A conceptual framework for the dynamic modeling of time-resolved phenotypes for sets of genotype-environment-management combinations: a model library.

Introduction: Dynamic crop growth models are an important tool to predict complex traits, like crop yield, for modern and future genotypes in their current and evolving environments, as those occurring under climate change. Phenotypic traits are the result of interactions between genetic, environmental, and management factors, and dynamic models are designed to generate the interactions producing phenotypic changes over the growing season. Crop phenotype data are becoming increasingly available at various levels of granularity, both spatially (landscape) and temporally (longitudinal, time-series) from proximal and remote sensing technologies. Methods: Here we propose four phenomenological process models of limited complexity based on differential equations for a coarse description of focal crop traits and environmental conditions during the growing season. Each of these models defines interactions between environmental drivers and crop growth (logistic growth, with implicit growth restriction, or explicit restriction by irradiance, temperature, or water availability) as a minimal set of constraints without resorting to strongly mechanistic interpretations of the parameters. Differences between individual genotypes are conceptualized as differences in crop growth parameter values. Results: We demonstrate the utility of such low-complexity models with few parameters by fitting them to longitudinal datasets from the simulation platform APSIM-Wheat involving in silico biomass development of 199 genotypes and data of environmental variables over the course of the growing season at four Australian locations over 31 years. While each of the four models fits well to particular combinations of genotype and trial, none of them provides the best fit across the full set of genotypes by trials because different environmental drivers will limit crop growth in different trials and genotypes in any specific trial will not necessarily experience the same environmental limitation. Discussion: A combination of low-complexity phenomenological models covering a small set of major limiting environmental factors may be a useful forecasting tool for crop growth under genotypic and environmental variation.

Identification of environment types and adaptation zones with self-organizing maps; applications to sunflower multi-environment data in Europe.

KEY MESSAGE: We evaluate self-organizing maps (SOM) to identify adaptation zones and visualize multi-environment genotypic responses. We apply SOM to multiple traits and crop growth model output of large-scale European sunflower data. Genotype-by-environment interactions (G × E) complicate the selection of well-adapted varieties. A possible solution is to group trial locations into adaptation zones with G × E occurring mainly between zones. By selecting for good performance inside those zones, response to selection is increased. In this paper, we present a two-step procedure to identify adaptation zones that starts from a self-organizing map (SOM). In the SOM, trials across locations and years are assigned to groups, called units, that are organized on a two-dimensional grid. Units that are further apart contain more distinct trials. In an iterative process of reweighting trial contributions to units, the grid configuration is learnt simultaneously with the trial assignment to units. An aggregation of the units in the SOM by hierarchical clustering then produces environment types, i.e. trials with similar growing conditions. Adaptation zones can subsequently be identified by grouping trial locations with similar distributions of environment types across years. For the construction of SOMs, multiple data types can be combined. We compared environment types and adaptation zones obtained for European sunflower from quantitative traits like yield, oil content, phenology and disease scores with those obtained from environmental indices calculated with the crop growth model Sunflo. We also show how results are affected by input data organization and user-defined weights for genotypes and traits. Adaptation zones for European sunflower as identified by our SOM-based strategy captured substantial genotype-by-location interaction and pointed to trials in Spain, Turkey and South Bulgaria as inducing different genotypic responses.

Reconstruction of Networks with Direct and Indirect Genetic Effects.

Genetic variance of a phenotypic trait can originate from direct genetic effects, or from indirect effects, i.e., through genetic effects on other traits, affecting the trait of interest. This distinction is often of great importance, for example, when trying to improve crop yield and simultaneously control plant height. As suggested by Sewall Wright, assessing contributions of direct and indirect effects requires knowledge of (1) the presence or absence of direct genetic effects on each trait, and (2) the functional relationships between the traits. Because experimental validation of such relationships is often unfeasible, it is increasingly common to reconstruct them using causal inference methods. However, most current methods require all genetic variance to be explained by a small number of quantitative trait loci (QTL) with fixed effects. Only a few authors have considered the "missing heritability" case, where contributions of many undetectable QTL are modeled with random effects. Usually, these are treated as nuisance terms that need to be eliminated by taking residuals from a multi-trait mixed model (MTM). But fitting such an MTM is challenging, and it is impossible to infer the presence of direct genetic effects. Here, we propose an alternative strategy, where genetic effects are formally included in the graph. This has important advantages: (1) genetic effects can be directly incorporated in causal inference, implemented via our PCgen algorithm, which can analyze many more traits; and (2) we can test the existence of direct genetic effects, and improve the orientation of edges between traits. Finally, we show that reconstruction is much more accurate if individual plant or plot data are used, instead of genotypic means. We have implemented the PCgen-algorithm in the R-package pcgen.

From QTLs to Adaptation Landscapes: Using Genotype-To-Phenotype Models to Characterize G×E Over Time.

Genotype by environment interaction (G×E) for the target trait, e.g. yield, is an emerging property of agricultural systems and results from the interplay between a hierarchy of secondary traits involving the capture and allocation of environmental resources during the growing season. This hierarchy of secondary traits ranges from basic traits that correspond to response mechanisms/sensitivities, to intermediate traits that integrate a larger number of processes over time and therefore show a larger amount of G×E. Traits underlying yield differ in their contribution to adaptation across environmental conditions and have different levels of G×E. Here, we provide a framework to study the performance of genotype to phenotype (G2P) modeling approaches. We generate and analyze response surfaces, or adaptation landscapes, for yield and yield related traits, emphasizing the organization of the traits in a hierarchy and their development and interactions over time. We use the crop growth model APSIM-wheat with genotype-dependent parameters as a tool to simulate non-linear trait responses over time with complex trait dependencies and apply it to wheat crops in Australia. For biological realism, APSIM parameters were given a genetic basis of 300 QTLs sampled from a gamma distribution whose shape and rate parameters were estimated from real wheat data. In the simulations, the hierarchical organization of the traits and their interactions over time cause G×E for yield even when underlying traits do not show G×E. Insight into how G×E arises during growth and development helps to improve the accuracy of phenotype predictions within and across environments and to optimize trial networks. We produced a tangible simulated adaptation landscape for yield that we first investigated for its biological credibility by statistical models for G×E that incorporate genotypic and environmental covariables. Subsequently, the simulated trait data were used to evaluate statistical genotype-to-phenotype models for multiple traits and environments and to characterize relationships between traits over time and across environments, as a way to identify traits that could be useful to select for specific adaptation. Designed appropriately, these types of simulated landscapes might also serve as a basis to train other, more deep learning methodologies in order to transfer such network models to real-world situations.

Combining Crop Growth Modeling and Statistical Genetic Modeling to Evaluate Phenotyping Strategies.

Genomic prediction of complex traits, say yield, benefits from including information on correlated component traits. Statistical criteria to decide which yield components to consider in the prediction model include the heritability of the component traits and their genetic correlation with yield. Not all component traits are easy to measure. Therefore, it may be attractive to include proxies to yield components, where these proxies are measured in (high-throughput) phenotyping platforms during the growing season. Using the Agricultural Production Systems Simulator (APSIM)-wheat cropping systems model, we simulated phenotypes for a wheat diversity panel segregating for a set of physiological parameters regulating phenology, biomass partitioning, and the ability to capture environmental resources. The distribution of the additive quantitative trait locus effects regulating the APSIM physiological parameters approximated the same distribution of quantitative trait locus effects on real phenotypic data for yield and heading date. We use the crop growth model APSIM-wheat to simulate phenotypes in three Australian environments with contrasting water deficit patterns. The APSIM output contained the dynamics of biomass and canopy cover, plus yield at the end of the growing season. Each water deficit pattern triggered different adaptive mechanisms and the impact of component traits differed between drought scenarios. We evaluated multiple phenotyping schedules by adding plot and measurement error to the dynamics of biomass and canopy cover. We used these trait dynamics to fit parametric models and P-splines to extract parameters with a larger heritability than the phenotypes at individual time points. We used those parameters in multi-trait prediction models for final yield. The combined use of crop growth models and multi-trait genomic prediction models provides a procedure to assess the efficiency of phenotyping strategies and compare methods to model trait dynamics. It also allows us to quantify the impact of yield components on yield prediction accuracy even in different environment types. In scenarios with mild or no water stress, yield prediction accuracy benefitted from including biomass and green canopy cover parameters. The advantage of the multi-trait model was smaller for the early-drought scenario, due to the reduced correlation between the secondary and the target trait. Therefore, multi-trait genomic prediction models for yield require scenario-specific correlated traits.

Exome sequences and multi-environment field trials elucidate the genetic basis of adaptation in barley.

Broadening the genetic base of crops is crucial for developing varieties to respond to global agricultural challenges such as climate change. Here, we analysed a diverse panel of 371 domesticated lines of the model crop barley to explore the genetics of crop adaptation. We first collected exome sequence data and phenotypes of key life history traits from contrasting multi-environment common garden trials. Then we applied refined statistical methods, including some based on exomic haplotype states, for genotype-by-environment (G×E) modelling. Sub-populations defined from exomic profiles were coincident with barley's biology, geography and history, and explained a high proportion of trial phenotypic variance. Clear G×E interactions indicated adaptation profiles that varied for landraces and cultivars. Exploration of circadian clock-related genes, associated with the environmentally adaptive days to heading trait (crucial for the crop's spread from the Fertile Crescent), illustrated complexities in G×E effect directions, and the importance of latitudinally based genic context in the expression of large-effect alleles. Our analysis supports a gene-level scientific understanding of crop adaption and leads to practical opportunities for crop improvement, allowing the prioritisation of genomic regions and particular sets of lines for breeding efforts seeking to cope with climate change and other stresses.

Tracing the ancestry of modern bread wheats.

For more than 10,000 years, the selection of plant and animal traits that are better tailored for human use has shaped the development of civilizations. During this period, bread wheat (Triticum aestivum) emerged as one of the world's most important crops. We use exome sequencing of a worldwide panel of almost 500 genotypes selected from across the geographical range of the wheat species complex to explore how 10,000 years of hybridization, selection, adaptation and plant breeding has shaped the genetic makeup of modern bread wheats. We observe considerable genetic variation at the genic, chromosomal and subgenomic levels, and use this information to decipher the likely origins of modern day wheats, the consequences of range expansion and the allelic variants selected since its domestication. Our data support a reconciled model of wheat evolution and provide novel avenues for future breeding improvement.

Modelling strategies for assessing and increasing the effectiveness of new phenotyping techniques in plant breeding.

New types of phenotyping tools generate large amounts of data on many aspects of plant physiology and morphology with high spatial and temporal resolution. These new phenotyping data are potentially useful to improve understanding and prediction of complex traits, like yield, that are characterized by strong environmental context dependencies, i.e., genotype by environment interactions. For an evaluation of the utility of new phenotyping information, we will look at how this information can be incorporated in different classes of genotype-to-phenotype (G2P) models. G2P models predict phenotypic traits as functions of genotypic and environmental inputs. In the last decade, access to high-density single nucleotide polymorphism markers (SNPs) and sequence information has boosted the development of a class of G2P models called genomic prediction models that predict phenotypes from genome wide marker profiles. The challenge now is to build G2P models that incorporate simultaneously extensive genomic information alongside with new phenotypic information. Beyond the modification of existing G2P models, new G2P paradigms are required. We present candidate G2P models for the integration of genomic and new phenotyping information and illustrate their use in examples. Special attention will be given to the modelling of genotype by environment interactions. The G2P models provide a framework for model based phenotyping and the evaluation of the utility of phenotyping information in the context of breeding programs.

Improvement of Predictive Ability by Uniform Coverage of the Target Genetic Space.

Genome-enabled prediction provides breeders with the means to increase the number of genotypes that can be evaluated for selection. One of the major challenges in genome-enabled prediction is how to construct a training set of genotypes from a calibration set that represents the target population of genotypes, where the calibration set is composed of a training and validation set. A random sampling protocol of genotypes from the calibration set will lead to low quality coverage of the total genetic space by the training set when the calibration set contains population structure. As a consequence, predictive ability will be affected negatively, because some parts of the genotypic diversity in the target population will be under-represented in the training set, whereas other parts will be over-represented. Therefore, we propose a training set construction method that uniformly samples the genetic space spanned by the target population of genotypes, thereby increasing predictive ability. To evaluate our method, we constructed training sets alongside with the identification of corresponding genomic prediction models for four genotype panels that differed in the amount of population structure they contained (maize Flint, maize Dent, wheat, and rice). Training sets were constructed using uniform sampling, stratified-uniform sampling, stratified sampling and random sampling. We compared these methods with a method that maximizes the generalized coefficient of determination (CD). Several training set sizes were considered. We investigated four genomic prediction models: multi-locus QTL models, GBLUP models, combinations of QTL and GBLUPs, and Reproducing Kernel Hilbert Space (RKHS) models. For the maize and wheat panels, construction of the training set under uniform sampling led to a larger predictive ability than under stratified and random sampling. The results of our methods were similar to those of the CD method. For the rice panel, all training set construction methods led to similar predictive ability, a reflection of the very strong population structure in this panel.