Simulating genotypic variation of fruit quality in an advanced peach x Prunus davidiana cross

Integration of Crop Growth Models and Genomic Prediction

Crop growth models (CGMs) consist of multiple equations that represent physiological processes of plants and simulate crop growth dynamically given environmental inputs. Because parameters of CGMs are often genotype-specific, gene effects can be related to environmental inputs through CGMs. Thus, CGMs are attractive tools for predicting genotype by environment (G×E) interactions. This chapter reviews CGMs, genetic analyses using these models, and the status of studies that integrate genomic prediction with CGMs. Examples of CGM analyses are also provided.

Combining Crop Growth Modeling With Trait-Assisted Prediction Improved the Prediction of Genotype by Environment Interactions

Plant breeders evaluate their selection candidates in multi-environment trials to estimate their performance in contrasted environments. The number of genotype/environment combinations that can be evaluated is strongly constrained by phenotyping costs and by the necessity to limit the evaluation to a few years. Genomic prediction models taking the genotype by environment interactions (GEI) into account can help breeders identify combination of (possibly unphenotyped) genotypes and target environments optimizing the traits under selection. We propose a new prediction approach in which a secondary trait available on both the calibration and the test sets is introduced as an environment specific covariate in the prediction model (trait-assisted prediction, TAP). The originality of this approach is that the phenotyping of the test set for the secondary trait is replaced by crop-growth model (CGM) predictions. So there is no need to sow and phenotype the test set in each environment which is a clear advantage over the classical trait-assisted prediction models. The interest of this approach, called CGM-TAP, is highest if the secondary trait is easy to predict with CGM and strongly related to the target trait in each environment (and thus capturing GEI). We tested CGM-TAP on bread wheat with heading date as secondary trait and grain yield as target trait. Simple CGM-TAP model with a linear effect of heading date resulted in high predictive abilities in three prediction scenarios (sparse testing, or prediction of new genotypes or of new environments). It increased predictive abilities of all reference GEI models, even those involving sophisticated environmental covariates.

Model-based QTL detection is sensitive to slight modifications in model formulation

Classical crop models have been developed to predict crop yield and quality, and they are based on physiological and environmental inputs. After molecular discoveries, models should integrate genetic variation to allow predictions that are more genotype-dependent. An interesting approach, Quantitative Trait Locus (QTL)-based ecophysiological modeling, has shown promising results for the design of ideotypes that are adapted to biotic and abiotic stresses, but there are still limitations to attaining a fully integrated model. The aim of this case study is to clarify the impact of choosing different model equations (closely related and with different numbers of parameters) and optimization methods on the detection of QTLs controlling the parameters of crop growth. Different growth equations were parameterized based on a genetic population by following different approaches. The correlations between parameters were analyzed, and two different strategies were adopted to address the correlation issue. QTL analysis was performed on the optimized values of the parameters of the growth equations and on the observed dry mass (DM) data to validate the QTLs detected. Overall, models and strategies resulted in different QTLs being detected. Similar LOD profiles but with peaks of different heights were observed, some of which were significant, resulting in different numbers of QTLs. In some cases, peaks had slightly different positions or were absent. Even closely related growth models led to the detection of different QTLs. The goodness of fit and complexity of the growth models were found to be insufficient to select the best model. Calculating parameters independently of observed data may not be a good strategy, whereas setting parameters independent of the genotype is recommended. Given the large-scale global optimization problem and the strong correlations between parameters, the two algorithms tested showed poor performance. Currently, the lack of effective algorithms is the main obstacle to answering the question posed. The authors therefore suggest testing different model formulations and comparing the QTLs detected before choosing the best formulation to use in an ecophysiological modeling approach based on QTLs.

Incorporating genome-wide association into eco-physiological simulation to identify markers for improving rice yields

We explored the use of the eco-physiological crop model GECROS to identify markers for improved rice yield under well-watered (control) and water deficit conditions. Eight model parameters were measured from the control in one season for 267 indica genotypes. The model accounted for 58% of yield variation among genotypes under control and 40% under water deficit conditions. Using 213 randomly selected genotypes as the training set, 90 single nucleotide polymorphism (SNP) loci were identified using a genome-wide association study (GWAS), explaining 42-77% of crop model parameter variation. SNP-based parameter values estimated from the additive loci effects were fed into the model. For the training set, the SNP-based model accounted for 37% (control) and 29% (water deficit) of yield variation, less than the 78% explained by a statistical genomic prediction (GP) model for the control treatment. Both models failed in predicting yields of the 54 testing genotypes. However, compared with the GP model, the SNP-based crop model was advantageous when simulating yields under either control or water stress conditions in an independent season. Crop model sensitivity analysis ranked the SNP loci for their relative importance in accounting for yield variation, and the rank differed greatly between control and water deficit environments. Crop models have the potential to use single-environment information for predicting phenotypes under different environments.

Scaling up and kinetic model validation of Direct Black 22 degradation by immobilized Penicillium chrysogenum

This research was undertaken to develop tools that facilitate the industrial application of an immobilized loofah-fungi system to degrade Direct Black 22 (DB22) azo dye. In laboratory-scale tests, the DB22, and loofah as support, were used. Assays without loofah were used as a free-cells control. The use of natural carriers to facilitate adhesion and growth of the fungi has shown favorable results. The degradation rate of immobilized cells increased twice as compared to free-cells control. At day 5 the decolorization was almost complete, while without loofah the total decolorization took more than 10 days. After 10 days, the extent of growth was nine times higher for the immobilized assays in comparison with the control flask. In subsequent experiments decolorization of DB22 was proven in a bench-scale reactor. A previously developed kinetic model was validated during the process. The model validation over free-cells assays gives an average normalized root mean squared error (ANRMSE) of 0.1659. Recalibration steps allowed prediction of the degradation with immobilized cells, resulting in an ANRMSE of 0.1891. A new calibration of the model during the scaling-up process yielded an ANRMSE of 0.1136 for DB22. The results presented encourage the use of this modeling tool in industrial scale facilities.

Optimization of multi-environment trials for genomic selection based on crop models

We propose a statistical criterion to optimize multi-environment trials to predict genotype × environment interactions more efficiently, by combining crop growth models and genomic selection models. Genotype × environment interactions (GEI) are common in plant multi-environment trials (METs). In this context, models developed for genomic selection (GS) that refers to the use of genome-wide information for predicting breeding values of selection candidates need to be adapted. One promising way to increase prediction accuracy in various environments is to combine ecophysiological and genetic modelling thanks to crop growth models (CGM) incorporating genetic parameters. The efficiency of this approach relies on the quality of the parameter estimates, which depends on the environments composing this MET used for calibration. The objective of this study was to determine a method to optimize the set of environments composing the MET for estimating genetic parameters in this context. A criterion called OptiMET was defined to this aim, and was evaluated on simulated and real data, with the example of wheat phenology. The MET defined with OptiMET allowed estimating the genetic parameters with lower error, leading to higher QTL detection power and higher prediction accuracies. MET defined with OptiMET was on average more efficient than random MET composed of twice as many environments, in terms of quality of the parameter estimates. OptiMET is thus a valuable tool to determine optimal experimental conditions to best exploit MET and the phenotyping tools that are currently developed.

Kinetic Modeling of Sunflower Grain Filling and Fatty Acid Biosynthesis

Grain growth and oil biosynthesis are complex processes that involve various enzymes placed in different sub-cellular compartments of the grain. In order to understand the mechanisms controlling grain weight and composition, we need mathematical models capable of simulating the dynamic behavior of the main components of the grain during the grain filling stage. In this paper, we present a non-structured mechanistic kinetic model developed for sunflower grains. The model was first calibrated for sunflower hybrid ACA855. The calibrated model was able to predict the theoretical amount of carbohydrate equivalents allocated to the grain, grain growth and the dynamics of the oil and non-oil fraction, while considering maintenance requirements and leaf senescence. Incorporating into the model the serial-parallel nature of fatty acid biosynthesis permitted a good representation of the kinetics of palmitic, stearic, oleic, and linoleic acids production. A sensitivity analysis showed that the relative influence of input parameters changed along grain development. Grain growth was mostly affected by the specific growth parameter (μ') while fatty acid composition strongly depended on their own maximum specific rate parameters. The model was successfully applied to two additional hybrids (MG2 and DK3820). The proposed model can be the first building block toward the development of a more sophisticated model, capable of predicting the effects of environmental conditions on grain weight and composition, in a comprehensive and quantitative way.

Sugars in peach fruit: a breeding perspective

The last decade has been characterized by a decrease in peach (Prunus persica) fruit consumption in many countries, foremost due to unsatisfactory quality. The sugar content is one of the most important quality traits perceived by consumers, and the development of novel peach cultivars with sugar-enhanced content is a primary objective of breeding programs to revert the market inertia. Nevertheless, the progress reachable through classical phenotypic selection is limited by the narrow genetic bases of peach breeding material and by the complex quantitative nature of the trait, which is deeply affected by environmental conditions and agronomical management. The development of molecular markers applicable in MAS or MAB has become an essential strategy to boost the selection efficiency. Despite the enormous advances in 'omics' sciences, providing powerful tools for plant genotyping, the identification of the genetic bases of sugar-related traits is hindered by the lack of adequate phenotyping methods that are able to address strong within-plant variability. This review provides an overview of the current knowledge of the metabolic pathways and physiological mechanisms regulating sugar accumulation in peach fruit, the main advances in phenotyping approaches and genetic background, and finally addressing new research priorities and prospective for breeders.

Optimization of Allelic Combinations Controlling Parameters of a Peach Quality Model

Process-based models are effective tools to predict the phenotype of an individual in different growing conditions. Combined with a quantitative trait locus (QTL) mapping approach, it is then possible to predict the behavior of individuals with any combinations of alleles. However the number of simulations to explore the realm of possibilities may become infinite. Therefore, the use of an efficient optimization algorithm to intelligently explore the search space becomes imperative. The optimization algorithm has to solve a multi-objective problem, since the phenotypes of interest are usually a complex of traits, to identify the individuals with best tradeoffs between those traits. In this study we proposed to unroll such a combined approach in the case of peach fruit quality described through three targeted traits, using a process-based model with seven parameters controlled by QTL. We compared a current approach based on the optimization of the values of the parameters with a more evolved way to proceed which consists in the direct optimization of the alleles controlling the parameters. The optimization algorithm has been adapted to deal with both continuous and combinatorial problems. We compared the spaces of parameters obtained with different tactics and the phenotype of the individuals resulting from random simulations and optimization in these spaces. The use of a genetic model enabled the restriction of the dimension of the parameter space toward more feasible combinations of parameter values, reproducing relationships between parameters as observed in a real progeny. The results of this study demonstrated the potential of such an approach to refine the solutions toward more realistic ideotypes. Perspectives of improvement are discussed.

Predictions of heading date in bread wheat (Triticum aestivum L.) using QTL-based parameters of an ecophysiological model

Prediction of wheat phenology facilitates the selection of cultivars with specific adaptations to a particular environment. However, while QTL analysis for heading date can identify major genes controlling phenology, the results are limited to the environments and genotypes tested. Moreover, while ecophysiological models allow accurate predictions in new environments, they may require substantial phenotypic data to parameterize each genotype. Also, the model parameters are rarely related to all underlying genes, and all the possible allelic combinations that could be obtained by breeding cannot be tested with models. In this study, a QTL-based model is proposed to predict heading date in bread wheat (Triticum aestivum L.). Two parameters of an ecophysiological model (V sat and P base , representing genotype vernalization requirements and photoperiod sensitivity, respectively) were optimized for 210 genotypes grown in 10 contrasting location × sowing date combinations. Multiple linear regression models predicting V sat and P base with 11 and 12 associated genetic markers accounted for 71 and 68% of the variance of these parameters, respectively. QTL-based V sat and P base estimates were able to predict heading date of an independent validation data set (88 genotypes in six location × sowing date combinations) with a root mean square error of prediction of 5 to 8.6 days, explaining 48 to 63% of the variation for heading date. The QTL-based model proposed in this study may be used for agronomic purposes and to assist breeders in suggesting locally adapted ideotypes for wheat phenology.

The Relationship between Metaheuristics Stopping Criteria and Performances

A major difficulty in the use of metaheuristics (i.e. evolutionary and particle swarm algorithms) to deal with multi-objective optimization problems is the choice of a convenient point at which to stop computation. Indeed, it is difficult to find the best compromise between the stopping criterion and the algorithm performance. This paper addresses this issue using the Non-dominated Sorting Genetic Algorithm (NSGA-II) and the Multi-Objective Particle Swarm Optimization with Crowding Distance (MOPSO-CD) for the model-based design of sustainable peach fruits. The optimization problem of interest contains three objectives: maximize fruit fresh mass, maximize fruit sugar content, and minimize the crack density on the fruit skin. This last objective targets a reduction in the use of fungicides and can thus enhance preservation of the environment and human health. Two versions of the NSGA-II and two of the MOPSO-CD were applied to tackle this difficult optimization problem: the original versions with a maximum number of generations used as stopping criterion and modified versions using the stopping criterion proposed by the authors of (Roudenko & Schoenauer, 2004). This second stopping criterion is based on the stabilization of the maximal crowding distance and aims to stop computation when many generations are performed without further improvement in the quality of the solutions. A benchmark consisting of four plant management scenarios has been used to compare the performances of the original versions (OV) and the modified versions (MV) of the NSGA-II and the MOPSO-CD. Twelve independent simulations were performed for each version and for each scenario, and a high number of generations were generated for the OV (e.g., 1500 for the NSGA-II and 200 for the MOPSO-CD). This paper compares the performances of the two versions of both algorithms using four standard metrics and statistical tests. For both algorithms, the MV obtained solutions similar in quality to those of the OV but after significantly fewer generations. The resulting reduction in computational time for the optimization step will provide opportunities for further studies on the sustainability of peach ideotypes.

Carotenoid responses to environmental stimuli: integrating redox and carbon controls into a fruit model

Carotenoids play an important role in plant adaptation to fluctuating environments as well as in the human diet by contributing to the prevention of chronic diseases. Insights have been gained recently into the way individual factors, genetic, environmental or developmental, control the carotenoid biosynthetic pathway at the molecular level. The identification of the rate-limiting steps of carotenogenesis has paved the way for programmes of breeding, and metabolic engineering, aimed at increasing the concentration of carotenoids in different crop species. However, the complexity that arises from the interactions between the different factors as well as from the coordination between organs remains poorly understood. This review focuses on recent advances in carotenoid responses to environmental stimuli and discusses how the interactions between the modulation factors and between organs affect carotenoid build-up. We develop the idea that reactive oxygen species/redox status and sugars/carbon status can be considered as integrated factors that account for most effects of the major environmental factors influencing carotenoid biosynthesis. The discussion highlights the concept of carotenoids or carotenoid-derivatives as stress signals that may be involved in feedback controls. We propose a conceptual model of the effects of environmental and developmental factors on carotenoid build-up in fruits.

Crop management impacts the efficiency of quantitative trait loci (QTL) detection and use: case study of fruit load×QTL interactions

Mapping studies using populations with introgressed marker-defined genomic regions are continuously increasing knowledge about quantitative trait loci (QTL) that correlate with variation in important crop traits. This knowledge is useful for plant breeding, although combining desired traits in one genotype might be complicated by the mode of inheritance and co-localization of QTL with antagonistic effects, and by physiological trade-offs, and feed-back or feed-forward mechanisms. Therefore, integrating advances at the genetic level with insight into influences of environment and crop management on crop performance remains difficult. Whereas mapping studies can pinpoint correlations between QTL and phenotypic traits for specific conditions, ignoring or overlooking the importance of environment or crop management can jeopardize the relevance of such assessments. Here, we focus on fruit load (a measure determining competition among fruits on one plant) and its strong modulation of QTL effects on fruit size and composition. Following an integral approach, we show which fruit traits are affected by fruit load, to which underlying processes these traits can be linked, and which processes at lower and higher integration levels are affected by fruit load (and subsequently influence fruit traits). This opinion paper (i) argues that a mechanistic framework to interpret interactions between fruit load and QTL effects is needed, (ii) pleads for consideration of the context of agronomic management when detecting QTL, (iii) makes a case for incorporating interacting factors in the experimental set-up of QTL mapping studies, and (iv) provides recommendations to improve efficiency in QTL detection and use, with particular focus on model-based marker-assisted breeding.

Modelling the size and composition of fruit, grain and seed by process-based simulation models

Understanding what determines the size and composition of fruit, grain and seed in response to the environment and genotype is challenging, as these traits result from several linked processes controlled at different levels of organization, from the subcellular to the crop level, with subtle interactions occurring at or between the levels of organization. Process-based simulation models (PBSMs) implement algorithms to simulate metabolic and biophysical aspects of cell, tissue and organ behaviour. In this review, fruit, grain and seed PBSMs describing the main phases of growth, development and storage metabolism are discussed. From this concurrent work, it is possible to identify generic storage organ processes which can be modelled similarly for fruit, grain and seed. Spatial heterogeneity at the tissue and whole-plant level is found to be a key consideration in modelling the effects of the environment and genotype on fruit, grain and seed end-use value. In the future, PBSMs may well become the main link between studies at the molecular and whole-plant levels. To bridge this phenotype-to-genotype gap, future models need to remain plastic without becoming overparameterized.

Simulating the impact of genetic diversity of Medicago truncatula on germination and emergence using a crop emergence model for ideotype breeding

BACKGROUND AND AIMS

Germination and heterotrophic growth are crucial steps for stand establishment. Numerical experiments based on the modelling of these early stages in relation to major environmental factors at sowing were used as a powerful tool to browse the effects of the genetic diversity of Medicago truncatula, one of the model legume species, under a range of agronomic scenarios, and to highlight the most important plant parameters for emergence. To this end, the emergence of several genotypes of M. truncatula was simulated under a range of sowing conditions with a germination and emergence simulation model.

METHODS

After testing the predictive quality of the model by comparing simulations to field observations of several genotypes of M. truncatula, numerical experiments were performed under a wide range of environmental conditions (sowing dates × years × seedbed structure). Germination and emergence was simulated for a set of five genotypes previously parameterized and for two virtual genotypes engineered to maximize the potential effects of genetic diversity.

KEY RESULTS

The simulation results gave an average value of 5-10 % difference in final emergence between genotypes, which was low, but the analysis underlined considerable inter-annual variation. The effects of parameters describing germination and emergence processes were quantified and ranked according to their contribution to the variation in emergence. Seedling non-emergence was mainly related to mechanical obstacles (40-50 %). More generally, plant parameters that accelerated the emergence time course significantly contributed to limiting the risk of soil surface crusting occurring before seedling emergence.

CONCLUSIONS

The model-assisted analysis of the effects of genetic diversity demonstrated its usefulness in helping to identify the parameters which have most influence that could be improved by breeding programmes. These results should also enable a deeper analysis of the genetic determinism of the main plant parameters influencing emergence, using the genomic tools available for this model plant.

Under what circumstances can process-based simulation models link genotype to phenotype for complex traits? Case-study of fruit and grain quality traits

Detailed information has arisen from research at gene and cell levels, but it is still incomplete in the context of a quantitative understanding of whole plant physiology. Because of their integrative nature, process-based simulation models can help to bridge the gap between genotype and phenotype and assist in deconvoluting genotype-by-environment (GxE) interactions for complex traits. Indeed, GxE interactions are emergent properties of simulation models, i.e. unexpected properties generated by complex interconnections between subsystem components and biological processes. They co-occur in the system with synergistic or antagonistic effects. In this work, different kinds of GxE interactions are illustrated. Approaches to link model parameters to genes or quantitative trait loci (QTL) are briefly reviewed. Then the analysis of GxE interactions through simulation models is illustrated with an integrated model simulation of peach (Prunus persica (L.) Batsch) fruit mass and sweetness, and with a model of wheat (Triticum aestivum L.) grain yield and protein concentration. This paper suggests that the management of complex traits such as fruit and grain quality may become possible, thanks to the increasing knowledge concerning the genetic and environmental regulation of organ size and composition and to the development of models simulating the complex aspects of metabolism and biophysical behaviours at the plant and organ levels.

Using a model-based framework for analysing genetic diversity during germination and heterotrophic growth of Medicago truncatula

BACKGROUND AND AIMS

The framework provided by an emergence model was used: (1) for phenotyping germination and heterotrophic growth of Medicago truncatula in relation to two major environmental factors, temperature and water potential; and (2) to evaluate the extent of genetic differences in emergence-model parameters.

METHODS

Eight cultivars and natural accessions of M. trunculata were studied. Germination was recorded from 5 to 30 degrees C and from 0 to -0.75 MPa, and seedling growth from 10 to 20 degrees C.

KEY RESULTS

Thermal time to reach 50 % germination was very short (15 degrees Cd) and almost stable between genotypes, while base temperature (2-3 degrees C) and base water potential for germination (-0.7 to -1.3 MPa) varied between genotypes. Only 35 degrees Cd after germination were required to reach 30 mm hypocotyl length with significant differences among genotypes. Base temperature for elongation varied from 5.5 to 7.5 degrees C. Low temperatures induced a general shortening of the seedling, with some genotypes more responsive than others. No relationship with initial seed mass or seed reserve distribution was observed, which might have explained differences between genotypes and the effects of low temperatures.

CONCLUSIONS

The study provides a set of reference values for M. trunculata users. The use of the ecophysiological model allows comparison of these values between such non-crop species and other crops. It has enabled phenotypic variability in response to environmental conditions related to the emergence process to be identified. The model will allow simulation of emergence differences between genotypes in a range of environments using these parameter values. Genomic tools available for the model species M. trunculata will make it possible to analyse the genetic and molecular determinants of these differences.

Model-assisted analysis of tomato fruit growth in relation to carbon and water fluxes

This work proposed a model of tomato growth adapted from the Fishman and Génard model developed to predict carbon and water accumulation in peach fruit. The main adaptations relied on the literature on tomato and mainly concerned: (i) the decrease in cell wall extensibility coefficient during fruit development; (ii) the increase in the membrane reflection coefficient to solute from 0 to 1, which accounted for the switch from symplasmic to apoplasmic phloem unloading, and (iii) the negative influence of the initial fruit weight on the maximum rate of active carbon uptake based on the assumption of higher competition for carbon among cells in large fruits containing more cells. A sensitivity analysis was performed and the model was calibrated and evaluated with satisfaction on 17 experimental datasets obtained under contrasting environmental (temperature, air vapour pressure deficit) and plant (plant fruit load and fruit position) conditions. Then the model was used to analyse the variations in the main fluxes involved in tomato fruit growth and accumulation of carbon in response to virtual carbon and water stresses. The conclusions are that this model, integrating simple biophysical laws, was able to simulate the complex fruit behaviour in response to external or internal factors and thus it may be a powerful tool for managing fruit growth and quality.

Analysing the genetic control of peach fruit quality through an ecophysiological model combined with a QTL approach

Ecophysiological models are increasingly expected to include genetic information via genotype-dependent parameters. These parameters could be considered as quantitative traits and submitted to analysis. A pre-existing ecophysiological model of fruit quality was used and the distribution of the genotypic parameters in a second backcross population derived from a clone of a wild peach (Prunus davidiana) and commercial nectarine varieties (P. persica (L.) Batsch) was analysed. The correlations between the two years of experimentation were higher for the genotypic parameters than for the quality traits commonly studied by breeders. The correlations between the genotypic parameters and the quality traits were low. Quantitative trait loci (QTLs) for the genotypic key parameters of the ecophysiological model were detected by linear regression. Co-locations of QTLs for parameters were observed as well as co-locations of QTLs for parameters and quality traits. The ecophysiological model and the results of the QTL analysis were combined by substituting each parameter in the model by the sum of QTL effects. This combined model can simulate the behaviour of genotypes carrying diverse combinations of alleles. The quality of this combined model was moderately suitable, but had some shortcomings. Improvements are suggested and further use of this combined model as a tool for breeders is discussed.