Varshney Rajeev
email: rajeev.varshney@murdoch.edu.au

Rajeev K Varshney
email: r.k.varshney@cgiar.org

Rutwik Barmukh

Manish Roorkiwal

Yiping Qi

Jana Kholova

Roberto Tuberosa

Matthew P Reynolds

Francois Tardieu

Kadambot H M Siddique

Breeding custom-designed crops for improved drought adaptation

Keywords: Genomic breeding, genome editing, speed breeding, contextdependent optimization, drought physiology, root system architecture

The current pace of crop improvement is inadequate to feed the burgeoning human population by 2050. Higher, more stable and sustainable crop production is required against a backdrop of drought stress, which causes significant losses in crop yields.

Tailoring crops for drought adaptation may hold the key to address these challenges and provide resilient production systems for future harvests. Understanding the genetic and molecular landscape of the functionality of alleles associated with adaptive traits will make designer crop breeding the prospective approach for crop improvement. Here, we highlight the potential of genomics technologies combined with crop physiology for high-throughput identification of the genetic architecture of key drought-adaptive traits and explore innovative genomic breeding strategies for designing future crops.

INTRODUCTION

Crop production must increase to meet the dietary needs of the global human population; however, this task is challenged by the fluctuating environmental conditions. The changing climate referred to as 'climate crisis', is heading us towards a warmer and drier Earth. [START_REF] Fao | Proactive approaches to drought preparedness -Where are we now and where do we go from here?[END_REF] In the last decade, global economic losses in agriculture stemming from drought totaled ~US $29 billion. [START_REF]Disasters causing billions in agricultural losses, with drought leading the way[END_REF] It is anticipated that water demand for agriculture could increase twofold by 2050, with freshwater availability decreasing by up to 50% due to increasing climatic variations. Food security necessitates urgent investments in this domain, particularly for the development of high-yielding crops that are climate-resilient and more effective and/or efficient in using water than their prevailing counterparts. [START_REF] Trnka | Mitigation efforts will not fully alleviate the increase in water scarcity occurrence probability in wheat-producing areas[END_REF] Conventional breeding programs have made impressive progress in the development of crop varieties adapted to drought conditions. [START_REF] Kumar | Breeding highyielding drought-tolerant rice: genetic variations and conventional and molecular approaches[END_REF][START_REF] Baenziger | Registration of 'NE01643' wheat[END_REF][START_REF] Naoman | Registration of 'Giza 2000' droughttolerant six-rowed barley for rainfed and new reclaimed areas in Egypt[END_REF] However, this labor-intensive process often takes many years to advance from the preliminary stages of assessing phenotypes and genotypes to initial crosses into commercial varieties. Conventional breeding ignores the genetic variability of adaptive traits that underlie yield, at the risk of (indirectly) selecting only those alleles that are beneficial in all tested environments. [START_REF] Tardieu | The physiological basis of drought tolerance in crop plants: A scenario-dependent probabilistic approach[END_REF] The alleles thus selected are infrequent compared with those alleles whose effects are context-dependent. [START_REF] Millet | Genome-wide analysis of yield in Europe: allelic effects as functions of drought and heat scenarios[END_REF] By contrast, context-dependent optimization of traits has the potential to maximize positive effects on yield under specific environmental conditions. Therefore, to improve the production of adapted varieties, future breeding programs must combine desirable plant traits that complement climate, soil, and management practices (e.g., sowing dates, fertilization, plant density, etc.) in target production systems.

Plant genomics plays a key role in improving crops, advancing environmental resilience and productivity. [START_REF] Zhao | Unlocking big data doubled the accuracy in predicting the grain yield in hybrid wheat[END_REF] Technical innovations in applied genomics coupled with the availability of large-scale sequencing data provide us with the capabilities for identifying genetic variation that underlies increasing crop performance and improving the efficiency of breeding. [START_REF] Wang | Genetic variation in ZmVPP1 contributes to drought tolerance in maize seedlings[END_REF][START_REF] Bevan | Genomic innovation for crop improvement[END_REF][START_REF] Abbai | Haplotype analysis of key genes governing grain yield and quality traits across 3K RG panel reveals scope for the development of tailor-made rice with enhanced genetic gains[END_REF] Furthermore, biotechnological approaches including targeted genome editing using CRISPR-Cas technologies have expedited advances in the temporal and spatial regulation of genes and major pathways for drought adaptation. [START_REF] Shi | ARGOS8 variants generated by CRISPR-Cas9 improve maize grain yield under field drought stress conditions[END_REF][START_REF] Liu | CRISPR/Cas9 targeted mutagenesis of SlLBD40, a lateral organ boundaries domain transcription factor, enhances drought tolerance in tomato[END_REF] A comprehensive understanding of the adaptive mechanisms under distinct drought scenarios is crucial for securing future harvests and fuelling the necessary genetic gain in crop improvement. Such gains can be driven by genetic variability and deployed by genomic breeding, more precise genetic modifications, and tailored management practices.

In this review, we start by discussing the major advances in crop leaf and root research associated with drought adaptation, and then describe how the context-dependent optimization of above-and below-ground traits offers opportunities to improve future crops. We discuss recent innovations in genomic breeding approaches that empower design-based crop improvement, including haplotype-based breeding, genome editing, systems biology, and genomic selection. Finally, we explore how speed breeding could interact with new-age genomic breeding technologies to speed-up crop development. Our goal is to provide a comprehensive overview of the processes related to drought and highlight possible ways to develop future crops in the face of increasing climatic fluctuations.

PHYSIOLOGICAL ADAPTATIONS TO DROUGHT

In times of drought, crops dynamically manage their water balance by: (i) limiting water loss, by reducing leaf area and stomatal conductance; [START_REF] Borrell | Drought adaptation of stay-green sorghum is associated with canopy development, leaf anatomy, root growth, and water uptake[END_REF][START_REF] Caine | Rice with reduced stomatal density conserves water and has improved drought tolerance under future climatic conditions[END_REF] (ii) enhancing soil water uptake, by altering root growth and architecture; [START_REF] Robbins | Growth is required for perception of water availability to pattern root branches in plants[END_REF][START_REF] Uga | Control of root system architecture by DEEPER ROOTING 1 increases rice yield under drought conditions[END_REF] and (iii) osmotic adjustment, via accumulation of solutes in the cells. [START_REF] Blum | Osmotic adjustment is a prime drought stress adaptive engine in support of plant production[END_REF] Here, we discuss some of the key adaptive traits in further detail.

Limiting water loss

Crops exposed to soil water deficit need to preserve available water by limiting transpiration while, in parallel, fixing adequate carbon to meet energy demands.

Reduction in leaf area and stomatal conductance display a rapid response against dehydration by limiting the transpiration rate, thus budgeting soil moisture and maintaining increased leaf water potential levels. For instance, drought adaptation of stay-green (Stg) sorghum is linked to reduced green leaf area at anthesis, lower tillering, and smaller size of upper leaves. [START_REF] Borrell | Drought adaptation of stay-green sorghum is associated with canopy development, leaf anatomy, root growth, and water uptake[END_REF] These mechanisms facilitate remarkable plasticity to the crop for modulating canopy development in response to the intensity of drought stress. Furthermore, reduced stomatal conductance and transpiration rate, leading to better water-use efficiency, enable increased drought adaptation in wheat. [START_REF] Li | Improving water-use efficiency by decreasing stomatal conductance and transpiration rate to maintain higher ear photosynthetic rate in drought-resistant wheat[END_REF] Low stomatal density also improves drought tolerance and water conservation properties in rice [START_REF] Caine | Rice with reduced stomatal density conserves water and has improved drought tolerance under future climatic conditions[END_REF] and barley. [START_REF] Hughes | Reducing stomatal density in barley improves drought tolerance without impacting on yield[END_REF] Leaf growth is mainly determined by vapor pressure deficit and available soil moisture, with a large genetic variability in the sensitivity to both conditions. As a result, leaf area evaluated at any particular time point is a consequence of the prevailing environmental conditions and genotype-dependent sensitivity. Canopy development traits are mainly driven by leaf area, [START_REF] Borrell | Drought adaptation of stay-green sorghum is associated with canopy development, leaf anatomy, root growth, and water uptake[END_REF] which is affected by other factors such as tillering or phyllochron, all of which depend on drought severity with genotype-dependent sensitivities. Therefore, if the phenotypes associated with leaf area are to be included in broader research and breeding programs, precise and dynamic measurement of leaf area becomes essential.

Phenotyping systems are being developed that strategically target leaf traits which are crucial and relatively easy to measure at the single-leaf or whole-canopy levels, and in some cases by remote sensing with drones. [START_REF] Jin | High-throughput estimation of crop traits: A review of ground and aerial phenotyping platforms[END_REF][START_REF] Liedtke | High-throughput phenotyping of dynamic canopy traits associated with stay-green in grain sorghum[END_REF]

Enhancing water uptake

The root system is the interface for soil water and nutrient acquisition, and physically anchors the plant to the soil substrate. In a plant root system, the coarse (or tap) roots play a role in plant anchorage and usually establish root system architecture, regulate rooting depth, and the capability of the plant to grow in dense soil layers. In contrast, fine (or lateral) roots are actively involved in water uptake, and mostly comprise of the length and surface area of the root system. [START_REF] Cuneo | Differences in grapevine rootstock sensitivity and recovery from drought are linked to fine root cortical lacunae and root tip function[END_REF] Root architecture and its capability to acclimate in response to environmental fluctuations are key factors determining overall plant robustness. [START_REF] Uga | Control of root system architecture by DEEPER ROOTING 1 increases rice yield under drought conditions[END_REF][START_REF] Ogura | Root system depth in Arabidopsis is shaped by EXOCYST70A3 via the dynamic modulation of auxin transport[END_REF][START_REF] Pinto | Common genetic basis for canopy temperature depression under heat and drought stress associated with optimized root distribution in bread wheat[END_REF] During soil water deficit, root systems change structurally to improve water and nutrient uptake from the soil profile. For instance, in soil environments with heterogeneous moisture distribution, roots can demonstrate hydropatterning, with a preference for lateral root emergence toward soil zones with higher water content, a process facilitated by auxin signaling. [START_REF] Orosa-Puente | Root branching toward water involves posttranslational modification of transcription factor ARF7[END_REF] Using maize roots, it is experimentally demonstrated that growth is essential for perception of water availability to pattern lateral roots in plants. [START_REF] Robbins | Growth is required for perception of water availability to pattern root branches in plants[END_REF] Hydrotropism represents another adaptive root response, where root tips propagate toward soil patches containing higher moisture content to optimize water procurement. [START_REF] Dietrich | Root hydrotropism is controlled via a cortex-specific growth mechanism[END_REF] Furthermore, root respiration provides the energy for root growth and maintenance, absorption of water molecules and ions followed by their transport into the xylem, highlighting the root physiological metabolic capability. A decline in root respiration and root biomass under severe water deficit is associated with improved grain yields and high drought adaptation in wheat cultivars. [START_REF] Liu | Root respiration, photosynthesis and grain yield of two spring wheat in response to soil drying[END_REF] Root system architecture is becoming a key target for crop improvement; however, progress in this domain has been fairly slow, partly owing to challenges with efficient phenotyping of roots. [START_REF] Bontpart | Affordable and robust phenotyping framework to analyse root system architecture of soil-grown plants[END_REF][START_REF] Atkinson | Uncovering the hidden half of plants using new advances in root phenotyping[END_REF] From a breeding viewpoint, more effective phenotyping approaches, which can evaluate large mapping populations or germplasm lines for proxies in the field and genetic variability of root characteristics on phenotyping platforms, are required to incorporate root traits in crop improvement programs.

Osmotic adjustment

Osmotic adjustment (OA) is a metabolic process that plays a key role in drought adaptation through turgor maintenance and the protection of defined cellular functions by intercellular solutes. [START_REF] Blum | Osmotic adjustment is a prime drought stress adaptive engine in support of plant production[END_REF] OA has been implicated in supporting crop yield under drought conditions. For instance, high OA wheat cultivars maintained better growth and yield, both of which were linked to enhanced leaf water potential relative to low OA cultivars. [START_REF] Abid | Physiological and biochemical changes during drought and recovery periods at tillering and jointing stages in wheat (Triticum aestivum L.)[END_REF] Mahmood et al. [START_REF] Mahmood | Incredible role of osmotic adjustment in grain yield sustainability under water scarcity conditions in wheat (Triticum aestivum L.)[END_REF] measured OA in 30 wheat genotypes subjected to well-watered and drought stress conditions in the field. Here, OA was positively associated with kernel weight that directly contributed to yield, suggesting that wheat achieves OA to uptake more soil water during low water potential. A significant and positive correlation was observed between yield and OA capacity under terminal drought stress conditions in barley. [START_REF] Gonzalez | Yield and osmotic adjustment capacity of barley under terminal water stress conditions[END_REF] Further, Moinuddin and Imas 35 evaluated eight chickpea varieties for OA and specific osmolytes such as sugars, proline, nitrogen, and potassium. The contribution of the osmolytes to OA became more crucial with an increase in water deficit towards the reproductive stage. Here, grain yield showed a linear and positive correlation with high OA and relative water content under water deficit. The importance of OA as a preferable selection target from a breeding viewpoint has been a continuing trickle of skepticism. This is mainly due to the belief that drought-adaptive genotypes with a better ability to adjust osmotically are typically characterized by slow growth and limited biomass production, because of metabolic needs for osmolyte biosynthesis. Under severe drought stress, increased accumulation of osmolytes may help crops withstand a prolonged drought episode and go through a more prompt and complete recovery after rehydration. [START_REF] Abid | Physiological and biochemical changes during drought and recovery periods at tillering and jointing stages in wheat (Triticum aestivum L.)[END_REF] OA by maintaining turgor in wheat exposed to slow drying soil, helps to partially sustain stomatal conductance, photosynthesis, and dry biomass accumulation at low levels of leaf water potentials. [START_REF] Nio | Pattern of solutes accumulated during leaf osmotic adjustment as related to duration of water deficit for wheat at the reproductive stage[END_REF] Importantly, the trade-off between metabolic costs associated with OA and the potential advantages to the crop differs on a case-to-case basis as a function of the genotype, and the dynamics and intensity of drought scenarios.

TRAIT-BASED BREEDING FOR DROUGHT ADAPTATION

Seed yield is usually the selection criterion when breeding crops for drought adaptation. However, yield is a complex and final-stage trait, which is influenced by the environmental interaction with growth and development processes that occur throughout the crop cycle. A conventional breeding strategy aimed at improving performance under drought by selecting genotypes merely based on higher absolute yields is predicted to fall short of meeting future crop production demands. [START_REF] Ray | Recent patterns of crop yield growth and stagnation[END_REF] Limited genetic variation in yield among improved cultivars, high genotype × environment × management (G × E × M) interactions, and low heritability are some critical factors that could restrict future crop improvement efforts through direct selection for yield. [START_REF] Reynolds | Translational research impacting on crop productivity in drought-prone environments[END_REF] By contrast, the genetic improvement of adaptive traits (such as biomass, harvest index, canopy temperature etc.) through changes in leaf and/or root ideotypes hold enormous potential to increase productivity and genetic gain under drought conditions, as demonstrated in wheat. [START_REF] Reynolds | Strategic crossing of biomass and harvest index -source and sink -achieves genetic gains in wheat[END_REF] This is because such traits are genetically more variable among present-day cultivars and have not been the target of conventional breeding efforts. [START_REF] Reynolds | Physiological breeding[END_REF] Designing a crop with better adaptation to drought conditions demands a major effort in improving such adaptive traits. Therefore, a trait-based strategy that evaluates genotypes on the basis of physiological responses to water deficit at the initial stages of plant growth could be more targeted to drought and time efficient.

CONTEXT-DEPENDENT OPTIMIZATION PROBLEM

Many drought-adaptive traits often possess a two-fold effect: positive in severe terminal stress conditions and negative in favorable (or milder drought stress) conditions, or vice versa. [START_REF] Tardieu | The physiological basis of drought tolerance in crop plants: A scenario-dependent probabilistic approach[END_REF] Remarkable results obtained in one drought scenario might confer only limited productivity gains in other geographical areas experiencing water deficit. Moreover, genetic trade-off among adaptive traits may also occur. For example, in wheat sister lines, investment in deeper root systems tended to be offset by reduced storage of water soluble carbohydrates in stems, the latter being important if sub-soil water is unavailable. [START_REF] Lopes | Partitioning of assimilates to deeper roots is associated with cooler canopies and increased yield under drought in wheat[END_REF] We highlight the context-dependent effects of major drought-adaptive traits on yield under water deficit.

Leaf area

For environments that experience long and severe drought episodes, genotypes possessing a small leaf area or reduced transpiration have an advantage, as they retain soil water for later phases of the crop cycle for grain filling (Figure 1). [START_REF] Blessing | Profligate and conservative: water use strategies in grain legumes[END_REF][START_REF] Mortlock | Bigger is not always better: Reducing leaf area helps stay-green sorghum use soil water more slowly[END_REF] For example, a reduced transpirational leaf area in sorghum Stg near-isogenic lines relative to their recurrent parent under severe water deficit enabled increased water extraction during grain filling, leading to better biomass production, grain number, and grain yield. [START_REF] Borrell | Stay-green alleles individually enhance grain yield in sorghum under drought by modifying canopy development and water uptake patterns[END_REF] Simulation modelling across a range of climatic scenarios and management practices suggests that reduced leaf area confers a yield reward under severe drought stress but negatively impacts crop yield and biomass accumulation under less severe circumstances in crops such as maize [START_REF] Parent | Maize yields over Europe may increase in spite of climate change, with an appropriate use of the genetic variability of flowering time[END_REF] and sorghum. [START_REF] Kholová | Modelling the effect of plant water use traits on yield and stay-green expression in sorghum[END_REF] By contrast, under rainfed field conditions that usually experience sporadic drought patterns, the ability to maintain leaf area during soil water deficit is mainly responsible for determining crop yields (Figure 1). For instance, simulation modelling revealed that early vigour traits in wheat resulted in up to 16% yield advantage via genotypes possessing doubled early leaf size, at wetter sites or years. [START_REF] Zhao | Modelling impact of early vigour on wheat yield in dryland regions[END_REF] Importantly, the maintenance of leaf growth characteristics could confer four major benefits to the crop: (i) a higher photosynthesis at canopy scale, in particular during the pre-flowering stage that affects grain number; [START_REF] Millet | Genomic prediction of maize yield across European environmental conditions[END_REF] (ii) a reduction in soil water evaporation, while facilitating efficient use of water via transpiration; [START_REF] Zhao | Modelling impact of early vigour on wheat yield in dryland regions[END_REF] (iii) a drop in leaf temperature due to higher transpiration rate; [START_REF] Medina | Physiological trade-offs of stomatal closure under high evaporative gradients in field grown soybean[END_REF] and (iv) a decrease in seed abortion rate caused by source-sink relationships. [START_REF] Nuccio | Expression of trehalose-6-phosphate phosphatase in maize ears improves yield in well-watered and drought conditions[END_REF]

Root architecture

A deep, wide-spreading, and branched root system is beneficial for most crops grown in deep soils under moisture deficit conditions. [START_REF] Uga | Control of root system architecture by DEEPER ROOTING 1 increases rice yield under drought conditions[END_REF][START_REF] Siddique | Genetics and genomics of root system variation in adaptation to drought stress in cereal crops[END_REF] This notwithstanding, breeding programs focused on improving grain yield under drought have often resulted in the development of crop varieties with reduced root biomass. [START_REF] Balanos | Eight cycles of selection for drought tolerance in lowland tropical maize. III. Responses in drought-adaptive physiological and morphological traits[END_REF][START_REF] Campos | Improving drought tolerance in maize: a view from industry[END_REF] This is mainly because, the spatial distribution of roots in the deep soil profile, but not root biomass or root length, governs the capability of root systems to efficiently uptake soil water. For instance, increased root distribution in deep soil layers (>30 cm soil depth) facilitated better water uptake and adaptation in drought tolerant chickpea genotypes. [START_REF] Purushothaman | Genotypic variation in soil water use and root distribution and their implications for drought tolerance in chickpea[END_REF] Therefore, longer and deeper roots with compact branching angles could be accompanied by high root length density in the deep soil profile to precisely capture water from the soil, which is dry at the surface but holds moisture in deeper layers (Figure 1). Soil nutrients such as phosphorous, potassium, iron, and manganese, are immobile and usually present in the upper soil layers. Hence, it should be considered that a substantial increase in root length density in the deep soil layers at the expense of upper layers would limit nutrient acquisition from the top soil and may be associated with crop yield penalties. [START_REF] Kong | Designer crops: optimal root system architecture for nutrient acquisition[END_REF] By contrast, in shallow soils that receive intermittent rainfall during the crop growing season or under optimal soil moisture conditions, an extensive, broad and shallow root system is preferable for enhancing crop productivity (Figure 1).

Crop cycle duration

Drought escape is an adaptive mechanism that involves the rapid development of a plant to complete its entire life cycle prior to the onset of drought stress. Following the concept of drought escape, the duration of the crop cycle, which is mostly determined by genes affecting flowering time, also plays a critical role in enhancing productivity under water deficit. A long crop cycle is advantageous under favorable conditions, since it increases the interception of incident solar radiation, but is associated with a yield penalty under severe terminal drought, because it depletes soil water reserves before the end of the crop cycle. [START_REF] Tardieu | The physiological basis of drought tolerance in crop plants: A scenario-dependent probabilistic approach[END_REF] This was found to be true for wheat genotypes selected in Mediterranean-type climates with frequent occurrences of terminal drought stress, where modern varieties with a drought escape strategy showed substantially higher production due to reduced risk of water stress during reproductive or grain filling stages. [START_REF] Álvaro | Breeding effects on grain filling, biomass partitioning, and remobilization in Mediterranean durum wheat[END_REF][START_REF] Perry | Yield improvement and associated characteristics of some Australian spring wheat cultivars introduced between 1860 and 1982[END_REF] The concurrent confounding effects of phenology-related components, such as the duration of vegetative period, flowering time, and crop cycle as the major factors affecting water uptake, suggest that interactions of these traits with specific leaf or root ideotypes can be explored through a combination of experiments and modelling (Box 1).

Taken together, the substantial context-dependency accompanied with above-and below-ground plant traits, highlights the need for more targeted studies considering G × E × M interactions in crops to stabilize yields in fluctuating environments. [START_REF] Cooper | Integrating genetic gain and gap analysis to predict improvements in crop productivity[END_REF] A major constraint for tailoring crop varieties is the limited genetic diversity for key traits available in modern crop gene pools, mainly due to domestication and breeding bottlenecks. [START_REF] Von Wettberg | Ecology and genomics of an important crop wild relative as a prelude to agricultural innovation[END_REF] National and international gene banks contain a great source of diverse alleles and may hold the key to addressing this limitation. Three major categories of genetic resources can be explored, namely crop wild relatives, secluded gene pools (e.g. landraces), and modern breeding lines.

Evaluating large germplasm collections for identifying variation in drought-adaptive traits may not always be feasible. In such cases, selecting an economically feasible set of accessions with a higher probability of capturing beneficial allelic variation is much more preferable. [START_REF] Varshney | Resequencing of 429 chickpea accessions from 45 countries provides insights into genome diversity, domestication and agronomic traits[END_REF] The Focused Identification of Germplasm Strategy (FIGS)

was used to enhance the efficiency of detecting specific drought-adaptive traits from faba bean germplasm collections. [START_REF] Khazaei | The FIGS (Focused Identification of Germplasm Strategy) approach identifies traits related to drought adaptation in Vicia faba genetic resources[END_REF] FIGS utilizes agro-ecological data to generate a priori information, which is then used to identify a group of accessions possessing the desired adaptive traits. An impressive illustration of this strategy came from a recent field evaluation of FIGS wheat panels prioritized based on tolerance to drought stress, which revealed over 45% of lines having greater plant biomass under drought than the adapted check varieties. [START_REF] Reynolds | Advances in Wheat Genetics: From Genome to Field[END_REF] With better access to the genetic variability found in natural populations of wild relatives and landraces, the door is open for retrieving droughtadaptive traits; several of which are encoded by alleles that disappeared in domesticated crops, or which evolved individually in diverse crop lineages. [START_REF] Varshney | Resequencing of 429 chickpea accessions from 45 countries provides insights into genome diversity, domestication and agronomic traits[END_REF] Next-generation sequencing and high-throughput genotyping platforms can be used to characterize allelic diversity in genetic resources, [START_REF] Rasheed | Crop breeding chips and genotyping platforms: progress, challenges, and perspectives[END_REF] and suitable lines carrying desired combinations of alleles can be used to develop specific leaf and/or root ideotypes for target environments. [START_REF] Placido | Introgression of novel traits from a wild wheat relative improves drought adaptation in wheat[END_REF] Recent sequencing efforts, including The 3000 Rice Genome [START_REF] Wang | Genomic variation in 3,010 diverse accessions of Asian cultivated rice[END_REF] and The 3000 Chickpea Genome 66 hold promise to provide novel insights into intra-species genetic variation and evolutionary crop history. The integration of gene bank passport data and weather data from the target population of environments (TPE) can be utilized to identify superior haplotypes for specific adaptive traits, which could be used in haplotype-based breeding (discussed below). [START_REF] Bevan | Genomic innovation for crop improvement[END_REF] Additionally, deleterious alleles (genetic load) associated with the trait(s) of interest could be identified by utilizing genomic evolution parameters and amino acid conservation modeling, as demonstrated in cassava [START_REF] Ramu | Cassava haplotype map highlights fixation of deleterious mutations during clonal propagation[END_REF] and chickpea, [START_REF] Varshney | A global reference for chickpea genetic variation based on the sequencing of 3,366 genomes[END_REF] and eliminated using molecular breeding or genome editing strategies. [START_REF] Johnsson | Removal of alleles by genome editing (RAGE) against deleterious load[END_REF] As a result, superior parental lines containing preferred alleles at each locus and with minimum undesirable genetic load could be identified and integrated into breeding programs to tailor crops with desired allelic combinations.

INNOVATIVE GENOMIC BREEDING STRATEGIES

Given the enormous genetic diversity available in germplasm repositories, extracting meaningful information from these resources require new-age breeding strategies.

Genomic breeding plays a significant role in crop improvement, [START_REF] Varshney | Designing future crops: Genomics-assisted breeding comes of the age[END_REF] as highlighted by the development of a large number of improved field-grown crops with better adaptation to drought conditions (Table 1). Some genomic breeding approaches are being successfully used in major crops such as rice, wheat, maize etc. in the highly industrialized world. However, crops grown in marginal environments such as pearl millet, sorghum, chickpea, pigeonpea, and cassava remain largely eluded from this success. Drought and desertification in the dryland regions result in an estimated loss of 12 million hectares of land every year, which accounts further in a loss of 20 million tons of food grain production. [START_REF]Desertification: The Invisible Frontline[END_REF] This demands an urgent investment in improving the drought adaptation of dryland crops using modern technologies, for ensuring future food security. Here, we describe how genomic innovations coupled with modern breeding efforts offer opportunities for designing drought-adaptive crops across the world, particularly in South Asia and Sub-Saharan Africa.

Haplotype-based breeding

Plant breeding depends on recombination to combine preferred combinations of traits for developing improved crop varieties. Traditional breeding uses heritability of phenotypes as a key criterion to evaluate genetic combinations. The genomic regions defined by quantitative trait loci (QTLs) typically contain multiple candidate genes and genetic variations, which either do not confer desired traits or possess harmful effects.

Combinations of genomic loci that contribute to the preferred phenotype can be considered as groups of haplotypes that are determined by underlying genetic variation. Use of such genomic information enables the breeder to select superior haplotypes for designing ideal crop varieties in silico and deploy them in breeding programs. We refer to this concept as haplotype-based breeding, representing the evolution and a much more accurate version of 'breeding by design'. [START_REF] Peleman | Breeding by design[END_REF] The retrospective and prospective approaches suggested by Bevan et al. [START_REF] Bevan | Genomic innovation for crop improvement[END_REF] hold great potential for deploying a haplotype-based breeding strategy to develop droughtadaptive crops. In the retrospective approach, the genomic regions and the underlying haplotypes preferred by breeders over time can be identified by sequencing the genomes of important breeding lines, which have been widely evaluated across multiple environments and years in past decades. This will provide an overview of the breeders' selection decisions over time and help determine superior haplotypes related to previous breeding success. This approach was demonstrated recently by identification of candidate genes and signatures of artificial selection associated with seed size and weight using sequencing data for 200 accessions of cultivated flax (Linum usitatissimum L.). [START_REF] Guo | Resequencing 200 flax cultivated accessions identifies candidate genes related to seed size and weight and reveals signatures of artificial selection[END_REF] Furthermore, the information acquired by employing a retrospective approach can be used to identify the function of genomic regions containing the haplotypes, referred to as haplotigs, [START_REF] Chin | Phased diploid genome assembly with single molecule real-time sequencing[END_REF] and determine the underlying desired and deleterious alleles associated with adaptive traits. By contrast, a prospective approach can be utilized by sequencing large ancestral populations and undomesticated crop varieties, to determine conserved inherited haplotigs with huge genetic variation and to identify combinations of superior haplotypes. This approach was used in a recent study to detect superior haplotypes for key genes related to drought tolerance component traits, which can be deployed in haplotype-based breeding of pigeonpea. [START_REF] Sinha | Superior haplotypes for haplotype-based breeding for drought tolerance in pigeonpea (Cajanus cajan L.)[END_REF] Haplotype-based breeding represents a promising strategy for crops in which large germplasm collections are characterized both at the sequencing and phenotyping level. Assembling desired haplotype combinations in elite crop varieties will enable informed decision-making in breeding programs. [START_REF] Varshney | Designing future crops: Genomics-assisted breeding comes of the age[END_REF] For instance, a combination of superior haplotypes of previously validated genes that confer small leaf area, deeper root system, early flowering, and higher yield can be used to design crop ideotypes for improved adaptation to terminal drought stress (Figure 2). Taken together, haplotypebased breeding is expected to design future crops with desired adaptive traits, while demanding less monetary investment and in the absence of challenging public acceptance.

Genome editing

Introgression of desired traits into an elite variety is often impaired by the random nature of recombination and linkage drag, making conventional breeding a timeconsuming and laborious process. Heavy dependence on natural or random genetic diversity is a major constraint delaying the breeding process and leading to an unpredictable outcome. [START_REF] Scheben | Towards a more predictable plant breeding pipeline with CRISPR/Cas-induced allelic series to optimize quantitative and qualitative traits[END_REF] In contrast, genome editing holds enormous potential to generate precise, efficient, and targeted alterations in crop plants. It can be performed with any crop, including those that possess complex genome architecture and that are not readily bred using conventional approaches. [START_REF] Abdallah | Genome editing for crop improvement: Challenges and opportunities[END_REF] The recent development of clustered regularly interspaced short palindromic repeats (CRISPR)-CRISPRassociated nuclease protein (Cas) systems have brought genome editing into the limelight. [START_REF] Shi | ARGOS8 variants generated by CRISPR-Cas9 improve maize grain yield under field drought stress conditions[END_REF][START_REF] Zhu | Applications of CRISPR-Cas in agriculture and plant biotechnology[END_REF] Several gene knockout, insertion or replacement mutants are developed by CRISPR-Cas9-mediated editing in field-grown crops to improve their drought adaptation characteristics (Table 1).

Technical breakthroughs in the genome editing toolkit provide opportunities to exploit mutations giving rise to optimal shoot and/or root architecture for designing crops for the future. CRISPR-Cas9-mediated base editing is one such example, which can precisely change one DNA base into another in the absence of a DNA repair template. [START_REF] Gaudelli | Programmable base editing of A•T to G•C in genomic DNA without DNA cleavage[END_REF][START_REF] Komor | Programmable editing of a target base in genomic DNA without double-stranded DNA cleavage[END_REF] Recent development of a PAM-less CRISPR-SpRY toolbox, which disrupts a PAM restriction barrier of targeting only GC-rich DNA regions, has greatly expanded base editing scope in crops. [START_REF] Ren | PAM-less plant genome editing using a CRISPR-SpRY toolbox[END_REF] Traditional transgene-mediated CRISPR-Cas delivery techniques (Figure 3) may be linked with undesirable genetic changes, [START_REF] Jupe | The complex architecture and epigenomic impact of plant T-DNA insertions[END_REF] with extended breeding cycles and regulatory constraints. Therefore, ribonucleoprotein (RNP)-based DNA-free genome editing [START_REF] Woo | DNA-free genome editing in plants with preassembled CRISPR-Cas9 ribonucleoproteins[END_REF] is considered a major leap towards developing genome-edited crops with a lower risk of undesired off-target modifications, and satisfying present and future agricultural needs from a regulatory perspective. This technology has been accomplished in grapevine and apple through protoplast transformation, [START_REF] Malnoy | DNA-free genetically edited grapevine and apple protoplast using CRISPR/Cas9 ribonucleoproteins[END_REF] in bread wheat via in planta particle bombardment, [START_REF] Liang | Efficient DNA-free genome editing of bread wheat using CRISPR/Cas9 ribonucleoprotein complexes[END_REF] and in tobacco by virus infection [START_REF] Ma | Highly efficient DNA-free plant genome editing using virally delivered CRISPR-Cas9[END_REF] (Figure 3). The newly emerged CRISPR-Cas12a 86 Drought adaptation processes in crops are often regulated by complex genetic mechanisms with the combined expression of numerous genes. Based on Golden Gate and Gateway assemblies, multiplex CRISPR-Cas expression systems have been developed for different applications in plants. [START_REF] Mccarty | Multiplexed CRISPR technologies for gene editing and transcriptional regulation[END_REF] For example, multiplex CRISPR-Cas systems have been used for generating quantitative trait variation in tomato by editing cis-regulatory elements in the promoter [START_REF] Rodríguez-Leal | Engineering quantitative trait variation for crop improvement by genome editing[END_REF] and for de novo crop domestication by simultaneous editing of multiple trait genes in wild tomato. [START_REF] Li | Domestication of wild tomato is accelerated by genome editing[END_REF] Furthermore, a fusion of diverse effector domains to catalytically inactivated Cas (dCas) proteins has repurposed CRISPR systems for transcriptional regulation and epigenome editing in plants. [START_REF] Pan | CRISPR/dCas-mediated transcriptional and epigenetic regulation in plants[END_REF] Such innovative genome editing strategies could be harnessed to tailor shoot and root architectural traits in custom-designed crops. Moreover, the integration of speed breeding (see later) with genome editing technology, referred to as 'Express Edit', [START_REF] Hickey | Breeding crops to feed 10 billion[END_REF] will enable genome editing to bypass the restrictions imposed by in vitro manipulation of plant tissues. This, in turn, will facilitate the inclusion of genome editing into large-scale breeding programs for crop improvement.

Systems biology-based breeding

Drought adaptation is a complex trait comprising an intricate regulatory network of phytohormones, transcription factors, and kinases. It is essential to further unfold the direct interactions between these key players and their downstream targets to shortlist most potential candidates for breeding purposes. This demands the use of a systems biology approach to unravel the temporal dynamics and spatial configurations specifying the biological phenomenon of interest.

In plants, cellular processes are typically governed by gene regulatory networks (GRNs) that can influence a trait of agronomic interest. [START_REF] Walley | Integration of omic networks in a developmental atlas of maize[END_REF] To design specific crop ideotypes, GRNs can identify the most promising candidate genes, predict the network behavior arising from the altered genes and the resulting phenotypes of the traits modulated by the network. For instance, a limited number of QTLs and candidate genes regulating leaf senescence, an important determinant of drought adaptation, have been identified till date in crops such as wheat. [START_REF] Verma | Mapping quantitative trait loci for flag leaf senescence as a yield determinant in winter wheat under optimal and drought-stressed environments[END_REF][START_REF] Wang | Quantitative trait loci mapping for traits related to the progression of wheat flag leaf senescence[END_REF][START_REF] Uauy | A NAC gene regulating senescence improves grain protein, zinc, and iron content in wheat[END_REF][START_REF] Zhao | Overexpression of a NAC transcription factor delays leaf senescence and increases grain nitrogen concentration in wheat[END_REF] A comprehensive understanding of the network of genes modulating this process may facilitate the development of wheat varieties having a senescence profile tailored to augment nutrient remobilization, while enabling improved yield and adaption to drought conditions. In a recent study, analyses of gene expression data and GRN modelling led to the identification of key transcriptional regulators (such as NAM-A2) that coordinate flag leaf senescence in wheat. [START_REF] Borrill | Identification of transcription factors regulating senescence in wheat through gene regulatory network modeling[END_REF] Such approaches will help to understand network performance and identify breeding targets that are usually not detected by traditional forward-and reverse-genetics strategies, and utilize them to manipulate an entire network to build the desired phenotype. Novel insights into the complex associations existing between different adaptive traits and their corresponding genes at the systems level will help to identify preferable haplotypes and to design haplotypebased breeding scheme. In rice, meta-expression analysis together with coexpression network offered insights into the function of multiple genes and their interactions at a systems level, which in turn helped in the selection of desired haplotypes for haplotype-based breeding. [START_REF] Abbai | Haplotype analysis of key genes governing grain yield and quality traits across 3K RG panel reveals scope for the development of tailor-made rice with enhanced genetic gains[END_REF] Furthermore, dynamic modelling and virtual mutations have shown promise in determining GRN engineering targets in order to tailor the desired phenotype. [START_REF] Scardoni | Node interference and robustness: performing virtual knock-out experiments on biological networks: the case of leukocyte integrin activation network[END_REF] Therefore, upcoming efforts to determine molecular breeding targets should focus on such candidates, and assess the impact of virtual mutations in silico by modifying the network model and capturing transient interactions among the GRN. 100 For drought adaptation in crops, such dynamic models will offer robust support for validating the hypothesis obtained from field experiments and accurately defining technologies for rationalizing breeding strategies.

A systems biology approach will provide hints to detect genetic regulators exercising the largest effect on GRNs, even where gene redundancies, mild-effect genes, or feedback loops hinder traditional gene investigation capabilities. [START_REF] Borrill | Identification of transcription factors regulating senescence in wheat through gene regulatory network modeling[END_REF] This approach will be particularly relevant for designing ideotypes for crops with complex genomes and multi-genic traits, where systems-scale strategies are predicted to outperform the restrictions of conventional breeding approaches in the context of efficacy and speed.

Genomic selection and speed breeding

Innovations in genomic technologies are of particular relevance for improving future crops. However, it takes multiple years for an improved crop variety to be advanced and released for commercial cultivation due to prolonged breeding cycles, which in turn hampers the gain in productivity. Genomic selection and speed breeding approaches are crucial to address the long breeding cycle issue in crops. Genomic selection, which estimates the genetic merit of breeding lines for complex traits such as drought adaptation and which increases the efficiency of selection process, is being successfully deployed in many crop breeding programs (Table 1). A good illustration of its impact came from recent field evaluation of drought tolerant maize hybrids (called as 'AQUAmax' hybrids), which possessed substantially higher yields under both optimal and drought stress conditions. 101,102 On the other hand, speed breeding by achieving up to six generations per year for wheat, barley, chickpea, and pea using specific and highly controlled environmental conditions such as 22 hour-long photoperiods, has emerged as a popular approach for accelerated crop development. 103 For custom-designed crops, genomic selection can save time and resources typically for traits that are phenotyped during the final stages of the variety development process and those that are costly to measure, e.g., yield. While speed breeding can decrease generation times drastically, the genetic gain associated with this technique can be further improved by applying genomic selection at every generation to choose parents for the next generation (Figure 4). The strategy of combining speed breeding with genomic selection, referred to as 'speed GS', holds potential for fast-forwarding the rate of genetic gain in crop improvement.

A particular haplotype with the highest genomic estimated breeding value can be determined for each genomic region and demarcated by linkage disequilibrium blocks.

Desired haplotypes can then be stacked in a cropping line by using an optimum array of crosses. This approach of combining genomic selection with superior haplotypes, called 'haplo-GS', can be integrated with speed breeding to rapidly tailor crop varieties with high performance across multiple adaptive traits. The use of haplo-GS approach could more precisely illustrate the complex relationships between genotype and phenotype, relative to individual SNPs, ultimately enhancing selection gain per unit of time.

CONCLUSIONS AND PERSPECTIVES

Future food security will depend on the continuous development of improved crop varieties, which sustain greater yields with minimum agronomic inputs and that are better adapted to climate change. Crops can encounter fluctuating drought scenarios, ranging from mild to severe drought episodes that occur at the beginning, mid, or towards the end of the crop cycle. Attributes such as soil depth and constitution, water availability, climate, and management practices also impact crop responses to water deficit. As a result, conceptualizing a drought-adaptive ideotype optimized for an array of scenarios may not be possible, but distinct traits related to drought adaptation that are similar across species grown under diverse field conditions could be used as targets for custom-designing crops for specific environments. Developing such designer crops that integrate individually strengthened leaf and root systems, can be simplified by implementing recent technical breakthroughs in crop modeling, second and third generation sequencing, novel breeding techniques, genome editing, deep learning approaches, and high-throughput phenotyping.

Combining genetic resources and transformative capabilities, ranging from genomic breeding to synthetic biology, will be essential for tailoring crops that improve food security and decrease the impact of agriculture on the environment. Notably, the integration of artificial intelligence (AI) and machine learning algorithms into the processing of hyperspectral images and weather data will enable early-stage prediction of drought scenarios. In turn, the AI system will allow farmers' to make more informed decisions at every step of the crop production cycle. Finally, the contextdependent effect of each trait, multiplicity of combined traits, and genotype × environment interactions for each trait necessitates the use of modeling, to predict the effect of thousands of allele combinations in thousands of fields. This will help to derive a probabilistic approach for identifying the most desirable allelic combinations in a given field/region depending on the scale of the target environment.

A custom-designed crop will be a valuable asset in our attempts to quench agriculture's growing thirst, and maximize productivity while enhancing yield stability in the face of enhancing environmental fluctuations. This ambitious aim needs the collaborative will and efforts of breeders, geneticists, physiologists, systems modelers, and bioinformaticians alike. conditions. Selection candidates could be phenotyped for grain yield secondary traits (e.g., root architecture) in the glasshouse, and plants that carry the desired trait could be selected. Context-dependent selection of the trait will enable plants to be better adapted to the target environment prior to selecting more complex traits, such as yield.

Phenotyping and selecting plants under speed breeding in the glasshouse could further improve selection intensity and the rate of genetic gain.

Box 1. A probabilistic approach for drought adaptation

A deeper understanding of the dual effects of most drought-adaptive traits is crucial for tailoring future crops with a phenotype matching the target climatic scenarios. In theory, custom-designed crops should carry a genetic predisposition for a particular leaf or root architecture together with mechanisms allowing growth plasticity in response to water deficit, as observed in wheat. [START_REF] Pinto | Common genetic basis for canopy temperature depression under heat and drought stress associated with optimized root distribution in bread wheat[END_REF] This could significantly increase a crop's ability to maximize resource capture from the surrounding environment while reducing the impact associated with climatic fluctuations. The context-dependency of nearly every trait on yield needs a two-step approach: (i) identify the combination of alleles that influence the response of studied traits to environmental conditions, and

(ii) detect the response of yield to traits or allelic combinations in most frequent scenarios sensed by plants in a given region. [START_REF] Tardieu | The physiological basis of drought tolerance in crop plants: A scenario-dependent probabilistic approach[END_REF] To this end, Millet et al. [START_REF] Millet | Genomic prediction of maize yield across European environmental conditions[END_REF] suggested a simplified approach using a regressive model of responses to environmental conditions in maize, with genotype-dependent sensitivities that were modelled by genomic prediction. This consisted of three major phases: (1) to establish response curves of yield components to soil water deficit, evaporative demand, and light in a multi-site field experiment; (2) to simulate the sensitivity of each genotype based on genomic prediction; and (3) to predict yield of hundreds of genotypes in hundreds of fields in which drought stress differed between years. Because farmers do not know at the time of sowing the actual environmental scenario that will be sensed by plants, the choice of genotype will ultimately depend on the probability of environmental scenarios in each farmers' field, [START_REF] Parent | Maize yields over Europe may increase in spite of climate change, with an appropriate use of the genetic variability of flowering time[END_REF] and the farmers' own choice between maximum gain vs. risk avoidance. Such a probabilistic approach, which is based largely on the genetic variability of adaptive traits and on their context-dependent effects, may eventually assist breeders to improve drought adaptation of major field-grown crops.

(

  formerly Cpf1) and Cas12b 87 (formerly C2c1) systems have several key advantages over Cas9, such as preferring T-rich PAMs (enabling alternative targeting sites to Cas9), and generating staggered ends of DNA double stranded breaks as opposed to blunt ends created by Cas9. Hence, the application of CRISPR-Cas12a and Cas12b could provide attractive alternatives to CRISPR-Cas9 systems in designing crop ideotypes for specific drought environments.

Table 1 . 44 ↓

 144 Key success stories of genomic breeding strategies to improve drought adaptation and grain yield in field-grown crops Tiller number ↓ Canopy size at anthesis ↑ Post-anthesis water use

Figure 1 :

 1 Figure 1: Yield benefits and drawbacks linked to leaf area and root system architecture under different drought scenarios. The most advantageous leaf and root phenotype is highly context-dependent and impacted by several components, including climate, soil, or management. Reduced leaf area retains soil moisture and decreases hydraulic gradients, and is associated with yield reward under terminal severe stress; whereas, it lowers cumulative photosynthesis during the crop cycle and displays a yield penalty under favorable conditions/mild drought stress. Deeper roots increase water uptake from very deep soil layers and possess yield reward under terminal severe drought stress conditions where deep water is available; whereas, it leads to a lower nutrient uptake and is suboptimal under favorable conditions for nutrient foraging in upper soil layers.

Figure 2 :

 2 Figure 2: Haplotype-based breeding scheme for designing drought-adaptive crops. (A) An example of haplotypic variation (H1-H4) underlying a particular gene (gene 3) on a chromosome. A combination of various haplotypes for different genes (gene 1, gene 2, gene 3, gene n …) has been shown in multiple genotypes (genotype 1, genotype 2, genotype 3, and genotype n). Superior haplotypes are selected for various genes based on the preferred combinations of phenotypes, expressed by the respective haplotype. (B) Difference in the performance of four traits associated with drought adaptation that are influenced by genetic variation in gene 1 (leaf area), gene (root depth), gene 3 (time to flower) and gene n (yield), is illustrated using violin plots. Analysis of variance results indicate that H3 is the superior haplotype for gene 1, H1 for gene 2, H2 for gene 3, and H3 for gene n. (C) Introgression of superior haplotypes for multiple adaptive traits in an elite variety using haplotype-based breeding approach will enable development of an introgression line possessing improved drought adaptation.

Figure 3 :

 3 Figure 3: Strategies for delivery of CRISPR-Cas systems to plants. Traditional delivery systems for genome editing include CRISPR-Cas DNA together with selection pressure. Genetic segregation via selfing and crossing results in the development of transgene-free plants. Transient delivery methods for DNA-free genome editing involves the use of CRISPR-Cas reagents, such as RNA and ribonucleoproteins

Figure 4 :

 4 Figure 4: Integrating genomic selection and speed breeding to fast-forward genetic gain in crops. The breeding cycle length decreased by genomic selection could be further reduced by performing population development under speed breeding

ACKNOWLEDGEMENTS

Rajeev K. Varshney is grateful to Bill & Melinda Gates Foundation, USA, and Department of Biotechnology, Ministry of Science & Technology, and Ministry of Agriculture & Farmers Welfare of Government of India for supporting research on drought adaptation. Thanks are also due to Science & Engineering Research Board (SERB) of Department of Science & Technology (DST), Government of India for providing the J C Bose National Fellowship (SB/S9/Z-13/2019) to Rajeev K. Varshney for writing this article. Rutwik Barmukh acknowledges the funding support from Council of Scientific and Industrial Research (CSIR), Government of India, for the award of a research fellowship. Yiping Qi is supported by NSF grants (IOS-1758745 and IOS-2029889) and USDA-NIFA grants (2018-33522-28789, 2020-33522-32274 and 2020-70029-33161).

AUTHOR CONTRIBUTIONS

Rajeev K. Varshney conceived the idea, Rajeev K. Varshney and Rutwik Barmukh wrote the manuscript. All authors substantially contributed to the discussion of content, and reviewed and/or edited the manuscript before submission.

COMPETING INTERESTS

The authors declare no competing interests.

Box 2: Glossary

Adaptive trait

A phenotypic trait that differs with existing environmental scenarios for a particular genotype, and which can maximise fitness or production in specific environmental conditions.

Anthesis

The period during which a flower is completely open and functional.

Drought adaptation

The ability to sustain biomass production or crop yield, despite the occurrence of drought episodes during the crop cycle.

Environmental scenario

A clustered pattern of time courses for soil moisture status, evaporative demand, light, and temperature in diverse fields (a particular field can experience different scenarios in different years).

Express Edit

A system that incorporates gene editing directly in the speed breeding system, and has the potential to bypass the bottlenecks of in vitro manipulation of plant materials.

Gene regulatory network (GRN)

A group of molecular factors (genes, RNA, and proteins) that interact directly or indirectly with each other and together influence a biological process of interest.

Genetic gain

Improvement in the average genetic value in a population or in the average phenotypic value due to selection within a population over multiple cycles of breeding.

Genomic breeding

A breeding approach that uses '-omics' data, knowledge resources, genes, and technologies, developed from genomics and genome editing research for crop improvement.

Haplotypes

A group of alleles within an organism that are inherited together from a single parent.

Haplotype-based breeding

A promising breeding approach for developing custom-made crop varieties by introgressing superior haplotypes in elite breeding lines.

Harvest index

Harvest index is defined as the ratio of harvested grain to total shoot dry matter, and it can be used as a measure of reproductive efficiency.

Hydro-patterning

A root developmental response where lateral roots preferentially initiate to the side in contact with water.

Hydrotropism

The directed growth of roots towards water or moisture gradients.

Hyperspectral images

Refers to the images in which one continuous spectrum is measured for each pixel.

Ideotype

A biological model that is anticipated to perform in a predictable manner within a specific environment.

Leaf water potential

Indicates the whole plant water status and contributes to plant-level physiological drought adaptation.

Linkage drag

The undesirable effects of deleterious alleles genetically associated with the desired trait.

Osmotic adjustment

A reduction in osmotic potential attained by the accumulation of solutes in response to osmotic stress.

Osmolyte biosynthesis

The synthesis and accumulation of diverse osmolytes in plants for combatting osmotic and oxidative stress.

Phyllochron

The time interval between the appearances of successive leaves on the main stem of the plant.

Protospacer adjacent motif (PAM)

The DNA motif flanking the target sequence that is indispensable for target recognition and cleavage by CRISPR-Cas systems.

Speed breeding

A breeding strategy that greatly shortens generation time in plants, by using supplemental lighting under glasshouse conditions and by extending the photoperiod to a day-length of 22 hours.

Stomatal conductance

A measure of the rate of carbon dioxide uptake and water loss (viz. transpiration) through the stomata of a leaf, as evaluated by the degree of stomatal aperture.

Systems biology

A holistic approach for deciphering the complexity of biological systems that starts from the understanding that networks that form the whole of living organisms are more than the sum of their parts.

Target population of environments (TPE)

The set of fields and future climate scenarios in which the crop varieties produced by a breeding program will be grown.

Tillering

The production of lateral shoots by a plant, mostly a grass or cereal, from the base of the stem.

GGN2_202100017_Figure_2.tif

GGN2_202100017_Figure_3.tif


Bruno Dato
email: bruno.dato@irit.fr

Marie-Pierre Gleizes
email: marie-pierre.gleizes@irit.fr

Frédéric Migeon
email: frederic.migeon@irit.fr

Cooperative Neighborhood Learning: Application to Robotic Inverse Model

Keywords: Multiagent Learning, Distributed Problem Solving, Learning by Endogenous Feedback, Inverse Kinematics Learning

In this paper we present a generic multiagent learning system based on context learning applied in robotics. By applying learning with multiagent systems in robotics, we propose an endogenous self-learning strategy to improve learning performances. Inspired by constructivism, this learning mechanism encapsulates models in agents. To enhance the learning performance despite the weak amount of data, local and internal negotiation, also called cooperation, is introduced. Agents collaborate by generating artificial learning situations to improve their model. A second contribution is a new exploitation of the learnt models that allows less training. We consider highly redundant robotic arms to learn their Inverse Kinematic Model. A multiagent system learns a collective of models for a robotic arm. The exploitation of the models allows to control the end position of the robotic arm in a 2D/3D space. We show how the addition of artificial learning situations increases the performances of the learnt model and decreases the required labeled learning data. Experimentations are conducted on simulated arms with up to 30 joints in a 2D task space.

Introduction

One of the challenges of robotic interactive systems is to learn without having any intrinsic knowledge of the tasks they will have to solve. To do so, they need internal curiosity mechanisms to avoid biases, maximize genericity and provide adaptation to their environment [START_REF] Oudeyer | Socially guided intrinsic motivation for robot learning of motor skills[END_REF]. Such a system is also called an agnostic system [START_REF] Kearns | Toward efficient agnostic learning[END_REF]. To design it, it is essential to generate knowledge through processes and actions that are purely internal to an interactive system. We call this type of process: "learning by endogenous feedback".

The constructivist approach has shown to be attractive for robotics where a child learner, using assimilation and accommodation [START_REF] Piaget | Piaget's theory[END_REF], can be replaced by a robot learner which is confronted to its physical real world (many parameters, many interconnections, feedback loops, non-linearity, threshold effects, dynamics...). Considering this physical world as a complex system allows to generalize the conceptualization of learning and thus to make it generic. Control in this context requires a complex artificial controller able to differentiate and face all kinds of situations [START_REF] Ashby | Cybernetics and requisite variety. An Introduction to Cybernetics[END_REF]. A relevant approach for this problem is context-based adaptive multiagent sys-tems. Inspired from contructivism, it is able to deal with complex systems. This self-adaptive approach allows communication between fragments of learnt models to enhance their performances. Our goal is to learn from small amount of examples as additional examples are internally generated. This paper focuses on self-enrichment of knowledge fragments through learning by multiagent systems. Another of our concern is the scalability of the proposed learning architecture that is applied to the inverse control of robotic arms.

In the paper, we begin by giving a quick overview of the work around inverse models in robotics and computer graphics. We follow with the presentation of the studies that led to Context Learning. We then detail our contribution which is Endogenous Context Learning coupled with a new exploitation of the learnt models. We evaluate the learning across metrics of control performance and data.

Background

In this section, we provide a brief outline of inverse models in robotics and computer graphics. We introduce Context Learning inspired by Constructivist Learning and present the state of various works carried out in this theme.

Inverse Models

Robotic applications usually rely on task space controllers. The model allowing to control a robot in its task space is called the Inverse Kinematic Model (IKM). It can be calculated with analytical approaches for rigid bodied robots of low DOF (Degrees Of Freedom). These approaches perform poorly on complex systems with lot of DOF or soft robots as they are difficult to model [START_REF] Thuruthel | Learning global inverse kinematics solutions for a continuum robot[END_REF]. Common methods for solving IKM of a redundant manipulator systems are numerical solutions: pseudo-inverse methods [START_REF] Gardner | Kinematics of mobile manipulators and implications for design[END_REF][START_REF] Bayle | Manipulability of wheeled mobile manipulators: Application to motion generation[END_REF] and Jacobian transpose methods [START_REF] Hootsmans | Large motion control of mobile manipulators including vehicle suspension characteristics[END_REF]. They allow better scalability for higher DOF but they still rely on the availability of accurate robot parameters which can be difficult to obtain. Recent motion caption techniques allow to generate pre-learnt postures and use datadriven approaches for Inverse Kinematics problems [START_REF] Ho | Topology aware data-driven inverse kinematics[END_REF][START_REF] Holden | A deep learning framework for character motion synthesis and editing[END_REF]. Hybrid methods combine previous techniques and attempt to reduce the complexity of the problem by decomposing it in several components [START_REF] Unzueta | Full-body performance animation with sequential inverse kinematics[END_REF]. Datadriven techniques are the most exploited approaches in the last decades in the domain of computer graphics [START_REF] Aristidou | Inverse kinematics techniques in computer graphics: A survey[END_REF]. We also found geometric approaches that provide direct solutions using geometrical heuristics [START_REF] Jamali | A new geometrical approach to solve inverse kinematics of hyper redundant robots with variable link length[END_REF]. From the point a view of developmental robotics, [START_REF] Baranes | Active learning of inverse models with intrinsically motivated goal exploration in robots[END_REF] tackled the Inverse Kinematics problem by using intrinsically motivated goal exploration while learning the limits of reachability.

Future robots will possess soft joints and high numbers of DOF making them difficult or yet impossible to model. Thus, learning the IKM for complex robots is an inevitable way. The implemented architecture for learning the IKM presented is this paper can be considered as a data-driven approach.

Constructivism and Multiagent Systems

Context Learning is inspired by Constructivist Learning, which is a theory from Piaget's work on child development [START_REF] Piaget | Piaget's theory[END_REF]. According to this theory, knowledge is a construction based on the observation of a subject's environment and the impact of its actions. The basic unit of knowledge in this theory is the schema. It aggregates several perceptions and, in most cases, several actions [START_REF] Guerin | Learning like a baby: a survey of artificial intelligence approaches[END_REF]. Proposed by Drescher [START_REF] Drescher | Made-up minds: a constructivist approach to artificial intelligence[END_REF] then formalized by Holmes [START_REF] Holmes | Schema learning: Experiencebased construction of predictive action models[END_REF], it has been reused by combining it with Self-Organizing Maps (SOM) [START_REF] Chaput | The constructivist learning architecture: A model of cognitive development for robust autonomous robots[END_REF][START_REF] Provost | Developing navigation behavior through self-organizing distinctive-state abstraction[END_REF] and model-based learning [START_REF] Perotto | A computational constructivist model as an anticipatory learning mechanism for coupled agent-environment systems[END_REF]. The Multiagent Systems approach [START_REF] Ferber | Multi-agent systems: an introduction to distributed artificial intelligence[END_REF], and in particular the AMAS (Adaptive Multiagent Systems) approach [START_REF] Georgé | Cooperation[END_REF], gives a system adaptive properties to deal with unexpected situations, which is appropriate for learning systems [START_REF] Mazac | On bootstrapping sensori-motor patterns for a constructivist learning system in continuous environments[END_REF][START_REF] Guériau | A constructivist approach for a self-adaptive decision-making system: application to road traffic control[END_REF]). An AMAS is a complex artificial system composed of fine-grained agents promoting the emergence of expected global properties. It allows to cope with the complexity of the world (non-linearity, dynamics, distributed information, noisy data and unpredictability) as defined by Ashby [START_REF] Ashby | Cybernetics and requisite variety. An Introduction to Cybernetics[END_REF]. Numerous experiments have shown such properties in areas such as the control of biological processes, the optimal control of motors or robotics learning [START_REF] Boes | The self-adaptive context learning pattern: Overview and proposal[END_REF].

Context Learning

The contribution in this paper is based on the AMOEBA system (Agnostic MOdEl Builder by self-Adaptation) [START_REF] Nigon | Selfadaptive model generation for ambient systems[END_REF]. It relies on Context Learning and implements supervised online agnostic learning capable of generalizing with continuous training data. This section presents the formalism of Context Learning and the functioning of the AMOEBA system.

Context Learning is a problem of exploring a search space with n dimensions and estimating a local model based on any machine learning technique (neural networks, linear regression, SVMs, nearest neighbor, k-means...). An instance of the learning system learns an output called the prediction vector O m ∈ R m according to a hidden function F (P n ) = F (p 1 , . . . , p i , . . . , p n ) = O m with O m ∈ R m the desired predictions or the oracle values. P n is the vector of inputs called the perceptions and P n = [p 1 , . . . , p n ] ∈ R n . The perceptions can be the state of robot (sensors, position, speed ...) or a situation of an environment (temperature, luminosity, noise...). The vector L n,m = [P n , O m ], composed of perceptions associated with desired predictions, defines a learning situation, which is similar to a schema in Piaget's theory. A learnt model is represented by a Context Agent

1 . A learning situation is then L n,1 = [P n , O 1 ].

Exogenous Learning Rules

Learning with Context Agents in AMOEBA [START_REF] Nigon | Selfadaptive model generation for ambient systems[END_REF] is based on several simple rules. Each execution cycle is either a learning cycle or an exploitation cycle. For learning cycles, the input is a learning situation L n,1 and for exploitation cycles, the input is an exploitation situation that is only perceptions P n .

Learning Cycles During learning cycles, if the perceptions P n belong to the validity ranges of an existing Context Agent, it is a Valid Context Agent (Fig. 2a). It proposes a prediction with its model. If there are several Valid Context Agents, the prediction of the one with the best confidence is retained. It is called the Best Context Agent for the current execution cycle. If it gives a good prediction, it increments its confidence. If the prediction is bad all Valid Context Agents reorganize themselves by following adaptive behaviors. To know if the prediction of a Context Agent is good or bad, an error margin and an inaccuracy margin are used. They are given by the user of the learning mechanism. A prediction is good if the error with the oracle's prediction O 1 is less than the inaccuracy margin.

Endogenous Context Learning

Endogenous Context Learning is an enhancement of Context Learning using internal information to self-generate new learning situations. In the next sections, we differentiate exogenous learning situations and endogenous learning situations which are respectively provided by an external entity and selfgenerated by the learning mechanism. This mechanism is based on a collaboration inside the neighbor- hood of the Context Agents. The presented process is operational regardless of the number of dimensions.

Neighborhood

A Context Agent is considered as a neighbor of the perceptions if its validity ranges intersect a neighborhood area surrounding the current perceptions. The size of this area results from the precision range, a parameter chosen by the user of the learning mechanism. For a perception p i , there is a default radius creation for a Context Agent r creation

Endogenous Learning Rules

To take advantage of the neighborhood in the learning process, it is necessary to modify the rules of AMOEBA. The inaccuracy margin is removed so there is only an error margin chosen by the user of the learning mechanism to define its accuracy expectations.

Bad Prediction Situation

The distance to the learning situation is greater than the error margin. The Context Agent is not valid for this learning situation. Its prediction is not accurate enough given expected precision. It moves one of its ranges to exclude the current perception and it decreases its confidence. It always chooses the range that least affects the volume of its validity ranges. If the distance to the learning situation is less than the error margin, the agent's confidence increases and it updates its model with the current learning situation. There is only one margin to define whether a Context Agent is good or bad. The

Cooperative Neighborhood Learning

In order to enhance the learning process, each Best Context Agent communicates with its neighbors to ask them for endogenous learning situations

L endo n = [P endo n , O endo 1
]. This has for objective to locally smooth the models between them. As for the perception neighborhood radiuses, the prediction neighborhood radius is defined as it follows r | is lesser than r N O 1 , the endogenous learning situations is retained. The set of all retained endogenous learning situations is used to update the Best Context Agent model with a weight w endo . To satisfy this weight, artificial Learning Situations are generated. They are distributed on the current model according to a normal law centered in the validity ranges center and with a standard deviation of ((r j i,endr j i,start )/10) 1 2 . This distribution ensures that the center of the model, is slightly altered. The endogenous learning situations are then used to estimate new regression parameters using Miller's regression [START_REF] Miller | Algorithm as 274: Least squares routines to supplement those of gentleman[END_REF].

N O 1 = k N .(O max 1 - O min

Context Exploitation

The addition of the neighborhood is useful to optimize the exploitation, specially when there aren't any valid Context Agents. In this case, the Best Context Agent is the closest Context Agent to the perceptions among the Context Agents neighbors (Fig. 2b). If they are no neighbors, it is the closest Context Agent among all the Context Agents. The neighborhood speeds up the exploitation when there are neighbors and a lot of Context Agents in the whole system.

In the case that all the perceptions are not provided for the exploitation, we propose a new way of exploiting the models. The given subset of perceptions is used to define the set of valid Context Agents. The Best Context Agent is then chosen using the distance to the sub-perceptions. The unspecified perceptions are set by default to the center of the validity ranges of the Best Context Agent. Fig. 2c shows an exploitation with the sub-perception p 1 only.

Inverse Kinematics Learning Case Study

For our experimentations, we repeat one of the experimental setups of [START_REF] Baranes | Active learning of inverse models with intrinsically motivated goal exploration in robots[END_REF] which is the learning of the inverse kinematics with a redundant arm. We consider a robotic arm with segments of equal length and n joints in a 2D plane: (θ 1 , θ i , . . . , θ n ) (Fig. 3 shows an example for 3 joints). To control it, one must use its Forward Kinematic Model FKM and its Inverse Kinematic Model IKM which are both non linear models dependent on the characteristics of the arm. The Forward Kinematic Model is used to calculate the position of the robot tool in a task space from the angles of each joint: FKM(θ 1 , θ i , . . . , θ n ) = (x T , y T ) for a task space of two dimensions. The analytical Inverse Kinematic Model gives all the possible angle vectors for a desired tool position:

IKM(x T , y T ) = (θ 1 , θ i , . . . , θ n ), (θ 1 , θ i , . . . , θ n ) , . . .
We propose here to learn the IKM using the FKM as a supervisor and to exploit the learning without using all the Perceptions. This approach is independent of the joints number of the considered robots.

Training

The training is made from several random joints configurations (θ rdn 1 , θ rdn i , . . . , θ rdn n ). The corresponding position of the end of the robot arm is given by the Forward Kinematic Model : FKM(θ rdn 1 , θ rdn i , . . . , θ rdn n ) = (x rdn T , y rdn T ). The perceptions for the learning mechanism are the position of the end of the robot (x rdn T , y rdn T ) and all the corresponding angles except the last one (θ rdn 1 , θ rdn i , . . . , θ rdn n-1 ).

The perceptions vector is (x rdn T , y rdn T , θ rdn 1 , θ rdn i , . . . , θ rdn n-1 ). The last angle θ rdn n is the prediction of the local models. The global function that is learnt by the mechanism is F θ n (x rdn T , y rdn T , θ rdn 1 , θ rdn i , . . . , θ rdn n-1 ) = θ rdn n . We define the training learning situations as exogenous learning situations given by the joints configuration of the robot and its FKM:

L exo n = [(x rdn
T , y rdn T , θ rdn 1 , θ rdn i , . . . , θ rdn n-1 ), θ rdn n ]. Exploration The generation of the random angles for the joints is done following a normal distribution. Considering that an outstretched arm is defined by all the angles being set to 0 rad, the distribution of each angle is centered around this value except for θ 1 which has an homogeneous random distribution between 0 and 2π. The dispersion is set empirically for 3, 10 and 30 joints with the objective of having homogeneous situations in the task space (Fig. 4 shows an example of exploration with 3 joints after 1000 exogenous learning situations). The obtained dispersion depending on the number of joints is : 2.5593n -0.479 . Exploitation As we are learning the IKM, the goal here is to get a set of angles to position the end of the robotic arm in a point P goal ).

Experimentations

In this section, we present our results achieved with the addition of endogenous leaning situations in the learning of robotic arms inverse models. A learning cycle corresponds to a configuration for the robotic arm. The learning mechanism receives an exogenous learning situation at each learning cycle. The inverse models to be learnt are non linear models of high dimensions (up to 30). We chose to stop at 30 to match the numbers of degrees of freedom on a usual humanoid robot. We are aware that on a humanoid all linkages are not serial. The goal here is to test our approach with the same degrees of freedom order of magnitude.

Metrics

Goal Error To appraise the score of the learnt IKM, we evaluate the proposals of the learning mechanism. We calculate the end position error of the robot in the task space E T . This error is the distance between the randomly asked positions P goal ||/D reachable . The prediction metric is calculated over exploitation cycles where the mechanism is asked to make angles predictions to get the goal position. Endogenous Data To evaluate the impact of the cooperative neighborhood mechanism on the goal performances, we are interested in the number of generated endogenous learning situations L endo n .

Results

The presented results are averaged over 15 learning experiences. Each learning experience is stopped after 1000 training cycles. The goal errors are averaged over 200 exploitation cycles. The stretched length for each tested arms is the same (50 units in our simulation). Each arm segment is the same size. For each arm size scenario, the size of the reachable space is the same. The error margin is set to 1. The weight w endo of endogenous learning situations is 0.1. The code is implemented in java with the framework AMAK [START_REF] Perles | Amaka framework for developing robust and open adaptive multi-agent systems[END_REF] and it is executed on a machine1 with Ubuntu 18.04.3 LTS.

Arm Dimensions Figure 5 shows that without cooperative neighborhood learning the best performance is obtained for 2 joints and with a precision range of 1%. The precision range of 1% also gives lower mean error for the arms of 2, 3 and 6 joints than the precision range of 3%. For arms with more joints the gap is less visible. We can also see that the mean error and its dispersion increase up to 10 joints. Then, they decrease as the number joints gets bigger. Neighborhood Sizes Figure 6 shows that the size of the neighborhood has an impact on the mean error for the arms of 2, 3 and 6 joints. With a precision range of 3% the error decreases and reaches a minimum value with a delay in the neighborhood size for the different arms. It then increases for 2 and 3 joints for high neighborhood sizes. For 10, 20 and 30 joints (Fig. 7), the error only decreases for 10 joints. The other cases are not impacted by the variation of neighborhood. Endogenous Data Figures 8 and9 represent the same experimentation than 6 and 7 but focusing on the variation of the error according to the endogenous learning situations. Fig. 8, for 6 joints and a precision range of 3%, the more endogenous learning situations there are, the lower the error is. For 2 and 3 joints, we find the same behavior than Fig. 6, there is an optimal situation beyond which the error increases. For 10 joints with a precision range of 3% (Fig. 9), more endogenous learning situations reduce the error. But for 20 and 30 joints, the endogenous learning situations don't reduce the goal error, they even slightly increase it.

Discussion

We have seen that the lowest error is obtained for the lowest arm dimensions. The error increases up to 10 joints and it decreases for higher arm dimensions. At low dimensions, the good performance is due to the low redundancy of the problem making the exploration less extensive. The decreasing of the error at high dimensions is caused by the exploitation of the Context Agents with sub-perceptions. If the requested goal P goal xy during the exploitation is in a less explored area, it is the closest model that is used for the last angle prediction. The smaller the size of the last arm segment, the smaller the distance error on the goal. Which is the case for the higher dimensions. The rest of the angles are fixed using the validity ranges of the Best Context Agent.

Figures 6, 7, 8 and 9 showed that the expansion of the neighborhood can lead to better or worse performances by generating more endogenous learning situation. The point of best performance is different for each arm sizes which shows that the neighborhood behaves differently with higher dimensions. Past this point, the error increases because the endogenous learning situations are too far from the Context Agent to bring a coherent smoothing. At high dimensions, endogenous learning situations are harder to generate because of the large exploration space. This is why, for the same neighborhood sizes, there are more endogenous learning situations at low dimensions. Moreover, beyond 10 joints, the performances are not affected by the endogenous learning situation.

Related Work

The magnitude of the mean goal reaching errors of the Self-Adaptive Goal Generation RIAC algorithm (SAGG-RIAC) [START_REF] Baranes | Active learning of inverse models with intrinsically motivated goal exploration in robots[END_REF]) is close to our results. The difference is that SAGG-RIAC uses around 10 4 micro actions for each goal to obtain comparable goal errors. Our approach instantaneously gives a set of angles to reach any goal after one training of 1000 learning situations.

Conclusion and Perspectives

In this paper, we have proposed an extension of a Context-based learning multi-agent system which has already proven to be suitable to complex systems and that is directly inspired by Constructivism. This is a generic approach because it does not rely on the underlying application. This work was applied on the learning of the Inverse Kinematic Models of robotic arms with different numbers of joints. Self-observation of self-adaptive multiagent systems allowed us to add collaboration between fragments of learning which are the Context Agents. Based on the internal detection of close Context Agents models, we proposed the generation of endogenous learning situations that led to better performances on Inverse Kinematic Model learning. This work has shown that the generation of endogenous learning situations makes it possible to reduce exogenous learning situations as the performance improvement with endogenous cooperative learning attests.

The proposed approach needs to be refined in order to select the right size of neighborhood according to the dimension of the exploring space to maximize performance. The scalability was not discussed here but the generation of endogenous learning situations at high dimensions needs also to be optimized to access to more neighbors with reasonable execution times. Another promising lead is to decompose the learning into several local instances of the learn-ing mechanism, one for each joint. This would reduce the high-dimensional problem into several lowdimensional problems where the cooperative neighborhood learning is more effective. It will also ensure that the performances are independent of the number of dimensions, and that the execution time is linearly dependent on the dimensions.

n

  with j the j th pavement in dimension n which represents a part of the schema. A Context Agent is an intelligent autonomous agent that locally represents a part of the global function F with a local function f j n (p 1 , . . . , p i , . . . , p n ) = o j m with o j m ∈ R m . It is a parallelotope of dimension n associated with a machine learning model. The parallelotope is defined by validity ranges R j n ] which represents a validity interval on a perception p i (Fig. 1). All Context Agents use the same set of inputs P n . Parallelotopes Validity Ranges in dimension 1 and 2. The Context Agents have a confidence c j ∈ Z to evaluate themselves in relation to others. A Context Agent is therefore defined by its validity ranges, its model and its confidence C j n = {R j n , f j n , c j }. In this study, each Context Agent has a local linear regression model f j n . In this case, the prediction vectors and the oracle predictions are a real values O 1 and O

  Figure 3: 3 joints robotic arm with segments of equal length l in a 2D task space.

  Figure 4: Exploration with a 3 joints robotic arm simulation after 1000 training situations.

  experienced values by the learning mechanism on the perception p i . From this, it results an approximation error distance d aed i = 0.25.r creation i . The neighborhood area radius is r N i = k N .r creation i .

  agents' models are regularly updated to be robust to noise. Uselessness Situation A Context Agent is useless if one of its validity ranges has a critical size below d aed i . Unproductive Situation The mechanism of extending the closest good Context Agent remains the same. The closest good Context Agent extends one of its ranges towards the new situation. The novelty appears at the creation of a new Context Agent if needed. If there are neighbors, they are used to initialize the properties of the new agent. If there are no neighbors, the created agent uses initialization values based on the perception limits of the search space and on the parameters chosen by the system user.

  1 ).precision range. The perceptions P endo n of the endogenous learning situation are chosen randomly in the intersection of the neighborhood and the neighbor's validity ranges (fig. 2d). The prediction O endo 1 is asked to the model of the neighbor. Only neighbors that have a close last prediction share an endogenous learning situation. If the difference between the endogenous prediction and the last Best Context Agent prediction |O endo 1

  All P goal xy are randomly generated in the reachable zone of the task space. It is an exploitation without all the perceptions and the sub-

  xy in the reachable task space and the position resulting from the exploitation of the learning P explo xy . This error is normalized by the diameter of the reachable space D reachable which is a disk in this case: E T = || # » P goal xy P explo xy

Figure 5 :

 5 Figure 5: Mean errors from goal depending on robotic arm sizes (2, 3, 6, 10, 20 and 30 joints) without cooperative neighborhood learning. Learning cycles = 1000; exploitation cycles = 200; averaged overs 15 learning experiences.

Figure 6 :

 6 Figure 6: Mean errors from goal depending on mean neighborhood sizes over robotic arms of 2,3 and 6 joints. Learning cycles = 1000; exploitation cycles = 200; averaged overs 15 learning experiences. precision range = 3%.

Figure 7 :

 7 Figure 7: Mean errors from goal depending on mean neighborhood sizes over robotic arms of 10,20 and 30 joints. Learning cycles = 1000; exploitation cycles = 200; averaged overs 15 learning experiences. precision range = 3%.

Figure 8 :Figure 9 :

 89 Figure 8: Mean errors from goal depending on mean endogenous learning situations over robotic arms of 2, 3 and 6 joints. Learning cycles = 1000; exploitation cycles = 200; averaged overs 15 learning experiences. precision range = 3%

  Exploitation Cycles During the exploitation, if they are several Valid Context Agents, the one with the higher confidence is the Best Context Agent. It provides the prediction output O 1 . If there aren't any Valid Context Agents, the closest Context Agent to the perceptions is designated as the Best Context Agent. Shortcomings The presented rules suffer from a lack of local interactions between the Context Agents. This approach proposes a distributed learning method that is adaptive with respect to the oracle values but not between the knowledge fragments. Another issue is the scalability of the local added interactions. AMOEBA does not possess any mechanism allowing Context Agents to communicate locally without activating all the Context Agent of the system. Context Agents Mechanisms; Best Context Agent, valid Context Agents and neighborhood areas are filled darker; Best Context Agents are boxed; the neighborhood is represented by a dotted box.

	p 2	p 2
	p 1	p 1
	(a) Valid Context Agent with all perceptions.	(b) Closest Context Agent with all perceptions in the neighborhood.
		p 2
	p 2
		p 1
	p 1	(d) Cooperative neighbor-
	(c) Valid Context Agents on exploitation with only the perception p 1 .	hood learning situations; the endogenous learning situations are represented with diagonal crosses.
	Figure 2:

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