and measure plant height produce 701
different outcomes. (A) Conventional RGB images of a single sorghum plant (PI 702
576401) taken on eight different days spanning the transition from vegetative to 703
reproductive development. Pixels identified as "plant" through whole plant 704
segmentation are outlined in red. Measured plant height, defined as the distance 705
between the plant pixels with the smallest and greatest y-axis value is indicated 706
by the horizontal blue bar in each image. (B) Semantically segmented images of 707
same plant taken on the same day from a moderately different viewing angle 708
using a hyperspectral camera. Pixels classified as "leaf" are indicated in green, 709
pixels classified as "stem" are indicated in orange, and pixels classified as 710
"panicle" are indicated in purple. Measured plant height, defined as the distance 711
between stem or panicle pixels with the smallest and greatest y-axis value is 712
indicated by the horizontal red bar in each image. (C) Observed and imputed 713
plant heights for the same sorghum plant on each day within the range of 714
phenotypic data collection. Blue and red circles indicate measured height values 715
from whole plant segmentation of RGB images and semantic segmentation of 716
hyperspectral images, respectively. Solid blue and solid red lines indicate height 717
values imputed for unobserved time points using nonparametric regression for 718
whole plant and semantic height datasets, respectively. 719
720
Figure 3. Comparison of change in plant height over time for members of the 721
SAP population when anchoring either on planting date (DAP) or panicle 722
emergence date (DAPE). (A) Growth curves imputed using nonparametric 723
regression for 20 representative sorghum genotypes, anchored for comparison 724
based on sharing the same date of planting. (B) Growth curves imputed using 725
nonparametric regression for the same 20 sorghum genotypes shown in panel A, 726
anchored for comparison based on sharing the same date of panicle emergence. 727
Lines with identical colors in panel A and panel B indicate data taken from the 728
same plants. Regression lines are not extended beyond the range of observed 729
datapoints. As panicle emergence occurred less than 18 days after the start of 730
imaging for some lines and less than 17 days before the last day of imaging for 731
others, curves in panel B are incomplete. 732
733
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23/30
Figure 4. Several known causal loci show statistically significant associations with 734
plant height when sequential genome wide association studies are conducted 735
using data anchored to the date of panicle emergence. A summary of where 736
statistically significant trait associated SNPs were identified in separate genome 737
wide association studies conducted using height data for each day between -14 738
to +10 days after panicle emergence (DAPE). Each vertical column summarizes 739
the results from one of the twenty-five independently conducted genome wide 740
association studies. Each sorghum chromosome is divided into sixteen bins 741
containing equal numbers of SNP markers. Each cell in each vertical column is 742
color coded based on the single most significant p-value observed for any marker 743
within that bin on that day. Light pink cells indicate bins which contain no 744
markers which exceed the multiple testing corrected threshold for statistical 745
significance. The locations of the two cloned dwarf genes and the one cloned 746
maturity gene which were successfully identified in analysis of data from at least 747
one time point are indicated with horizontal dashed lines. 748
749
750
Figure 5 Two functional principal components explain >97% of variance in the 751
sorghum growth curves observed in this study. Functional principal component 752
analysis seeks to describe the pattern of change in height over time of each 753
observed plant using a mean function combined with variable weightings of a set 754
of eigenfunctions. (A) Comparison of the empirical mean function (red) for all 755
growth curves observed in this study (gray) and the mean function estimated 756
using functional principal component analysis (blue). (B) Illustration of how 757
changing the score for functional principal component one alters the resulting 758
growth curve. (SD = Standard Deviation) (C) Illustration of how changing the score 759
for functional principal component two alters the resulting growth curve. 760
761
762
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Figure 6. Mapping genes associated with variation in functional principal 763
component scores among sorghum genotypes. (A) Distribution of functional 764
principal component one scores among the 292 genotypes phenotyped as part of 765
this study. Genotypes with the most negative values for functional principal 766
component one are indicated in red, and genotypes with the most positive values 767
for functional principal component one are indicated in blue. (B) Growth curves 768
for a subset of genotypes with the most negative values for functional principal 769
component one are indicated in red. Growth curves for a subset of genotypes 770
with the most positive values for functional principal component one are 771
indicated in blue. (C) Distribution of functional principal component two scores 772
among the 292 genotypes phenotyped as part of this study. Genotypes with the 773
most negative values for functional principal component two are indicated in red, 774
and genotypes with the most positive values for functional principal component 775
two are indicated in blue. (D) Growth curves for a subset of genotypes with the 776
most negative values for functional principal component two are indicated in red. 777
Growth curves for a subset of genotypes with the most positive values for 778
functional principal component two are indicated in blue. (E) Results of 779
conducting a genome wide association analysis for functional principal 780
component one scores. (F) Results of conducting a genome wide association 781
analysis for functional principal component two scores. In panels E and the 782
positions of three cloned dwarf genes Dw1, Dw2, and Dw3 as well as the cloned 783
maturity gene Ma1 are indicated using vertical dash lines. Horizontal dash lines 784
indicate multiple testing corrected cutoff of a statistically significant association. 785
786
787
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1
Figure 1. Reduced power to identify causal loci in phenotypically constrained populations. (A) A genome wide
association analyses for plant height, defined as the distance between the soil surface and the top of the panicle at
maturity, using field collected data for 357 lines from sorghum association panel and the set of genotype call data
used in this study. The location of Dw1, Dw2 and Ma1 are indicated with dashed lines, as is an additional known
height locus (KHL) identified in multiple prior GWAS conducted on height in this population using different genetic
marker data. (B) Distribution of observed heights for the 357 lines employed for association analysis in panel A.
The set of thirty eight lines above two meters in height are marked in red. (C) An genome wide association analysis
identical to that shown in panel A but with the exclusion of lines with the field heights >2 meters (38 lines) and
those which we were not able to successfully germinate and phenotype in this study (27 lines).
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1
Figure 2. Different methods to define and measure plant height produce different outcomes. (A) Conventional
RGB images of a single sorghum plant (PI 576401) taken on eight different days spanning the transition from
vegetative to reproductive development. Pixels identified as "plant" through whole plant segmentation are
outlined in red. Measured plant height, defined as the distance between the plant pixels with the smallest and
greatest y-axis value is indicated by the horizontal blue bar in each image. (B) Semantically segmented images of
same plant taken on the same day from a moderately different viewing angle using a hyperspectral camera. Pixels
classified as "leaf" are indicated in green, pixels classified as "stem" are indicated in orange, and pixels classified as
"panicle" are indicated in purple. Measured plant height, defined as the distance between stem or panicle pixels
with the smallest and greatest y-axis value is indicated by the horizontal red bar in each image. (C) Observed and
imputed plant heights for the same sorghum plant on each day within the range of phenotypic data collection.
Blue and red circles indicate measured height values from whole plant segmentation of RGB images and semantic
segmentation of hyperspectral images, respectively. Solid blue and solid red lines indicate height values imputed
for unobserved time points using nonparametric regression for whole plant and semantic height datasets,
respectively.
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1
Figure 3. Comparison of change in plant height over time for members of the SAP population when anchoring
either on planting date (DAP) or panicle emergence date (DAPE). (A) Growth curves imputed using nonparametric
regression for 20 representative sorghum genotypes, anchored for comparison based on sharing the same date of
planting. (B) Growth curves imputed using nonparametric regression for the same 20 sorghum genotypes shown
in panel A, anchored for comparison based on sharing the same date of panicle emergence. Lines with identical
colors in panel A and panel B indicate data taken from the same plants. Regression lines are not extended beyond
the range of observed datapoints. As panicle emergence occurred less than 18 days after the start of imaging for
some lines and less than 17 days before the last day of imaging for others, curves in panel B are incomplete.
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1
Figure 4. Several known causal loci show statistically significant associations with plant height when sequential
genome wide association studies are conducted using data anchored to the date of panicle emergence. A
summary of where statistically significant trait associated SNPs were identified in separate genome wide
association studies conducted using height data for each day between -14 to +10 days after panicle emergence
(DAPE). Each vertical column summarizes the results from one of the twenty-five independently conducted
genome wide association studies. Each sorghum chromosome is divided into sixteen bins containing equal
numbers of SNP markers. Each cell in each vertical column is color coded based on the single most significant p-
value observed for any marker within that bin on that day. Light pink cells indicate bins which contain no markers
which exceed the multiple testing corrected threshold for statistical significance. The locations of the two cloned
dwarf genes and the one cloned maturity gene which were successfully identified in analysis of data from at least
one time point are indicated with horizontal dashed lines.
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1
Figure 5. Two functional principal components explain >97% of variance in the sorghum growth curves observed in
this study. Functional principal component analysis seeks to describe the pattern of change in height over time of
each observed plant using a mean function combined with variable weightings of a set of eigenfunctions. (A)
Comparison of the empirical mean function (red) for all growth curves observed in this study (gray) and the mean
function estimated using functional principal component analysis (blue). (B) Illustration of how changing the score
for functional principal component one alters the resulting growth curve. (SD = Standard Deviation) (C) Illustration
of how changing the score for functional principal component two alters the resulting growth curve.
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1
Figure 6. Mapping genes associated with variation in functional principal component scores among sorghum
genotypes (A) Distribution of functional principal component one scores among the 292 genotypes phenotyped as
part of this study. Genotypes with the most negative values for functional principal component one are indicated
in red, and genotypes with the most positive values for functional principal component one are indicated in blue.
(B) Growth curves for a subset of genotypes with the most negative values for functional principal component one
are indicated in red. Growth curves for a subset of genotypes with the most positive values for functional principal
component one are indicated in blue. (C) Distribution of functional principal component two scores among the 292
genotypes phenotyped as part of this study. Genotypes with the most negative values for functional principal
component two are indicated in red, and genotypes with the most positive values for functional principal
component two are indicated in blue. (D) Growth curves for a subset of genotypes with the most negative values
for functional principal component two are indicated in red. Growth curves for a subset of genotypes with the
most positive values for functional principal component two are indicated in blue. (E) Results of conducting a
genome wide association analysis for functional principal component one scores. (F) Results of conducting a
genome wide association analysis for functional principal component two scores. In panels E and the positions of
three cloned dwarf genes Dw1, Dw2, and Dw3 as well as the cloned maturity gene Ma1 are indicated using vertical
dash lines. Horizontal dash lines indicate multiple testing corrected cutoff of a statistically significant association.
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