Using numerical plant models and phenotypic correlation space to design achievable ideotypes

Numerical plant models can predict the outcome of plant traits modifications resulting from genetic variations, on plant performance, by simulating physiological processes and their interaction with the environment. Optimization methods complement those models to design ideotypes, i.e. ideal values of a set of plant traits resulting in optimal adaptation for given combinations of environment and management, mainly through the maximization of a performance criteria (e.g. yield, light interception). As use of simulation models gains momentum in plant breeding, numerical experiments must be carefully engineered to provide accurate and attainable results, rooting them in biological reality. Here, we propose a multi-objective optimization formulation that includes a metric of performance, returned by the numerical model, and a metric of feasibility, accounting for correlations between traits based on field observations. We applied this approach to two contrasting models: a process-based crop model of sunflower and a functional-structural plant model of apple trees. In both cases, the method successfully characterized key plant traits and identified a continuum of optimal solutions, ranging from the most feasible to the most efficient. The present study thus provides successful proof of concept for this enhanced modeling approach, which identified paths for desirable trait modification, including direction and intensity.Comment: 25 pages, 5 figures, 2017, Plant, Cell and Environmen

Development and applications of Plabsoft : a computer program for population genetic data analyses and simulations in plant breeding

Marker-assisted breeding approaches are promising tools for enhancement of the conventional plant breeding process. They have been successfully applied in many areas such as plant variety protection, classification of germplasm, assessment of genetic diversity, mapping of genes underlying important agronomic traits, and using the mapping information for selection decisions. Powerful and flexible bioinformatic tools are urgently required for a better integration of molecular marker applications and classical plant breeding methods. The objective of my thesis work was to develop and apply Plabsoft, a computer program for population genetic data analyses and simulations in plant breeding. The assumption of Hardy-Weinberg equilibrium is a cornerstone of many concepts in population and quantitative genetics. Therefore, tests for Hardy-Weinberg equilibrium are of crucial importance, but the assumptions underlying asymptotic chi-square tests are often not met in datasets from plant breeding programs. I developed and implemented in Plabsoft a new algorithm for exact tests of Hardy-Weinberg equilibrium with multiple alleles. The newly derived algorithm has considerable computational advantages over previously described algorithms and extends substantially the range of problems that can be tested. Knowledge about the amount and distribution of linkage disequilibrium (LD) in breeding populations is of fundamental importance to assess the prospects for gene mapping with whole-genome association studies. To analyze LD in breeding populations, I implemented various LD measures in Plabsoft and developed a new significance test for these LD measures. The routines were employed to analyze LD in 497 elite maize lines from a commercial hybrid breeding program, which were fingerprinted by 81 simple sequence repeat (SSR) markers covering the entire genome. Strong LD was detected and, therefore, whole-genome association studies were recommended as promising. However, LD between unlinked loci will most likely result in a high rate of false positives. The prediction of hybrid performance with DNA markers facilitates the identification of superior hybrids. The single marker models used so far do not take into account the correlation between allele frequencies at linked markers. To overcome this problem, the concept of haplotype blocks was proposed. I developed and implemented in Plabsoft three alternative algorithms for haplotype block detection suitable for plant breeding. The algorithms were applied for the haplotype-based prediction of the hybrid performance of 270 hybrids, the parents of which were fingerprinted with 20 amplified fragment length polymorphism (AFLP) primer combinations. Employing haplotypes resulted in an improved prediction of hybrid performance compared with single marker models. Consequently, haplotype-based prediction methods have a high potential to improve substantially the efficiency of hybrid breeding programs. Computer simulations can be employed to solve population genetic problems in plant breeding, for which the simplifying assumptions underlying the classical population genetic theory do not hold true. However, before the start of my thesis no flexible simulation software was available. I developed algorithms for simulation of single breeding steps and entire plant breeding programs and implemented these in Plabsoft. The routines allow the simulation of plant breeding programs as they are conducted in practice. The simulation routines of Plabsoft were validated by simulating two marker-assisted backcross programs in rice conducted by the International Rice Research Institute (IRRI). In the simulations, the frequency distributions of the proportion of recurrent parent genome in the backcross populations were assessed. The simulation results were in good agreement with the experimental data. Therefore, computer simulations are a useful tool for pre-test estimation of selection response in marker-assisted backcrossing. The application of Plabsoft was exemplified by two studies in maize. In the first study, the expected LD decay in the intermating generations of two recurrent selections programs was determined with simulations. This application demonstrates the use of Plabsoft to solve problems for which analytical results are not available. In the second study, the forces generating and maintaining LD in a hybrid maize breeding program were investigated with computer simulations. This application demonstrates the capability of modeling complex long-term breeding programs as performed in practice. The studies of my thesis provide an example for the broad range of possible applications of Plabsoft. In addition to the presented studies, Plabsoft has so far been employed in about 40 further studies, which corroborates the usefulness of Plabsoft for integrating new genomic tools in applied plant breeding programs.DNA Marker werden in der Pflanzenzüchtung zum Erkennen von Sortenplagiaten, zur Gruppierung von Zuchtmaterial, zur Überwachung der genetischen Diversität, zur Kartierung von Genen, die für die Ausprägung wichtiger agronomischer Merkmale verantwortlich sind, sowie zur marker-gestützten Selektion eingesetzt. Um die Markertechnologie in die Methodik der klassischen Pflanzenzüchtung zu integrieren, werden dringend flexible und leistungsfähige bioinformatische Konzepte und darauf basierende Computerprogramme benötigt. Das Ziel dieser Arbeit war es, Plabsoft, ein Computerprogramm zur populationsgenetischen Datenanalyse und Simulation von Pflanzenzüchtungsprogrammen, zu entwickeln und anzuwenden. Die Annahme, dass sich eine Population im Hardy-Weinberg Gleichgewicht befindet, liegt vielen Konzepten der Populationsgenetik und der quantitativen Genetik zugrunde. Deswegen sind statistische Tests auf Hardy-Weinberg Gleichgewicht von großer Bedeutung. In Datensätzen aus Pflanzenzüchtungsprogrammen treffen die statistischen Annahmen, welche den oft verwendeten Chi-Quadrat-Tests zugrunde liegen, häufig nicht zu. Aus diesem Grund wurde in dieser Arbeit ein neuer Algorithmus für einen exakten Test auf Hardy-Weinberg Gleichgewicht mit multiplen Allelen entwickelt und in Plabsoft umgesetzt. Der neu implementierte Algorithmus ist deutlich schneller als alle vorher beschriebenen Algorithmen und erlaubt somit eine bedeutende Erweiterung für den Anwendungsbereich exakter Hardy-Weinberg Tests. Die genaue Kenntnis der Höhe und Verteilung von Gametenphasenungleichgewicht (linkage disequilibrium, LD) in pflanzenzüchterischen Populationen ist von großer Bedeutung, um die Erfolgsaussichten genomweiter Assoziationsstudien abschätzen zu können. Zu diesem Zweck wurde die Berechnung der wichtigsten LD Maße in Plabsoft implementiert und ein neuer Signifikanztest für die LD Maße entwickelt. Die neu entwickelten Routinen wurden zur Analyse des LD in einem kommerziellen Hybridmaiszüchtungsprogramm verwendet. Hierzu wurden 497 Inzuchtlinien mit 81 SSR (simple sequence repeat, Mikrosatelliten) Markern genotypisiert und ein hohes Ausmaß an LD detektiert, so dass genomweite Assoziationskartierungsansätze vielversprechend erscheinen. Jedoch ist zu erwarten, dass aufgrund des hohen Ausmaßes an LD zwischen ungekoppelten Markerloci viele falsch positive Assoziationen beobachtet werden. Eine markergestützte Vorhersage der Hybridleistung vereinfacht die Identifizierung überlegener Kreuzungskombinationen. Bisher wurden hierfür nur Vorhersagemodelle verwendet, die auf einzelnen Markerloci basieren und die Korrelationsstruktur zwischen Allelen an benachbarten Markerloci nicht berücksichtigen. In der Humangenetik wurde vorgeschlagen, benachbarte Markerloci zu sogenannten Haploblöcken zusammenzufassen, um das Problem der Multikolinearität zu lösen. Im Rahmen dieser Arbeit wurden drei unterschiedliche Algorithmen zur Detektion von Haploblöcken im Zuchtmaterial erarbeitet und in Plabsoft umgesetzt. Die Routinen wurden für eine haplotyp-basierte Vorhersage der Leistung von 270 Hybriden verwendet, deren Eltern mit 20 AFLP (amplified fragment length polymorphism) Primerkombinationen untersucht wurden. Die Vorhersage der Hybridleistung konnte durch die Verwendung von Haploblöcken verbessert werden. Folglich haben haplotyp-basierte Vorhersagemethoden ein großes Potential, die Effizienz von Hybridzuchtprogrammen zu steigern. Computersimulationen können in der Pflanzenzüchtung zur Lösung populationsgenetischer Fragestellungen auch dann angewendet werden, wenn die Annahmen, welche der klassischen populationsgenetischen Theorie zugrunde liegen, nicht erfüllt sind. Vor Beginn dieser Arbeit stand jedoch keine Software zur Verfügung, welche auf flexible Art und Weise Simulationen pflanzenzüchterischer Fragestellungen ermöglicht hätte. Aus diesem Grund wurden Algorithmen entwickelt, die die Simulation einzelner Züchtungsschritte sowie kompletter Pflanzenzüchtungsprogramme ermöglichen. Die entwickelten Algorithmen wurden im Computerprogramm Plabsoft umgesetzt, so dass es jetzt möglich ist, komplexe Pflanzenzüchtungsprogramme praxisnah zu simulieren. Die Simulationsroutinen von Plabsoft wurden an einem experimentellen Datensatz zur markergestützten Introgression eines Überflutungstoleranzgens in Reis validiert. Hierzu wurde das gesamte Zuchtprogramm, wie es in der Praxis durchgeführt wurde, simuliert. In den Simulationen wurde die Häufigkeitsverteilung des rekurrenten Eltergenomanteils in den Rückkreuzungspopulationen erfasst. Die Simulationsergebnisse stimmten nahezu vollständig mit den experimentell beobachteten Daten überein. Dies belegt, dass Computersimulationen ein äußerst effektives Hilfsmittel sind, um den Selektionserfolg bei der markergestützten Rückkreuzung abzuschätzen. Die Anwendung der Simulations- und Analysesoftware Plabsoft wurde exemplarisch an zwei Studien dargestellt. In der ersten Studie wurde mit Hilfe von Simulationen der zu erwartende Abfall an LD in den Durchkreuzungsgenerationen bei zwei rekurrenten Selektionsprogrammen in Mais bestimmt. Diese Studie demonstriert die Anwendung von Plabsoft zur Lösung von Fragestellungen, für welche keine analytische Lösungen zur Verfügung stehen. In der zweiten Studie wurden mit Hilfe von Computersimulationen die Ursachen untersucht, welche in einem Hybridmaiszuchtprogramm LD generieren und aufrecht erhalten. Hiermit wurde gezeigt, dass mit Plabsoft komplexe praktische Zuchtprogramme modelliert werden können. Die Studien dieser Arbeit geben einen Überblick über das breite Anwendungsspektrum der entwickelten Simulations- und Analysesoftware Plabsoft. Darüber hinaus wurde Plabsoft bis jetzt in vierzig weiteren Studien verwendet, womit die Nützlichkeit von Plabsoft für die Integration neuer genomischer Werkzeuge in die angewandte Züchtungsforschung zweifelsfrei belegt wird

Measurement of plant growth in view of an integrative analysis of regulatory networks

As the regulatory networks of growth at the cellular level are elucidated at a fast pace, their complexity is not reduced; on the contrary, the tissue, organ and even whole-plant level affect cell proliferation and expansion by means of development-induced and environment-induced signaling events in growth regulatory processes. Measurement of growth across different levels aids in gaining a mechanistic understanding of growth, and in defining the spatial and temporal resolution of sampling strategies for molecular analyses in the model Arabidopsis thaliana and increasingly also in crop species. The latter claim their place at the forefront of plant research, since global issues and future needs drive the translation from laboratory model-acquired knowledge of growth processes to improvements in crop productivity in field conditions

The optimization of introgression projects for plant genetic improvement

We approach the problem of trait introgression as an optimization challenge with clearly defined objectives in 3 different scenarios that largely capture the introgression problem in a diploid outcrossing selfing-tolerant species: 1) the introgression of a single allele into a recipient background via backcrossing, 2) the introgression of multiple alleles from one line into a recipient line, and 3) the introgression of several alleles from multiple lines into the background of a recipient line. For each of the 3 cases, we present a mathematical formulation, based on optimization principles from Operations Research (OR), defining the objectives to be optimized, decision variables and constraints of the introgression problem. We then use simulation, with genome size and reproductive biology based on maize, to estimate the probability of achieving a set of breeding goals. Algorithms from OR and combinatorics are used to optimize selections. Finally, Pareto response surfaces are presented for each of the 3 cases to concisely show the tradeoffs between objectives. With this systematic approach of defining quantifiable objectives, translating the objectives into a mathematical model, then building simulation models that allow for analysis of the tradeoffs between objectives, we show a way forward where plant breeding has a deeper engagement with applied mathematics

Multi-trait ensemble genomic prediction and simulations of recurrent selection highlight importance of complex trait genetic architecture for long-term genetic gains in wheat

Cereal crop breeders have achieved considerable genetic gain in genetically complex traits, such as grain yield, while maintaining genetic diversity. However, focus on selection for yield has negatively impacted other important traits. To better understand multi-trait selection within a breeding context, and how it might be optimized, we analysed genotypic and phenotypic data from a genetically diverse, 16-founder wheat multi-parent advanced generation inter-cross population. Compared to single-trait models, multi-trait ensemble genomic prediction models increased prediction accuracy for almost 90 % of traits, improving grain yield prediction accuracy by 3–52 %. For complex traits, non-parametric models (Random Forest) also outperformed simplified, additive models (LASSO), increasing grain yield prediction accuracy by 10–36 %. Simulations of recurrent genomic selection then showed that sustained greater forward prediction accuracy optimized long-term genetic gains. Simulations of selection on grain yield found indirect responses in related traits, involving optimized antagonistic trait relationships. We found multi-trait selection indices could effectively optimize undesirable relationships, such as the trade-off between grain yield and protein content, or combine traits of interest, such as yield and weed competitive ability. Simulations of phenotypic selection found that including Random Forest rather than LASSO genetic models, and multi-trait rather than single-trait models as the true genetic model accelerated and extended long-term genetic gain whilst maintaining genetic diversity. These results (i) suggest important roles of pleiotropy and epistasis in the wider context of wheat breeding programmes, and (ii) provide insights into mechanisms for continued genetic gain in a limited genepool and optimization of multiple traits for crop improvement

International Symposium on Evolutionary Breeding in Cereals

Evolutionary plant breeding has a long history, but has so far not become part of mainstream breeding research, nor has it been implemented in practice to any substantial degree. However, over the last decade, research in evolutionary plant breeding has markedly intensified. For example, there are currently major research projects on-going in this area, including the EU funded project SOLIBAM, the Wheat Breeding LINK project in the UK, and the Danish Biobreed project. Also, a new 3-year international research project called COBRA on this topic is due to start in March 2013. Funded by the CORE Organic 2 Eranet the project brings together over 40 partner organizations from 18 European countries. In addition, interest in evolutionary plant breeding is growing among farmers, breeders and policy makers. In fact, there are currently encouraging developments in the imminent revision of seed legislation in Europe that could lead to more room for evolutionary plant breeding approaches in the future. This renewed interest in evolutionary plant breeding is partly due to the recognition that mainstream plant breeding is limited in terms of its engagement with end users, i.e. farmers and growers. More urgently however, effects of climate change on agricultural production have become more noticeable and there is also a growing awareness of increasing resource constraints; together, these will create more stressful growing conditions for agricultural crops. With this background, it is now being recognized that crops need to be able to cope with more variable, contrasting, fluctuating, and generally more unpredictable growing conditions. To be able to deal with this large and increasing environmental variability, plant breeding needs to become more decentralized and diversified. Evolutionary plant breeding offers great potential in this respect. The contributions collated from this symposium explore this potential as well as the limitations of evolutionary plant breeding. While they only show a part of the on-going research activities in Europe, we hope that these proceedings provide inspiration both for further research and for implementation in practice