Field trial, expression profiling and phenotyping

One hundred Brassica napus plants of the winter-type accession Darmor were grown in a field in a 10x10 equispaced grid pattern with 0.5 m distance between rows and columns (Fig 1). On November 28, 2016, the eighth rosette leaf (leaf 8) of 62 non-border plants was harvested, and the harvested leaves were expression-profiled individually (see Methods and S1 Data). After leaf sampling, the plants were allowed to overwinter and set seed in spring. 62 phenotypes were recorded for all plants, ranging from rosette areas and individual leaf measurements in autumn to root and shoot measurements at harvest the following spring (S1 Data). Likely because of the low planting density, many of the plants developed one or more secondary inflorescence stems at ground level, which is not usually observed for B. napus grown under lab conditions or in the field at agronomically relevant planting densities. These secondary stems (further referred to as side stems) were harvested separately from the primary inflorescence stem with its cauline secondary inflorescences (further referred to as stem 1). Several yield phenotypes were measured for both stem 1 and the entire shoot (i.e. stem 1 plus side stems), including dry weight, seed weight, seed count and silique count. Cauline secondary inflorescence stems on stem 1 and tertiary inflorescence stems on the side stems (both further referred to as branches) were also counted, and branch counts are reported for both stem 1 and the entire shoot (the latter being the sum of branch counts on stem 1 and the side stems). Shoot growth phenotypes such as the time of maximum shoot growth, the maximum shoot growth rate and the end of shoot growth were derived from plant height time series data through curve fitting (see Methods). Several phenotypes were defined as ratios of other phenotypes, e.g. the ratio of total seed weight to shoot dry weight and the ratio of the total number of seeds to the total number of siliques per plant.

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Fig 1. Field trial layout and PCA plots for gene expression and phenotypes.

A. Plants were sown on a 10x10 equispaced grid with 0.5 m between rows and columns. Plant identifiers combine a number indicating the row (01–08) and a letter indicating the column (A-H) in which the plant was sown. Only plants with leaf 8 gene expression and phenotype profiles are labeled, border plants and grid positions at which no plants emerged are indicated by grey squares. B. Plot of the first two principal components of the leaf 8 gene expression dataset, after normalization and RNA-seq batch correction (see Methods). C. Plot of the first two principal components in the phenotype dataset. Individual plants in B and C are colored according to the color gradient in A, with similar coloring of plants indicating spatial proximity in the field.

https://doi.org/10.1371/journal.pcbi.1011161.g001

Exploratory data analysis

Principal component analysis (PCA) suggests that there are no clearly separated subpopulations of plants with distinct expression or phenotype profiles (Fig 1). A few relative outliers are visible however, e.g. plants 03C and 04G in the phenotype PCA plot (Fig 1C), both small plants that yielded few seeds (S1 Data). Single-nucleotide polymorphism (SNP) analysis of the RNA-seq data (see Methods) did not uncover signs of substantial genetic substructure in the plant population (S1 Fig).

On the other hand, mapping of the field coordinates on the expression and phenotype PCA plots (Fig 1) and analysis of the correlation of the distance between plants in transcriptome or phenotype space with the physical distance between plants in the field (S2 Fig) suggest that there is spatial structure in the data. However, the levels of only 140/76,808 transcripts (0.18%) and 1/41 phenotypes (2.44%, root system width) were found to be significantly spatially autocorrelated across the field (Moran’s I, Benjamini-Hochberg (BH) adjusted permutation test p-values (q-values) ≤ 0.05, S2 Data and S3 Fig). In a previous study on a similar number of field-grown maize plants [28], 14.17% of transcripts were found to be significantly spatially autocorrelated at q ≤ 0.01, which is considerably more than the 0.18% recovered here at q ≤ 0.05. This is mostly due to differences in the way Moran’s I values and their significance were calculated in the present study versus Cruz et al. [28] (use of a queen contiguity-based spatial weight matrix and permutation-based testing for determining p-values in the present study, versus an inverse distance-based spatial weight matrix and parametric testing in Cruz et al. [28], see Methods and S2 Data) and to a stronger effect of BH p-value adjustment for B. napus than for maize (76,808 transcripts were tested for B. napus versus 18,171 for maize). Using the method from Cruz et al. [28] on the present dataset yields 5,371/76,808 (6.99%) significantly spatially autocorrelated transcripts and 2/41 (4.88%) significantly spatially autocorrelated phenotypes at q ≤ 0.05 (S2 Data). The Spearman rank correlations between the Moran’s I values obtained by both methods are 0.8761 and 0.8645 for gene expression profiles and phenotype profiles, respectively. Although the method from Cruz et al. [28] yields more significant spatial autocorrelations, we consider the method using non-parametric permutation testing to be more reliable, as the parametric method assumes a normal distribution of the Moran’s I value under the assumption of no spatial autocorrelation, which does not always hold. The results presented below are therefore based on the method using a queen contiguity-based spatial weight matrix and permutation-based testing.

To assess whether some functional classes of genes have on average a stronger or weaker spatial autocorrelation signal than other classes, regardless of the statistical significance of the Moran’s I values, two-sided Mann-Whitney U (MWU) tests [30] were performed on the transcript list ranked in order of decreasing Moran’s I value. Genes involved in e.g. photosynthesis, translation, the response to abiotic stimuli, response to cytokinin, regulation of circadian rhythm, photoperiodism and the vegetative to reproductive phase transition were found to have a significantly higher Moran’s I on average than other genes (MWU q ≤ 0.05, S2 Data). This suggests that there is spatial patterning in the data, but that its discovery may be hampered by a lack of statistical power due to the small size of the field trial.

Most continuous phenotypes and high-count discrete phenotypes (e.g. seed and silique counts) are at least approximately normally distributed (Anderson-Darling and Shapiro-Wilk normality tests, p > 0.01, S3 Data), with the exception of five ratio phenotypes (seeds per silique, seeds per silique stem 1, seed weight/dry weight stem 1, total seed weight/shoot dry weight and branches per stem), leaf count (74 DAS) and two shoot growth phenotypes (time of max shoot growth and end of shoot growth). Many of these phenotypes exhibit relative outliers that may influence normality testing results (S4 Fig). When removing outliers (see Methods), four additional phenotypes (seeds per silique, seeds per silique stem 1, stem 1 seed weight/stem 1 dry weight, total seed weight/shoot dry weight) were found to be approximately normally distributed (Anderson-Darling and Shapiro-Wilk normality test, p > 0.01, S3 Data).

Some phenotypes were found to be more variable across the field than others. Dry weight, seed and silique phenotypes at harvest are the most variable, with coefficients of variation (CVs) between 43.7% and 51.9% (S3 Data). Taproot length also has a high CV (42.8%). Plant height (278 DAS) and shoot growth parameters exhibit the lowest CV values (< 7%). Most ratio phenotypes also have relatively low CV values (≤ 20.3%), with the exception of siliques per branch (35.3%), siliques per branch stem 1 (35.0%) and branches per stem (33.6%). When removing outliers, the CV of some of these ratio phenotypes is further reduced, notably for seed weight stem 1/dry weight stem 1 (20.3% → 9.5%), total seed weight/shoot dry weight (18.1% → 8.9%), seeds per silique (19.5% → 14.7%) and seeds per silique stem 1 (19.4% → 14.6%). Leaf and branch phenotypes generally exhibit intermediate CVs. Whereas leaf 8 fresh weight (81 DAS), leaf 8 area (81 DAS), total branch count and rosette area (42 DAS) have a CV ≥ 30%, other leaf 8 and leaf 6 phenotypes and branch count stem 1 exhibit a CV in the range 19.1%-23.2%, and leaf 8 chlorophyll content (81 DAS) has a CV of only 12.5%.

Gene expression also exhibits substantial variability across the field. Ignoring genes expressed in less than 10 samples, the median gene has an expression CV of 34.2% (S3 Data). To investigate whether some classes of genes vary more in expression than others across the field, we ranked B. napus genes based on a normalized version of their expression CV (normCV, see Methods and S3 Data). MWU tests [30] were performed to assess whether any Gene Ontology (GO) biological processes are represented more at the top or bottom of the normCV-ranked gene list than expected by chance (S3 Data). As observed in earlier studies on populations of lab-grown Arabidopsis thaliana Col-0 plants [31] and field-grown Zea mays B104 plants [28], genes involved in photosynthesis and responses to biotic and abiotic stimuli were found to be on average more variably expressed than other genes, while genes involved in housekeeping functions related to protein, RNA and DNA metabolism were found to be on average more stably expressed across the field (S3 Data). To what extent high gene expression variability is due to either variability in the levels of external stimuli experienced by the individual plants or due to a higher intrinsic noisiness of a gene’s expression levels (on the scale of entire leaves) is unclear. Some categories of genes with more variable expression across the field, such as genes involved in photosynthesis or response to abiotic stimuli, also exhibit higher Moran’s I values on average, suggesting that their variability may be linked to external stimuli that are spatially patterned. On the other hand, most genes with highly variable expression do not exhibit strong spatial patterns (S5 Fig), which indicates that their expression variability may be caused by intrinsic stochastic factors, or alternatively by extrinsic factors that are not spatially autocorrelated at the field sampling resolution employed.

Linking phenotypes to the leaf 8 expression profiles of single genes

In order to get an overall view on which leaf 8 gene expression profiles significantly relate to which phenotypes, linear mixed-effects (lme) models were used to assess the relation between each gene expression profile and each phenotype separately (further referred to as single-gene models). lme models were used for this instead of ordinary linear models because they can take into account spatial autocorrelation effects (see Methods), which can bias significance testing in ordinary linear models [32]. Between 11,986 and 14,032 gene expression profiles, out of 76,808, were found to be significantly associated (q ≤ 0.05) with leaf 8 phenotypes such as leaf 8 length, width, area and fresh weight (Table 1 and S4 Data). That leaf 8 phenotypes yield more associated genes than other phenotypes is not surprising, given that leaf 8 was used for gene expression profiling. Next to leaf 8 phenotypes, also other leaf and rosette phenotypes feature more associated genes than non-leaf phenotypes, except for leaf 6 length (74 DAS). The gene sets associated with leaf phenotypes are generally significantly enriched (hypergeometric test, q ≤ 0.05) in genes involved in e.g. response to biotic and abiotic stimuli (salt), photosynthesis, circumnutation, cell wall biogenesis, amino acid metabolism and response to sulfate and nitrogen starvation (S5 Data). Additionally, leaf phenotype-related gene lists show significant enrichment, notably among transcription factors, in genes involved in dorsal/ventral, adaxial/abaxial and radial pattern formation, phloem, xylem and procambium histogenesis, and meristem development (S5 Data).

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Table 1. Numbers of significant gene expression-phenotype associations.

https://doi.org/10.1371/journal.pcbi.1011161.t001

Interestingly, appreciable numbers of gene-phenotype associations were found as well for several phenotypes that are only distantly related in space and time to the leaf 8 material profiled for RNA-seq. In particular seed, silique and shoot dry weight phenotypes yielded high numbers of associated genes, ranging from 1,859 genes for total shoot dry weight to 1,248 genes for the silique count on stem 1 at harvest (Table 1 and S4 Data). Many of the gene sets associated with these phenotypes are enriched in genes involved in nitrate assimilation, superoxide metabolism, circumnutation, circadian rhythm, response to biotic and abiotic stimuli (cold, salt, water deprivation), response to nutrient levels (nitrogen, sulphate and phosphate starvation), and, in particular among transcription factors, phosphate ion homeostasis, histone modification, regulation of the vegetative to reproductive phase transition and floral organ morphogenesis (S5 Data). 1,110 genes were found associated with the branch count on stem 1, with GO enrichments similar to those obtained for dry weight, silique and seed phenotypes (S5 Data). In contrast, the total branch count phenotype only yields a set of 89 associated genes (Table 1 and S4 Data), which is however also strongly enriched in e.g. superoxide metabolism and salt stress genes. The fact that the total branch count is composed of cauline secondary inflorescence stems on stem 1 and tertiary inflorescence stems on the side stems may render this phenotype less relevant. No genes were found associated (q ≤ 0.05) with taproot length and only four with root system width, suggesting that autumnal leaf 8 gene expression may not contain a lot of information on root phenotypes. On the other hand, given the difficulty of recovering intact root systems from the soil, it is not excluded that root measurement errors may have influenced these results.

Phenotypes with very low CV such as leaf 8 chlorophyll content (81 DAS), the maximum shoot growth rate and end of shoot growth yielded no significantly associated genes, suggesting that the biological variation of these phenotypes is limited and that the observed variation may be dominated by technical noise (Table 1 and S4 Data). The phenotype with the lowest CV on the other hand, the time of maximal shoot growth (CV = 0.6%), features 3,498 significant leaf 8 gene expression correlates. The associated gene set is strongly enriched in genes involved in e.g. cell wall biogenesis and response to biotic stimuli (S5 Data). For plant height (278 DAS) (CV = 6.8%), 99 associated genes are found with minor GO enrichments.

Ratio phenotypes exhibit between 0 and 593 associated genes. In particular the branches per stem and siliques per branch ratios do poorly (0 and 3 associated genes, respectively). Both involve the total branch count, which is itself only associated with 89 genes. Ratios involving the branch count on stem 1 on the other hand yield between 240 and 593 associated genes. One potential reason for ratio phenotypes having at most a few hundred gene associations is that ratios suffer from increased error levels due to the propagation of measurement errors from both the numerator and denominator. This may be particularly problematic for ratios of highly correlated variables such as the seeds per silique and seed weight/dry weight phenotypes (both for stem 1 and the entire shoot), which exhibit a low CV and likely have even lower true biological variation. No genes were found associated at q ≤ 0.05 with qualitative or low-count discrete phenotypes such as rosette lesions (74 DAS), leaf 6 lesions (74 DAS), leaf 8 lesions (76 DAS) and stem count (i.e. stem 1 plus the number of side stems).

Leaf and final yield phenotypes of individual field-grown B. napus plants can be predicted to a considerable extent from their autumnal leaf 8 transcriptome

Most phenotypes feature many significantly related gene expression profiles (Table 1). To assess to what extent phenotypes can be predicted from the entire leaf 8 transcriptome, we used models using all gene expression profiles as predictive features, or a sizeable subset thereof (further referred to as multi-gene models). As the feature space (76,808 gene expression profiles) is huge compared to the number of samples (62 plants), simply using ordinary linear models or lme models with all gene expression values as features makes no sense, as there’s a myriad different ways to perfectly explain a given phenotype for 62 plants from 76,808 gene expression profiles. Most of these models will be seriously overfit and will generalize badly to unseen data. Instead, we used elastic net [33] and random forest [34] models. Elastic net (enet) is a regularized regression method that uses a penalty on the sum of feature coefficient magnitudes (L1-norm, as in lasso) and an additional penalty on the magnitude of the coefficient vector (L2-norm or Euclidean norm, as in ridge regression) to shrink the feature coefficients and limit the amount of features used to explain an outcome variable, with the purpose of reducing overfitting and hence enhancing the generalizability of the resulting model to unseen data. Random forest (RF) reduces overfitting by training a ‘forest’ of decision trees, in which each tree is trained on a dataset sampled with replacement from the original data, and at each tree split only a random subset of features are taken into account as possible predictors. The predicted outcome for a given input is then taken to be the average of the output of the different trees in the forest. The main reason for using both enet and RF models is that the former can only capture linear relationships in the data, while the latter can also capture non-linear effects.

Models were learned using either the set of all genes (n = 76,808) or the (much smaller) set of all transcription factors (TFs, n = 2,521) as features. In both cases, to further reduce the number of features used to train the machine learning models, we used a priori feature selection to select subsets of features that are potentially interesting. As different feature selection techniques may have different biases, we used three different feature selection techniques, namely HSIC lasso [35], a Spearman correlation filter and a filter selecting only genes with median rlog gene expression > 0 (see Methods).

To assess to what extent the models generalize to unseen data, the enet and RF models were trained in a 10-fold cross-validation setup (i.e. the data was split in 10 data subsets, each set was selected in turn as the test set, the model was trained on the remaining 9 sets and applied to the test set, see Methods). To assess the variance of the test set predictions, the 10-fold cross-validation procedure was repeated 9 times with different splits, giving rise to 90 test sets and 9 test set predictions per plant for each combination of phenotype, model type (RF or enet), potential feature set (all genes or TFs) and feature selection technique. The best model for a given phenotype and potential feature set was taken to be the one with the highest median test R² value across all 90 test sets for continuous and high-count phenotypes (see Methods), or the highest median test accuracy for qualitative or low-count discrete phenotypes (Table 2 and S6 Data).

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Table 2. Best-performing multi-gene and single-gene models for each phenotype.

https://doi.org/10.1371/journal.pcbi.1011161.t002

Not surprisingly, leaf 8 phenotypes, which are most closely related in space and time to the material sampled for transcriptome profiling, are the most predictable. Except for the leaf 8 chlorophyll content at sampling time (81 DAS), which features very poor prediction performance, the median test R² scores for leaf 8 phenotypes range from 0.48 to 0.70 when using all genes as potential features. Other leaf-related phenotypes such as leaf 6 width (74 DAS, median test R² = 0.38), rosette area (42 DAS, median test R² = 0.23) and leaf 6 length (74 DAS, median test R² = 0.07) are comparatively less predictable.

Surprisingly, many of the final seed, silique and shoot dry weight phenotypes are more predictable from the autumnal leaf 8 transcriptome than leaf 6 and rosette phenotypes, with seed weight on stem 1 rivaling the leaf 8 phenotypes in terms of median test R² value (Table 2, S6 Data and Figs 2 and S6). All seed weight, seed and silique count and shoot dry weight phenotypes have median test R² values in the range [0.35, 0.51] for the all-genes models, which is in all cases higher than the 95^th percentile of test R² values obtained from single train-test splits on 90 datasets in which the phenotype values were permuted (S6 Data). In other words, the model for the real data train-test split with median test R² outperforms 95% of the models for comparable train-test splits on randomized data. Note that this serves only as an indication of model performance on real versus randomized data, not as a formal test assessing whether the median test R² score on real data is significantly higher than expected at random. The latter would require the 9 times repeated 10-fold cross-validation setup used on the real data to be used on each of the permuted datasets as well (instead of the single train-test split per permutation used here), which is computationally prohibitive.

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Fig 2. Predictions versus observations for the best-scoring leaf and yield phenotypes.

A. Predicted versus measured values for leaf 8 width (76 DAS), using the all-genes model with the best median test R² score (enet + median feature selection, Table 2). B. Predicted versus measured values for seed weight stem 1, using the all-genes model with the best median test R² score (enet + Spearman feature selection, Table 2). Vertical grey lines range from the minimum to the maximum predicted value for a given plant across all model repeats, and colored dots represent predictions for the repeat with the median pooled R² score (i.e. the R² score of the pooled test set predictions in the repeat concerned). Different marker colors indicate the 10 different test sets in this repeat. Perfect predictions are located on the dashed diagonal line in each panel. Similar plots for other phenotypes are presented in S6 Fig.

https://doi.org/10.1371/journal.pcbi.1011161.g002

Interestingly, seed count and weight, silique count and dry weight phenotypes measured for stem 1 are generally slightly more predictable than the corresponding phenotypes measured for the entire shoot, with median test R² score differences between stem 1 and total shoot phenotypes in the range [0.02, 0.09] for the all-genes models and [0.05, 0.13] for the TF models. This suggests that gene expression levels in leaf 8 of the rosette may be more predictive for phenotypes of stem 1 (i.e. the primary inflorescence stem and its cauline secondary inflorescences) than for phenotypes measured on the whole shoot (i.e. including the secondary inflorescence stems branching at ground level).

Root phenotypes, branching phenotypes, final plant height (278 DAS) and shoot growth phenotypes are generally poorly predictable (Table 2). Plant height and shoot growth phenotypes are likely poorly predictable because they show little variation across the field (S3 Data), increasing the risk that measurement error outweighs biological variation. Also taproot length and root system width may suffer from measurement errors. The total branch count and branch count stem 1 phenotypes on the other hand have a high CV and likely limited measurement error, suggesting that leaf 8 gene expression profiles may contain less information on these branching phenotypes than on leaf, seed, silique and dry weight phenotypes.

Most phenotypes calculated as ratios of other phenotypes are very poorly predictable, even if the constituent phenotypes have high prediction performance values. For instance, the median test R² value for seeds per silique (total seed count divided by total silique count) in the best all-genes model is negative (-0.14), whereas both total seed count and total silique count have median test R² values ≥ 0.38 (Table 2). In many cases however, the numerator and denominator phenotypes of a ratio are highly correlated, leading to a derived phenotype with a small range that may be dominated by noise propagated from measurement errors in the constituent phenotypes rather than biological variability. The number of siliques per branch on stem 1 and the entire shoot are notable exceptions with high CV values and reasonable prediction performance in the best all-genes models (Table 2). The latter ratio phenotypes are highly correlated with the number of siliques on stem 1 (PCC = 0.92) and the entire shoot (PCC = 0.72), respectively, indicating that the number of siliques per branch is an important determinant of silique count, in addition to the number of branches (PCC between total branch count and total silique count = 0.87, PCC between branch count stem 1 and silique count stem 1 = 0.82).

The best all-genes model and best TF model generally have comparable performance for leaf 8 phenotypes, seed count and weight phenotypes, silique count phenotypes and branch count phenotypes, with median test R² differences (median test R² of best all-genes model—median test R² of best TF model) for these phenotypes in the range [-0.07, 0.08] (Table 2). In most of these cases, the median test R² score of the all-genes model is slightly higher than that of the TF model, but whether these differences are significant is hard to assess, as a commonly accepted framework for assessing the significance of out-of-sample R² differences between models is currently lacking. The R² differences between the best all-genes and TF models for dry weight phenotypes range from 0.05 to 0.10, suggesting that all-genes models may perform slightly better than TF models for these phenotypes. Among the other phenotypes for which either the best all-genes or best TF model has a median test R² score higher than the 95^th percentile of test R² values obtained on permuted data (S6 Data, stars in Table 2), the best all-genes models for leaf 6 width (74 DAS) and siliques per branch stem 1 have a substantially higher median test R² score than the corresponding best TF models (R² difference = 0.31 and 0.23, respectively), while the best TF models for leaf count (74 DAS), rosette area (42 DAS) and root system width have a higher R² score than the corresponding best all-genes models (R² difference = -0.16, -0.13 and -0.16, respectively). In summary, the all-genes and TF models exhibit similar overall performance, in particular for the most predictable phenotypes. This indicates that, from the perspective of quantitative phenotype prediction, most of the information present in the complete gene expression dataset is also present in the TF gene expression data subset.

To compare multi-gene models, with either all genes or all TFs as potential features, to single-gene models in terms of phenotype prediction performance, we used the same repeated cross-validation setup as used for the multi-gene models to calculate median test R² scores and median pooled PCC values for single-gene models (lme models with spatial structure, see previous section). Cross-validation scores were calculated for each of the 100 genes most significantly associated with a given phenotype (lowest q-value for gene coefficient in lme model, S4 and S6 Data).

For leaf 8 phenotypes, the best multi-gene models and best single-gene models have comparable median test R² scores (ΔR² in the range [-0.05, 0.03], with ΔR² = max(median test R² of best all-genes model, median test R² of best TF model)−median test R²of best single-gene model, Table 2). In other words, multi-gene models offer no benefit over single-gene models for quantitative prediction of leaf 8 phenotypes. Single- and multi-gene models also have comparable prediction performance for many of the yield traits measured on the entire shoot, such as total seed weight, total seed count, total silique count and total dry weight with and without seeds (ΔR² in the range [-0.05, 0.06], Table 2). There is also little difference in prediction performance for the dry weight of stem 1 with and without seeds (ΔR² = 0.04 and 0.03, respectively). Many of the seed and silique traits related to stem 1 on the other hand (seed weight, seed count and silique count on stem 1, the number of siliques per branch on stem 1) are somewhat better predicted by multi-gene models than by single-gene models (ΔR² in the range [0.09, 0.12], Table 2). This indicates that several distinct gene expression patterns may be relevant for quantitative prediction of stem 1 seed and silique traits.

For several other phenotypes, single-gene models outperform multi-gene models, sometimes with a wide margin, e.g. for plant height (278 DAS) (ΔR² = -0.18), branch count on stem 1 (ΔR² = -0.19) and leaf 6 length (74 DAS) (ΔR² = -0.24). This suggests that the multi-gene models are vulnerable to overfitting. In particular phenotypes with low single-gene model performance tend to exhibit a multi-gene model performance that is even lower, suggesting that the extent of multi-gene model overfitting is inversely correlated with the proportion of trait variance explained by single genes. An alternative explanation for the observation that the best single-gene models sometimes outperform the corresponding multi-gene models may be the ‘winner’s curse’ effect, also known as selection bias [36], whereby the apparently best-performing single-gene models may overestimate prediction performance.

For most ratio phenotypes, both the multi-gene and single-gene models have very poor prediction performance, in particular when the numerator and denominator phenotypes that make up the ratio are very highly correlated. In these cases, the denominator is essentially already a good predictor of the numerator. To assess whether any gene expression profiles contain additional information on the numerator given knowledge of the denominator, we used alternative single-gene models with a log link (see Methods) to predict the numerators of the seeds per silique ratio on stem 1 and the branches per stem ratio (seed count stem 1 and total branch count, respectively) conditioned on their denominator (silique count stem 1 and stem count, respectively). These models are not suited for making predictions in practice, given the need to know the denominator, but they may indicate whether prediction of the ratio based on gene expression is at all feasible and if so, which genes may be important. If no genes are found to be predictive for the numerator (and hence the ratio) conditioned on the denominator, then attempts to predict the ratio phenotype unconditionally are likely to be unsuccessful. For both seeds per silique stem 1 and branches per stem, the fitted coefficients and residuals look reasonable for the best predictor genes (S7 and S8 Figs). The corresponding models succeed in suppressing a few of the more extreme residuals of the base model (without gene expression effect), without improving predictions for most other plants. However, no gene coefficients were found to be significantly different from zero for either phenotype after BH correction (q ≤ 0.05), neither in models assuming constant error variance nor in models with heteroscedastic and/or spatially covarying error structures (see Methods). This indicates that the poor performance of the original multi-gene and single-gene models for these phenotypes is to be expected.

Top predictors for leaf phenotypes

The best multi-gene prediction performance scores were obtained for leaf 8 phenotypes. To assess whether the genes featuring most prominently in the multi-gene models for leaf phenotypes make biological sense, we focused on the top-10 predictor lists of the TF-based models for leaf 8 length and width (76 DAS and 81 DAS), fresh weight (81 DAS) and area (81 DAS), and leaf 6 length and width (74 DAS) (S6 Data). As these leaf phenotypes are generally highly correlated (PCC between leaf 8 phenotype in the range [0.78,0.97], PCC between leaf 8 and leaf 6 phenotypes in range [0.45, 0.60]), many of the most important predictors (TFs) in the random forest and elastic net models are shared among phenotypes. We therefore grouped the top-10 predictor lists for the different phenotypes in two sets, one for the RF models (Fig 3, n = 42) and one for the enet models (S9 Fig, n = 35). The rationale for looking at the TF models instead of the models built on all genes is that TFs are more likely than the average gene to have been functionally characterized to some extent, and are more likely to be causally involved in phenotype regulation (although it needs to be stressed that our analysis remains entirely correlational). Given the relative lack of experimentally determined gene functions in B. napus, most of the functional interpretation given below and in S7 Data for B. napus genes is based on experimentally determined functions of likely orthologs in A. thaliana (see Methods).

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Fig 3. Top predictor genes in RF models of leaf phenotypes.

A clustered heatmap of the z-scored gene expression profiles of the top genes for predicting leaf phenotypes is shown centrally (blue-red color scale, Ward.D2 hierarchical clustering). The leaf phenotypes concerned and their z-scored profiles across plants are shown at the bottom (dark blue-yellow heatmap with plant identifiers at the bottom). For each of these phenotypes, the top-10 most important genes (highest median gini importance across all 90 cross-validation splits) of the RF model with the highest median test R² score are included on the figure (gene identifiers are shown at right). The mostly dark blue score panel to the left of the expression heatmap shows the median gini importance scores of the selected genes in each of the selected phenotype models, normalized to the maximum importance score per model to make the color scales of the different models (columns) comparable. The mostly yellow frequency panel to the left of the score panel shows the frequencies at which genes were selected as features across all 90 cross-validation splits of a given model. Grey squares in the score and frequency panels indicate that a given gene was not selected as a feature in a given model. The phenotypes in the score and frequency panels are identified by numbers (1–8) on top of the panels, corresponding to the numbers associated with the phenotypes in the bottom phenotype panel. On top of the score panel, the feature selection techniques used in the best-scoring RF models for each phenotype are shown (median = selection of features with median rlog gene expression > 0, spearman = Spearman correlation, hsic-5000 = HSIC lasso, see Methods), as well as the corresponding test and pooled R² scores rounded to the nearest 0.1 and then multiplied by ten (e.g. a test R² score of 0.38 would be denoted as 4). Genes that are also found in the top-10 enet predictor lists for leaf phenotypes (S9 Fig) are highlighted in red, while genes that are also found in the top-10 enet or RF predictor lists for yield phenotypes (Figs 4 and S10) are highlighted in blue. Genes found in both the top-10 enet predictor lists for leaf phenotypes and the top-10 enet or RF predictor lists for yield phenotypes are highlighted in magenta.

https://doi.org/10.1371/journal.pcbi.1011161.g003

Many of the top TF predictors for leaf phenotypes have A. thaliana orthologs that have known functions in leaf development or exhibit overexpression, knockout or other mutant phenotypes related to leaf development (details in S7 Data). Both the RF and enet top predictor lists contain BnaCnng05590D and BnaA05g33840D, putative orthologs of the homeodomain leucine zipper class I (HD-ZIP I) gene ARABIDOPSIS THALIANA HOMEOBOX 1 (AtHB1/AT3G01470). The enet top predictor list for leaf phenotypes also contains another HD-ZIP I gene, BnaC02g43700D, which is putatively orthologous to AtHB5 (AT5G65310) or AtHB16 (AT4G40060). Both AtHB1 and AtHB16 exhibit mutant phenotypes related to leaf development, seed yield and the timing of the vegetative-to-reproductive phase transition (S7 Data).

The RF and enet top predictor lists also contain several other HD-ZIP genes. BnaA06g18550D in the RF top predictor list is putatively orthologous to the A. thaliana HD-ZIP III gene REVOLUTA (AtREV/AT5G60690), which is involved in regulating postembryonic meristem initiation [37] and several polarity-associated growth processes in A. thaliana, including abaxial-adaxial patterning in leaves [38] (S7 Data). Additionally, BnaC06g05240D and BnaA06g01940D in the RF top predictor list are HD-ZIP III genes putatively orthologous to AtHB8 (AT4G32880) or AtHB15 (AT1G52150). AtHB8 and AtHB15 are thought to have effects on postembryonic meristem initiation that are antagonistic to the effects of AtREV [39], and to function prominently in vascular development, possibly antagonistically [40–43]. Furthermore, the enet top predictor list includes the HD-ZIP II gene BnaC03g02700D, putatively orthologous to AtHAT3 (AT3G60390), AtHAT14 (AT5G06710), AtHB17 (AT2G01430) or AtHB18 (AT1G70920). AtHAT3 is known to be involved in leaf abaxial/adaxial patterning [44], and to be regulated by AtREV [45].

Both the RF and enet top predictor lists prominently feature putative orthologs of A. thaliana WUSCHEL RELATED HOMEOBOX (AtWOX) genes: BnaA05g27750D (RF and enet) and BnaC05g41930D (enet). Both genes are putatively orthologous to AtWOX5 (AT3G11260) or AtWOX7 (AT5G05770). Next to roles in root development, AtWOX5 is known to also have functions in leaf development (S7 Data).

Not all transcription factors in the RF and enet models are equally important for all leaf phenotypes. BnaCnng06440D (AtMYB60/AT1G08810) for instance has higher RF and (to a lesser extent) enet importance scores for leaf 8 area (81 DAS) and leaf 8 fresh weight (81 DAS) than for other leaf phenotypes. Its likely A. thaliana ortholog AtMYB60 is involved in regulating stomatal opening, and its expression is downregulated under drought [46] (S7 Data). A second TF in the RF models with higher importance for leaf 8 area (81 DAS) and leaf 8 fresh weight (81 DAS) than for other leaf phenotypes is BnaC06g36000D (AtHB33/AtZHD5/AT1G75240). Its likely ortholog AtHB33 codes for a zinc-finger homeodomain TF downregulated in response to abscisic acid (ABA), which e.g. induces stomatal closure [47]. A third TF in the RF models with mildly higher importance for leaf 8 area (81 DAS) and leaf 8 fresh weight (81 DAS) is BnaCnn59450D, whose putative orthologs AtSHN2 (AT5G11190) and AtSHN3 (AT5G25390) have been linked to regulation of stomatal density and drought response [48] (S7 Data).

Both the RF and enet top-10 lists feature several orthologs of A. thaliana NUCLEAR FACTOR Y, SUBUNIT A (AtNF-YA) genes (putative A. thaliana orthologs in parentheses): BnaAnng02740D (AtNF-YA2/10, AT3G05690/AT5G06510, RF), BnaA10g24470D (AtNF-YA2/10, AT3G05690/AT5G06510, RF and enet), BnaC06g33980D (AtNF-YA3/8, AT1G72830/AT1G17590, enet) and BnaC01g37260D (AtNF-YA5/6, AT1G54160/AT3G14020, RF). All four genes are negatively correlated with leaf phenotypes in the field expression dataset (S4 Data). NF-Y transcription factor complexes are heterotrimers, consisting of A, B and C subunits, that function in various developmental programs and abiotic stress responses in plants [49]. Various AtNF-YA gene family members were previously found to function in the regulation of leaf size, drought resistance or the juvenile-to-adult (vegetative) phase change (S7 Data).

Interestingly, several of the top-TFs recovered in the multi-gene models for leaf phenotypes are linked to the regulation of flowering. Plant NF-Y complexes for instance are known to also function in the regulation of flowering time (S7 Data) [49]. It has been suggested that the photoperiodic flowering regulator CONSTANS (AtCO) may compete with NF-YA subunits in the NF-Y complex to form an alternative complex activating FLOWERING LOCUS T (FT) expression in A. thaliana, thereby promoting flowering [50]. AtHB1, AtHB16 and AtHB15, the A. thaliana orthologs of several of the aforementioned B. napus HD-ZIP genes, have also been linked to regulation of the juvenile-to-adult and/or vegetative-to-reproductive phase changes [42, 51, 52]. Furthermore, both the enet and RF predictor lists contain BnaA06g39930D, a putative ortholog of EARLY FLOWERING MYB PROTEIN (AtEFM/AT2G03500) in A. thaliana. AtEFM is known to directly repress the expression of FLOWERING LOCUS T (AtFT, AT1G65480) in the leaf vasculature, and is thought to mediate the effects of temperature and light cues on the timing of the floral transition [53]. The RF predictor list additionally contains BnaC05g31460D, a putative ortholog of AtJMJD5 (AtJMJ30, AT3G20810), the protein product of which interacts with AtEFM to repress AtFT [53]. The RF and enet top predictor lists also contain BnaA07g12050D, a putative ortholog of the floral homeotic gene APETALA2 (AtAP2/AT4G36920) or the related AtTOE3 (AT5G67180). Both AtAP2 and AtTOE3 are known to repress AGAMOUS (AtAG) expression during floral patterning [54].

In summary, 15/42 and 11/35 transcription factors in the RF and enet lists of top leaf phenotype predictors, respectively, have putative A. thaliana orthologs linked to leaf development and patterning, the juvenile-to-adult phase change, the floral transition or drought response (S7 Data).

Top predictors for seed, silique and shoot dry weight phenotypes

Next to leaf 8 phenotypes, also the seed, silique and shoot dry weight phenotypes (further referred to as ‘yield’ phenotypes) of the individual plants at harvest (late spring) could be predicted to a considerable extent from autumnal leaf 8 transcriptome data (see above). Similar to the leaf phenotypes, the yield phenotypes are highly correlated (PCC range [0.84–0.99]) and hence have a lot of high-scoring RF and enet predictors in common (S6 Data and Figs 4 and S10). Furthermore, these phenotypes are also significantly correlated with leaf phenotypes (PCC range [0.47, 0.74]), leading to a substantial overlap between the top-10 predictor lists of yield and leaf phenotypes.

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Fig 4. Top predictor genes in enet models of yield phenotypes.

A clustered heatmap of the z-scored gene expression profiles of the top genes for predicting yield phenotypes is shown centrally (blue-red color scale, Ward.D2 hierarchical clustering). The yield phenotypes concerned and their z-scored profiles across plants are shown at the bottom (dark blue-yellow heatmap with plant identifiers at the bottom). For each of these phenotypes, the top-10 most important genes (highest median elastic net coefficients across all 90 cross-validation splits) of the enet model with the highest median test R² score are included on the figure (gene identifiers are shown at right). The mostly green-blue score panel to the left of the expression heatmap shows the median elastic net coefficients of the selected genes in each of the selected phenotype models, normalized to the maximum coefficient per model to make the color scales of the different models (columns) comparable. The mostly yellow frequency panel to the left of the score panel shows the frequencies at which genes were selected as features across all 90 cross-validation splits of a given model. Grey squares in the score and frequency panels indicate that a given gene was not selected as a feature in a given model. The phenotypes in the score and frequency panels are identified by numbers (1–8) on top of the panels, corresponding to the numbers associated with the phenotypes in the bottom phenotype panel. On top of the score panel, the feature selection techniques used in the best-scoring enet models for each phenotype are shown (median = selection of features with median rlog gene expression > 0, spearman = Spearman correlation, hsic-5000 = HSIC lasso, see Methods), as well as the corresponding test and pooled R² scores rounded to the nearest 0.1 and then multiplied by ten (e.g. a test R² score of 0.38 would be denoted as 4). Genes that are also found in the top-10 RF predictor lists for yield phenotypes (S10 Fig) are highlighted in red, while genes that are also found in the top-10 enet or RF predictor lists for leaf phenotypes (Figs 3 and S9) are highlighted in blue. Genes found in both the top-10 RF predictor lists for yield phenotypes and the top-10 enet or RF predictor lists for leaf phenotypes are highlighted in magenta.

https://doi.org/10.1371/journal.pcbi.1011161.g004

In particular, virtually all TF genes in the leaf top-10 predictor lists with links to the juvenile-to-adult or vegetative-to-reproductive phase changes and flowering also feature prominently in the RF or enet top-10 predictor lists for yield phenotypes, including the AtHB1 ortholog BnaCnng05590D, the AtHB5/16 ortholog BnaC02g43700D, the AtAP2 ortholog BnaA07g12050D and the AtNF-YA orthologs BnaAnng02740D, BnaA10g24470D, BnaC06g33980D and BnaC01g37260D. Furthermore, like the top predictor lists for leaf phenotypes, the enet top predictor list for yield phenotypes contains a putative ortholog of AtEFM, but a different one (BnaAnng34750D) (S7 Data).

Furthermore, many of the top predictor TF genes for yield phenotypes that are absent from the top-10 predictor lists for leaf phenotypes also have A. thaliana orthologs involved in processes related to the floral transition and flowering. In the combined set of top-10 enet predictors for shoot dry weight, seed and silique phenotypes (Fig 4, n = 29), five genes code for AGAMOUS-LIKE MADS-box transcription factors: BnaC05g17630D (AtAGL104/AT1G22130), BnaA02g15390D (AtAGL12/AT1G71692), BnaA02g00370D (BnFLC.A2, AtFLC/AT5G10140), BnaA01g02900D (AtAGL16/AT3G57230), and BnaA09g53680D (AtAGL30/AT2G03060). BnFLC.A2 is orthologous to A. thaliana FLOWERING LOCUS C (AtFLC), a key repressor of the floral transition [55, 56]. Two AGAMOUS-LIKE genes feature in the combined set of top-10 RF predictors for yield phenotypes (S10 Fig, n = 21): BnaA02g15390D (AtAGL12/AT1G71692) and BnaA09g05500D (AtAGL8/AtFUL/FRUITFULL/AT5G60910). AtFUL is thought to regulate the floral transition downstream of AtFT in the shoot apical meristem, partially redundantly with AtSOC1 (AtAGL20, AT2G45660) [57, 58] (S7 Data).

The enet top predictor list also features BnaA09g18260D, a HD-ZIP II gene putatively orthologous to JAIBA (AtJAB/AtHAT1/AT4G17460) or AtHAT2 (AT5G47370). AtJAB was shown to be involved in male and female reproductive development and floral meristem determination in A. thaliana [59] (S7 Data). The enet top predictor list also contains the HD-ZIP IV gene BnaA09g50360D (AtHDG2/AT1G05230). A combination of hdg2 and pdf2 null mutant alleles in A. thaliana was shown earlier to produce flowers with sepaloid petals and carpeloid stamens [60].

Furthermore, the gene BnaA08g12050D is ranked highly in both the enet and RF top predictor lists. The best candidate ortholog of this gene in A. thaliana is AtMYB3R1 (AT4G32730), coding for a regulator of cell proliferation that acts in a module with AtTSO1 to balance cell proliferation with differentiation in developing roots and shoots [61]. BnaA08g12050D also features as a predictor for leaf 6 length (74 DAS) and leaf 8 area (81 DAS) in S9 Fig.

BnaC07g27110D and BnaC01g22040D in the enet predictor list are putative orthologs of AtGATA16 (AT5G49300) and AtGATA17 (AT3G16870) or AtGATA17L (AT4G16141), respectively. Evidence suggests these and other LLM-domain B-GATA transcription factors are involved (at least partially redundantly) in the regulation of flowering time, silique length, seed set and other developmental processes [62]. The enet top predictor list also contains BnaC04g33670D and BnaA08g16860D, BZIP genes putatively orthologous to the A. thaliana genes DRINK ME (AtDKM/AtBZIP30/AT2G21230) and DRINK ME-LIKE (AtDKML/AtBZIP29/AT4G38900), respectively. AtDKM and AtDKML are negative regulators of reproductive development and growth (S7 Data). AtDKM was shown to interact in planta with several regulators of meristem development, including WUSCHEL (AtWU), HECATE1 (AtHEC1), the aforementioned JAIBA and NGATHA1 (AtNGA1) [63]. Interestingly, the RF top predictor list contains a putative ortholog of NGATHA1 (AtNGA1/AT2G46870) or NGATHA2 (AtNGA2/AT3G61970), namely BnaA09g39540D. AtNGA1 and AtNGA2 are known to be involved in gynoecium development [64, 65] and were recently shown to also have a function in regulating shoot apical meristem development [66]. Another likely regulator of meristem development, BnaC07g43590D, is found in the enet predictor list. BnaC07g43590D is most likely an ortholog of ARABIDOPSIS RESPONSE REGULATOR 10 (AtARR10/AT4G31920) or 12 (AtARR12/AT2G25180), both known to directly activate the expression of WUSCHEL and to play a role in shoot apical meristem regeneration and maintenance [67].

In summary, 16/29 and 11/21 TF genes in the enet and RF lists of top yield predictors, respectively, have putative A. thaliana orthologs linked to the juvenile-to-adult phase change, the floral transition, flowering or regulation of meristem development.

Predicting final yield phenotypes from early growth phenotypes

As a baseline to assess the prediction performance of the molecular models, we trained models predicting plant phenotypes in spring (mostly phenotypes at harvest) from single or multiple autumnal leaf and rosette phenotypes. For these single- and multi-phenotype models, the same modeling approaches were used as for the single- or multi-gene models, respectively (see Methods).

Interestingly, many of the mature plant phenotypes can be predicted to a considerable extent from phenotypes measured earlier in the growing season (Table 3 and S8 Data). In particular the models for phenotypes measured on the entire shoot (total seed, silique and branch count, total seed weight, total shoot dry weight) perform surprisingly well. For most of these phenotypes, the performance of the early-phenotype models is only slightly less than that of the best single-gene or multi-gene model, and the early-phenotype models for total seed weight and total branch count even outperform the molecular models (ΔR² = −0.04 and −0.14, with ΔR² = max(median test R² of best multi-gene model, median test R² of best single-gene model)−max(median test R² of best multi-phenotype model, median test R² of best single-phenotype model), Tables 2 and 3). Also for branching phenotypes related to stem 1 (branch count stem 1, branch count stem 1/length stem 1), the best early-phenotype models feature high prediction performance scores. For other stem 1 phenotypes however (seed weight, seed count, silique count and siliques per branch on stem 1, stem 1 dry weight with and without seeds), the molecular models clearly outperform the early-phenotype models (ΔR² in range [0.09, 0.23], Tables 2 and 3).

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Table 3. Best-performing multi-phenotype and single-phenotype models for mature plant phenotypes.

https://doi.org/10.1371/journal.pcbi.1011161.t003

Most multi-phenotype models with appreciable prediction performance (median test R² > 0.10), both for whole-shoot and stem 1 phenotypes, feature leaf 8 area (81 DAS) as the top predictor (Table 3). Leaf 8 area (81 DAS) is generally also the most predictive early phenotype in the corresponding sets of single-phenotype models. The multi-phenotype models with the best prediction performance scores, i.e. those for whole-shoot phenotypes and stem 1 branching phenotypes (but not the other stem 1 phenotypes), generally also feature rosette area (42 DAS) as a predictor of some importance (S8 Data). For total branch count, branch count stem 1 and branch count stem 1/length stem 1, rosette area (42 DAS) is even the top predictor in either the RF or enet model, or both (S8 Data). Rosette area (42 DAS) itself is only moderately predictable from the leaf 8 molecular data, which may explain why multi-phenotype models are better at predicting these branching phenotypes than multi-gene models.

Our results indicate that the leaf 8 molecular data offer little benefit over early-phenotype measurements for quantitative prediction of mature phenotypes measured on the entire plant. On the other hand, the leaf 8 molecular data yields substantially better models than the early-phenotype data for most mature stem 1 phenotypes. Often, the multi-gene models for stem 1 phenotypes are also slightly better than the multi-gene models for the corresponding whole-plant phenotypes (see previous section). This suggests that the molecular makeup of the 8th rosette leaf at the time of sampling contained more information on the development of the primary flowering stem and its cauline secondary inflorescences than on the development of side stems at ground level. Early phenotypes on the other hand may contain more information on whole-plant yield phenotypes than on phenotypes specifically related to stem 1.

Given that even the earliest of the autumnal phenotypes considered thus far, the rosette area at 42 DAS, still has some predictive power for several yield phenotypes (median test R² > 0.10 for total branch count, seed count, seed weight and silique count, total dry weight with and without seeds, branch count stem 1 and branch count stem 1/length stem 1), we assessed whether earlier rosette areas (v2, see Methods) are also predictive for these phenotypes (Fig 5 and S9 Data). Median test R² scores were found to decrease when using earlier rosette areas as predictors, with rosette areas measured ≤ 28 DAS generally yielding low (< 0.10) and in many cases negative median test R² scores. When using the earliest rosette area (14 DAS) as predictor, the median pooled R² and PCC scores are however still in the ranges [0.05, 0.20] and [0.27, 0.45], respectively, indicating that even the earliest rosette area measurements contain some information on final yield phenotypes (S9 Data).

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Fig 5. Predictive power of early rosette areas for yield phenotypes.

In each subplot, median test R² values are plotted for lme models predicting the given phenotype from early rosette areas v2 (14–42 DAS, x-axis). Only mature phenotypes that can be predicted from rosette area (42 DAS) with a median test R² > 0.1 are shown. Blue lines are ordinary least-squares linear regressions, with shaded areas indicating 95% confidence intervals on the trendline. Most phenotypes exhibit a rather dichotomous median test R² profile with rosette areas v2 from 14 to 28 DAS yielding substantially lower median test R² values than rosette areas v2 from 32 to 42 DAS. Accordingly, linear model fits at 28 and 32 DAS are often poor.

https://doi.org/10.1371/journal.pcbi.1011161.g005

Field trial setup

Seeds from the winter-type Brassica napus accession Darmor (BnASSYST-120) were sown in a field in Merelbeke, Belgium (50°58’24.9"N 3°46’49.1"E) on September 8, 2016. Three seeds were sown at ~2 cm depth at each of 100 points arranged in a 10x10 grid with 0.5 m spacing within and between rows. Seedlings were thinned out to leave one seedling growing at each grid point. Early- and late-emerging seedlings were pruned preferentially (based on visual assessment) to make the remaining seedling population as homogeneous as possible. At two points, no seedlings emerged.

Plots of Miscanthus sinensis, M. sacchariflorus and Miscanthus hybrids were grown to the northeast and southeast of the B. napus field trial, and maize was grown to the northwest, at distances > 5 m. The field plot was surrounded by chicken wire and covered by netting to keep out birds and large herbivores. The netting was removed in spring when plants grew taller than ~1 m. Additionally, perimeter fencing was used to protect the field trial and the mobile weather station on site (see S1 Data for weather station data).

After germination, individual plant images were taken twice a week between September 22 and October 20, 2016 (9 time points) to assess the projected leaf area of the growing rosettes. Nadir images were taken using a D90 camera (Nikon Inc., USA) equipped with a 35 mm lens (AF-S DX Nikkor 35 mm F1.8G, Nikon Inc., USA) set at iso 200, f/8. The shutter speed could vary to allow for a proper exposure, determined by the camera. The camera/tripod was positioned away from the sun to avoid shadows in the images taken. For each time point a grey calibration card (Novoflex grey card 15 x 20 cm, NOVOFLEX Präzisionstechnik GmbH, Germany) was used to correct the white balance. This card was also used as reference to convert pixels to areas in cm² (see below). The ground sampling difference (GSD) was 0.015 cm/pixel.

At 74 DAS, the length and width of leaf 6 (counting upward from the first true leaf) were measured non-destructively, leaf 6 lesion and total rosette lesion severity were scored and the number of fully emerged rosette leaves (area > ~2 cm²) was recorded. At 76 DAS, leaf 8 length and width were measured and leaf 8 lesions were scored. The width of leaf blades was measured at the widest point. Leaf lengths were measured from the leaf tip to the point where the petiole first lacked conspicuous laminar tissue (looking from the leaf tip toward the base). Lesion severity was scored qualitatively on a scale from 0 (lesions cover at most five percent of the leaf blade or rosette) to 2 (more than half of the leaf or rosette eaten).

At 81 DAS, on November 28, 2016, the eighth rosette leaves of 62 non-border plants (i.e. the plants at all non-border locations where seedlings emerged) were harvested for RNA-sequencing in a time span of ~1 hour (13:25–14:27). Leaves were cut off where the petiole first lacked conspicuous laminar tissue (looking from the leaf tip toward the base) and washed with DEPC-treated and sterilized water. The chlorophyll content of each leaf was measured at four different positions on the leaf with a CCM-200 chlorophyll content meter (Opti-Sciences, Inc., Hudson, USA), and the average of these measurements was used in the analyses. Leaves were then photographed twice against a white background with a piece of millimeter paper to assess the image scale and perspective, a ruler, and color and greyscale references, the second time covered with a glass plate to flatten them. Next, the midvein of every leaf was cut out using scissors, and the residual leaf material was folded into a pre-weighed 50 ml tube. The filled 50 ml tube and the midvein were weighed together to measure leaf fresh weight, after which the tube was stored in liquid nitrogen on the field. The entire leaf processing pipeline, from cutting a leaf to storing it in liquid nitrogen, was completed for each leaf in less than 5 minutes.

After leaf sampling, the plants were left to overwinter and set seed in spring. After bolting, plant height was measured from ground level to the top of the primary flowering stem at 13 time points between 189 and 231 DAS (S1 Data). One of the plants sampled in autumn for RNA-seq, 01C, did not survive until the end of the growth season. The remaining 61 non-border plants were harvested on June 13, 2017 (278 DAS), at which time ~50% of seeds had started changing color from green to black but no significant pod shattering or seed predation had occurred. Final plant height at 278 DAS was measured on the field, from ground level to the top of the primary flowering stem. Afterwards, shoots were cut off and the root systems were dug up. Taproot length was measured from ground level to the deepest root tip. Root system width was measured perpendicular to the taproot at the root system’s widest point.

For each harvested plant, the primary flowering stem plus its cauline secondary inflorescences (stem 1) and the secondary inflorescence stems branching at ground level (side stems) were dried in two separate bags in a well-ventilated, dry attic. The number of branches and siliques per stem, the total shoot dry weight and the dry weight of stem 1 were measured on dried plants. Seeds were recovered manually from the dried-out pods for stem 1 and the side stems separately, and separated from dust and small pod debris using a customized seed aspirator with vibration channel (Baumann Saatzuchtbedarf GmbH, Waldenburg, Germany). The resulting seed batches for stem 1 and the side stems were weighed and counted using an elmor C3 seed counter (elmor AG, Schwyz, Switzerland). Seed counts and weights are reported for stem 1 and the entire plant (i.e. the sum of stem 1 and the side stems).

Determination of shoot growth parameters

Shoot growth parameters (time of maximum shoot growth t_m, maximum shoot growth rate and the end of shoot growth t_e) were derived by fitting a beta-sigmoid growth curve to the time series of 14 plant height measurements between 189 and 278 DAS [84]: (Eq 1)

With h(t) the plant height at plant age t, h₀ and h_max the initial and final plant height at t = 0 and t = t_e, respectively, t_e the plant age at the end of growth and t_m the plant age at the moment of maximal growth. Before curve fitting, the time points in day of year (DOY) at which the plant heights were measured were translated to plant ages t in growing degree days (GDD), i.e. with i the time point in DOY, T_j the average air temperature at j DOY (S1 Data) and T_b = 5°C a base temperature below which no growth is assumed to occur [70, 85]. Optimization of the parameters h₀, h_max, t_e and t_m was done with the nls function in R using the ‘port’ algorithm. The maximum shoot growth rate was obtained by calculating the derivative of h(t) (Eq 1) at t_m. After curve fitting, the values obtained for t_m and t_e were converted back from GDD to DOY and subsequently to DAS.

Image-based phenotyping

Leaf 8 areas (81 DAS) were estimated by segmenting the flattened leaf images taken at the time of leaf harvest. The millimeter grid scale on each image was used to correct for perspective distortion and to create a uniform spatial resolution across the entire image of 100 pixels per cm. Images were cropped to remove the grid scale and sample label. Segmentation was done by training a U-Net convolutional neural network [86] on a small dataset of 25 images for which random patches of foreground and background were annotated using VGG Image Annotator (via) v:2.0.7 [87]. Random cropping, resizing, rotating (by multiples of 90 degrees), mirroring, color-jittering and gaussian blurring were applied to artificially increase the training dataset size. The training was done using the Adam optimizer [88] in Pytorch v:1.7.1 [89] with default settings. The pixel-wise cross-entropy loss was back-propagated only for annotated regions of each image. The learning rate was initially set to 1e-3 and was automatically halved as soon as the minimal training loss stagnated for more than 3 epochs. The network was trained for 16 epochs. The trained network was validated by visually evaluating it on unseen images, and then applied to all flattened leaf images.

Leaf 8 length and width at 81 DAS were measured on the flattened leaf images using ImageJ v:1.50 [90]. For measuring leaf 8 length, the midvein was traced from the leaf tip to the cutting point (i.e. where the petiole first lacked conspicuous laminar tissue) using the ImageJ segmented line tool. Leaf 8 width was measured at the widest point.

For measuring the projected area of the rosettes photographed at 42 DAS (i.e. the rosette imaging date closest to leaf sampling), a dedicated script was developed using the image analysis software HALCON (version 13.0.1.1, MVTec Software GmbH, Germany). First, the images were cropped to remove parts of adjacent plants visible on the pictures. To remove noise, both a gentle Gaussian filter and a median filter were applied. Each RGB image was then converted to the HSV color space, where the Hue channel was used to select the green plant parts using a threshold range for the green pixels (34–80) defined based on trial and error. Care was taken to also include the petioles. After this, a ‘closing_circle’ operator was used and remaining small lesions (due to insect damage) were filled up using the ‘fill_up’ operator. Only the largest segmented area was taken into account, to differentiate between the plant of interest and small weeds nearby.

The HALCON segmentation strategy worked well for the rosette images taken at 42 DAS, but regularly produced segmentation errors for images of smaller rosettes taken closer to the sowing date. An alternative segmentation approach was therefore used on rosette images taken at 14, 18, 21, 25, 28, 32, 35 and 39 DAS (and 42 DAS as control). The main difficulty for the earlier time points is distinguishing small rosettes from weeds and other distracting objects occurring on the field. This requires an algorithm with a larger field of view than what a HALCON script or standard U-net (see above) can provide. Instead, a standard pre-trained DenseNet M161 [91] was taken and augmented with additional bilinear upsampling layers after each ‘dense’ layer of the original algorithm. That is, the last feature layer of DenseNet was upsampled with bilinear interpolation and a weighted sum was made with the higher resolution ‘dense’ features. This was repeated for each dense layer up to the original input resolution. The network was trained for 175 epochs (final mean epoch loss = 0.01) on 54 hand-labeled images (6 images per time point) using stochastic gradient descent (SGD) with momentum (learning rate = 0.001 and momentum = 0.99). The learning rate was divided by 10 each time the train loss plateaued for more than 4 epochs. Image rotations, mirroring and HSV augmentations were used to augment the training data. The trained model was used to segment all rosette images. After segmentation, a post-processing step was performed to remove segmented parts of B. napus plants adjacent to the plant of interest and remaining weeds, using scikit-image v: 0.19.2 [92]. Only the connected component closest to the centroid of the image and other components within a 25-pixel distance of this central component (e.g. leaves of which the stalk was segmented incorrectly because of a lower chlorophyll content) were associated with the plant of interest. Connected components with an area less than 10,000 pixels were filtered out to eliminate small weeds. This approach was evaluated visually for all segmentations and proved to work well for most plants. Segmentations with missing plant parts or weeds that weren’t filtered out by this post-processing step were manually corrected. A grey calibration card (Novoflex grey card 15 x 20 cm, NOVOFLEX Präzisionstechnik GmbH, Germany) was used as a reference to convert pixels to areas in cm². The projected rosette areas at 42 DAS estimated by this segmentation approach exhibit a Pearson correlation of 0.997 with the areas estimated by the aforementioned HALCON script.

RNA sequencing

The frozen leaf samples for the 62 harvested non-border plants were grinded, and total RNA was extracted using the guanidinium thiocyanate-phenol-chloroform extraction method using TRI-reagent (Thermo Fisher Scientific) followed by DNA digestion using the RQ1 RNase-free DNase kit (Promega). ds cDNA was prepared using the Maxima H Minus Double-Stranded cDNA Synthesis Kit (#K2561, Thermo Fisher Scientific) to a concentration of ~17–38 ng/ul in 10mM Tris-Cl buffer (pH 8.5) at a minimum volume of 30ul. (~0.6–1.1 ug total). ds cDNA samples were sent to the University of Missouri Genomics Technology Core, where library preparation was performed (average insert size of 500 bp) using the Illumina TruSeq DNA PCR-Free Library Prep Kit according to the protocol described in [93]. 250 bp paired-end sequencing was performed at the Tufts University Genomics Core on an Illumina HiSeq 2500 machine in Rapid Run mode. The samples were sequenced in 3 batches (S1 Data).

The raw RNA-seq data was processed using a custom Galaxy pipeline [94] implementing the following steps. First, the fastq files were quality-checked using FastQC (v:0.5.1) [95]. Next, Trimmomatic (v:0.32.1) [96] was used to remove adapters, read fragments with average quality below 20 and trimmed reads shorter than 125 base pairs. The trimmed and filtered reads were mapped to the Brassica napus Darmor-bzh reference genome v:5 (https://www.genoscope.cns.fr/brassicanapus/data/) [83] using HISAT2 v:2.0.5 [97] with default values for all parameters. Only the uniquely mapping reads or (in the case of multiple mappings) the best secondary alignment were kept for the following analyses. The mapping files were quantified using HTSeq v:0.6.1p1 [98] with the option ‘Intersection-union’, using the genome annotation of the Brassica napus Darmor-bzh reference genome v:5 (https://www.genoscope.cns.fr/brassicanapus/data/). No filtering steps were performed during preprocessing except for removing genes that were not expressed in any samples. Counts were normalized across samples and batches using a modified regularized log (rlog) model of the DESeq2 [99] package in R. Counts are still modeled in the same way as in the original rlog implementation, that is: (Eq 2)

Where k_ij∈ℕ⁺ is the count of gene i in sample j, which is assumed to be sampled from a negative binomial distribution (NB) with estimated mean μ_ij∈ℝ⁺ and estimated dispersion of the ith gene α_i. μ_ij is taken as the expected count q_ij for a ‘typical’ library size (i.e. with a size factor s_j = 1), scaled by a library size normalization factor s_j for sample j. Note that q_ij still contains batch effects: x_j∈ℝ^p is a vector of p = 65 predictors for sample j, including an intercept, 2 dummy variables for the smallest sequencing batches (1 and 3) that capture batch effects relative to the largest sequencing batch (2, the effects of which are absorbed in the intercept) and dummy variables for each of the 62 plants that were sampled. β_i∈ℝ^p contains the estimated coefficients for those predictors for gene i. As in [99], an empirical Bayes shrinkage procedure is used to estimate β_i, using a flat prior for the intercept β_i0 and the sequencing batch coefficients, and a zero-centered normal prior for each plant coefficient (with p_j the index of the plant corresponding to sample j), with prior variance estimated using quantile matching as described in Love et al. [99]. There are only two differences compared to Love et al. [99]: the first is the addition of two batch coefficients as fixed effects in the design matrix, and the second is that log-fold changes used in the prior random effect variance computation are estimated relative to the mean of each batch instead of to the mean of all samples. Once the model is estimated, rlog counts are computed as in Love et al. [99], that is: (Eq 3)

Note that all samples j belonging to the same plant (technical repeats) have the same value for . The modified rlog transformation removes library size effects and batch effects, unites technical repeats into one estimate and log-transforms the data (reducing heteroscedasticity) in a single step. In addition, using random effects for each plant allows pooling information from technical repeats while simultaneously basing variance estimates on all samples (including samples without technical repeats). This method therefore makes maximal use of the available data. The resulting data is show in S11 Fig.

SNP detection and population structure analysis

Trimmed and filtered RNA-seq reads were aligned to the Brassica napus Darmor-bzh reference genome v:5 (https://www.genoscope.cns.fr/brassicanapus/data/) [83] using HISAT2 v:2.0.5 [97] with default values for all parameters. Genomic variants were detected for each plant using NGSEP v:3.3.2 [100] on the aligned reads. For downstream analyses, we focused on biallelic SNPs with a minimum genotype quality of 40 and called in at least 49 samples (80% of the population). Missing calls were imputed using Beagle v:5.1 [101] using default parameters, and only SNPs with minor allele frequency (MAF) ≥ 0.05 after imputation were kept, resulting in a dataset of 23,188 SNPs.

A neighbor-joining tree was made based on the SNP dataset with TASSEL v:5.2.60 [102], using 1-IBS (identity by state) as the distance measure while setting the distance from an individual to itself to zero. The tree was rendered using the polar tree layout in FigTree v:1.4.3 [103].

Spatial autocorrelation analysis

Moran’s I was calculated for each gene (phenotype) as . Where x is a column vector of rlog gene expression (phenotype) values, n is the number of samples and w is the sum of elements of the connectivity matrix C. For C a binary n×n queen contiguity-based spatial weight matrix was chosen, meaning that neighboring horizontal, vertical and diagonal plants are seen as connected. Note that C can differ from one phenotype to the next since not all phenotypes were available for all samples. For each gene (phenotype), the Moran’s I was recalculated on 10⁵ random permutations of x to obtain an empirical null distribution, which was then compared to the real Moran’s I to obtain a p-value. Finally, p-values were adjusted for multiple testing across all genes (phenotypes) using the BH procedure [104]. All calculations were done using the PySAL python library [105].

To assess the cause of the qualitative difference between the results obtained with the method above on the present dataset and the results obtained with a different method on a maize single-plant dataset in Cruz et al. [28], we also calculated Moran’s I values and their significance as in Cruz et al. [28], using an inverse distance-based spatial weight matrix and parametric testing as implemented in the R package ape v:5.7 [106]. p-values were again adjusted for multiple testing across all genes (phenotypes) using the BH procedure [104].

Variance analysis

Principal component analysis was done on various normalized versions of the gene expression count matrix and on the phenotype dataset (including qualitative phenotypes such as leaf 6 lesion severity (74 DAS) but excluding the plant height and rosette area time series except for the final time points, i.e. plant height (278 DAS) and rosette area (42 DAS)), using the ‘prcomp’ function in the R stats package on the centered gene expression datasets and the ‘ppca’ method in pcaMethods v:1.88.0 [107] on the z-scored phenotype dataset. Phenotype distributions were plotted using the ‘histogram’ function in Matlab R2018b with probability normalization option. Shapiro-Wilk and Anderson-Darling tests were performed using the ‘normalitytest’ script [108] and ‘adtest’ functions in Matlab R2018b, respectively. Outliers were defined as values more than three scaled median absolute deviations (MAD) away from the median, as is default in the Matlab R2018b ‘isOutlier’ function. Outliers were only removed for the purpose of calculating their effect on the phenotypes’ normality and coefficient of variation, all other analyses used the complete phenotype dataset.

Normalized coefficients of variation (normCVs) for gene expression profiles were computed on batch and library size corrected data (without rlog transform). Normalized counts were obtained as where is the batch effect for gene i in sample j as estimated in the rlog calculation (see above). Since batch 2 is absorbed in the intercept, for samples of batch 2. Contrary to the rlog transform, this method does not collapse technical repeats, and they were instead collapsed by averaging (as in S11 Fig, panel B, but without the log₂-transform). From here on, variance analysis followed the same procedure as described in Cruz et al. [28]. Briefly, a trendline was fitted to the CV² versus mean expression relationship (omitting genes expressed in < 10 samples) using a generalized linear model of the gamma family with identity link of the form , with fitting parameters a and b [109] (S12 Fig). Code from the M3Drop R package [110] was used for this purpose. A normalized CV accounting for the observed mean-variance relationship was then calculated as where is the fitted value at the mean of x.

GO enrichment analysis

A Gene Ontology annotation for Brassica napus was generated using the TRAPID v.2.0 platform [111] with default parameters on April 16, 2020. Transcript sequences parsed from the B. napus Darmor-bzh reference genome annotation v:5 [83] using the gffread v.0.9.6 utility [112] were used as input for TRAPID, and PLAZA 4.5 dicots [113] was used as the reference database. GO enrichment p-values were calculated with hypergeometric tests and adjusted for multiple testing (q-values) using the BH procedure [104], either using custom R scripts or using BiNGO v:3.0.3 [114]. GO categories gravitating toward the top or bottom of gene lists ranked in order of decreasing Moran’s I or normalized CV were detected using two-sided Mann-Whitney U tests (with genes belonging to the GO category of interest classified as group 1 and other genes as group 2), as implemented in the ‘wilcox.test’ function in the R stats package v:4.0.5, followed by BH p-value adjustment.

Ortholog inference

Putative A. thaliana orthologs of B. napus genes were identified in two steps. First, putative orthologs of B. napus genes were identified in B. rapa and B. oleracea (source of the A and C subgenomes of B. napus, respectively), based on best similarity hits returned by TRAPID v.2.0 [111] and on the syntenic relationships reported in Chalhoub et al. [83] and Sun et al. [115]. Second, putative A. thaliana orthologs of the identified B. rapa and B. oleracea genes were retrieved from PLAZA 4.5 dicots [113], which provides orthology inferences integrating four different lines of evidence: orthogroup inference within gene families using OrthoFinder [116], orthology inference using gene tree-species tree reconciliation, orthology inference from best DIAMOND [117] hits and their inparalogs, and positional orthology inference through collinearity analysis [118]. The most likely A. thaliana orthologs of a given B. napus gene were taken to be the putative orthologs that are most strongly supported across both inference steps.

Single-feature phenotype prediction models

Multi-feature phenotype prediction models