Deep Time Series Forecasting With Shape and Temporal Criteria.

This paper addresses the problem of multi-step time series forecasting for non-stationary signals that can present sudden changes. Current state-of-the-art deep learning forecasting methods, often trained with variants of the MSE, lack the ability to provide sharp predictions in deterministic and probabilistic contexts. To handle these challenges, we propose to incorporate shape and temporal criteria in the training objective of deep models. We define shape and temporal similarities and dissimilarities, based on a smooth relaxation of Dynamic Time Warping (DTW) and Temporal Distortion Index (TDI), that enable to build differentiable loss functions and positive semi-definite (PSD) kernels. With these tools, we introduce DILATE (DIstortion Loss including shApe and TimE), a new objective for deterministic forecasting, that explicitly incorporates two terms supporting precise shape and temporal change detection. For probabilistic forecasting, we introduce STRIPE++ (Shape and Time diverRsIty in Probabilistic for Ecasting), a framework for providing a set of sharp and diverse forecasts, where the structured shape and time diversity is enforced with a determinantal point process (DPP) diversity loss. Extensive experiments and ablations studies on synthetic and real-world datasets confirm the benefits of leveraging shape and time features in time series forecasting.

A divide-and-conquer approach for genomic prediction in rubber tree using machine learning.

Rubber tree (Hevea brasiliensis) is the main feedstock for commercial rubber; however, its long vegetative cycle has hindered the development of more productive varieties via breeding programs. With the availability of H. brasiliensis genomic data, several linkage maps with associated quantitative trait loci have been constructed and suggested as a tool for marker-assisted selection. Nonetheless, novel genomic strategies are still needed, and genomic selection (GS) may facilitate rubber tree breeding programs aimed at reducing the required cycles for performance assessment. Even though such a methodology has already been shown to be a promising tool for rubber tree breeding, increased model predictive capabilities and practical application are still needed. Here, we developed a novel machine learning-based approach for predicting rubber tree stem circumference based on molecular markers. Through a divide-and-conquer strategy, we propose a neural network prediction system with two stages: (1) subpopulation prediction and (2) phenotype estimation. This approach yielded higher accuracies than traditional statistical models in a single-environment scenario. By delivering large accuracy improvements, our methodology represents a powerful tool for use in Hevea GS strategies. Therefore, the incorporation of machine learning techniques into rubber tree GS represents an opportunity to build more robust models and optimize Hevea breeding programs.

Optimizing imputation of marker data from genotyping-by-sequencing (GBS) for genomic selection in non-model species: Rubber tree (Hevea brasiliensis) as a case study.

Genotyping-by-sequencing (GBS) provides the marker density required for genomic predictions (GP). However, GBS gives a high proportion of missing SNP data which, for species without a chromosome-level genome assembly, must be imputed without knowing the SNP physical positions. Here, we compared GP accuracy with seven map-independent and two map-dependent imputation approaches, and when using all SNPs against the subset of genetically mapped SNPs. We used two rubber tree (Hevea brasiliensis) datasets with three traits. The results showed that the best imputation approaches were LinkImputeR, Beagle and FImpute. Using the genetically mapped SNPs increased GP accuracy by 4.3%. Using LinkImputeR on all the markers allowed avoiding genetic mapping, with a slight decrease in GP accuracy. LinkImputeR gave the highest level of correctly imputed genotypes and its performances were further improved by its ability to define a subset of SNPs imputed optimally. These results will contribute to the efficient implementation of genomic selection with GBS. For Hevea, GBS is promising for rubber yield improvement, with GP accuracies reaching 0.52.

Unravelling Rubber Tree Growth by Integrating GWAS and Biological Network-Based Approaches.

Hevea brasiliensis (rubber tree) is a large tree species of the Euphorbiaceae family with inestimable economic importance. Rubber tree breeding programs currently aim to improve growth and production, and the use of early genotype selection technologies can accelerate such processes, mainly with the incorporation of genomic tools, such as marker-assisted selection (MAS). However, few quantitative trait loci (QTLs) have been used successfully in MAS for complex characteristics. Recent research shows the efficiency of genome-wide association studies (GWAS) for locating QTL regions in different populations. In this way, the integration of GWAS, RNA-sequencing (RNA-Seq) methodologies, coexpression networks and enzyme networks can provide a better understanding of the molecular relationships involved in the definition of the phenotypes of interest, supplying research support for the development of appropriate genomic based strategies for breeding. In this context, this work presents the potential of using combined multiomics to decipher the mechanisms of genotype and phenotype associations involved in the growth of rubber trees. Using GWAS from a genotyping-by-sequencing (GBS) Hevea population, we were able to identify molecular markers in QTL regions with a main effect on rubber tree plant growth under constant water stress. The underlying genes were evaluated and incorporated into a gene coexpression network modelled with an assembled RNA-Seq-based transcriptome of the species, where novel gene relationships were estimated and evaluated through in silico methodologies, including an estimated enzymatic network. From all these analyses, we were able to estimate not only the main genes involved in defining the phenotype but also the interactions between a core of genes related to rubber tree growth at the transcriptional and translational levels. This work was the first to integrate multiomics analysis into the in-depth investigation of rubber tree plant growth, producing useful data for future genetic studies in the species and enhancing the efficiency of the species improvement programs.

Genomic Selection in Rubber Tree Breeding: A Comparison of Models and Methods for Managing G×E Interactions.

Several genomic prediction models combining genotype × environment (G×E) interactions have recently been developed and used for genomic selection (GS) in plant breeding programs. G×E interactions reduce selection accuracy and limit genetic gains in plant breeding. Two data sets were used to compare the prediction abilities of multienvironment G×E genomic models and two kernel methods. Specifically, a linear kernel, or GB (genomic best linear unbiased predictor [GBLUP]), and a nonlinear kernel, or Gaussian kernel (GK), were used to compare the prediction accuracies (PAs) of four genomic prediction models: 1) a single-environment, main genotypic effect model (SM); 2) a multienvironment, main genotypic effect model (MM); 3) a multienvironment, single-variance G×E deviation model (MDs); and 4) a multienvironment, environment-specific variance G×E deviation model (MDe). We evaluated the utility of genomic selection (GS) for 435 individual rubber trees at two sites and genotyped the individuals via genotyping-by-sequencing (GBS) of single-nucleotide polymorphisms (SNPs). Prediction models were used to estimate stem circumference (SC) during the first 4 years of tree development in conjunction with a broad-sense heritability (H 2) of 0.60. Applying the model (SM, MM, MDs, and MDe) and kernel method (GB and GK) combinations to the rubber tree data revealed that the multienvironment models were superior to the single-environment genomic models, regardless of the kernel (GB or GK) used, suggesting that introducing interactions between markers and environmental conditions increases the proportion of variance explained by the model and, more importantly, the PA. Compared with the classic breeding method (CBM), methods in which GS is incorporated resulted in a 5-fold increase in response to selection for SC with multienvironment GS (MM, MDe, or MDs). Furthermore, GS resulted in a more balanced selection response for SC and contributed to a reduction in selection time when used in conjunction with traditional genetic breeding programs. Given the rapid advances in genotyping methods and their declining costs and given the overall costs of large-scale progeny testing and shortened breeding cycles, we expect GS to be implemented in rubber tree breeding programs.

QTL detection for growth and latex production in a full-sib rubber tree population cultivated under suboptimal climate conditions.

BACKGROUND: Rubber tree is cultivated in mainly Southeast Asia and is by far the most significant source of natural rubber production worldwide. However, the genetic architecture underlying the primary agronomic traits of this crop has not been widely characterized. This study aimed to identify quantitative trait loci (QTLs) associated with growth and latex production using a biparental population established in suboptimal growth conditions in Brazil. RESULTS: A full-sib population composed of 251 individuals was developed from crossing two high-producing Asiatic rubber tree cultivars, PR 255 and PB 217. This mapping population was genotyped with microsatellite markers from enriched genomic libraries or transcriptome datasets and single-nucleotide polymorphism (SNP) markers, leading to construction of a saturated multipoint integrated genetic map containing 354 microsatellite and 151 SNP markers. Height and circumference measurements repeated over a six-year period and registration of cumulative latex production during six consecutive months on the same individuals allowed in-depth characterization of the genetic values of several growth traits and precocious latex production. Growth traits, circumference and height, were overall positively correlated, whereas latex production was not correlated or even negatively correlated with growth traits. A total of 86 distinct QTLs were identified, most of which were detected for only one trait. Among these QTLs, 15 were linked to more than one phenotypic trait (up to 4 traits simultaneously). Latex production and circumference increments during the last wintering period were associated with the highest numbers of identified QTLs (eleven and nine, respectively), jointly explaining the most significantly observed phenotypic variances (44.1% and 44.4%, respectively). The most important QTL for latex production, located on linkage group 16, had an additive effect of the male parent PB 217 and corresponded to a QTL at the same position detected in a previous study carried out in Thailand for the biparental population RRIM 600 x PB 217. CONCLUSIONS: Our results identified a set of significant QTLs for rubber tree, showing that the performance of modern Asiatic cultivars can still be improved and paving the way for further marker-assisted selection, which could accelerate breeding programs.

High-Resolution Genetic Map and QTL Analysis of Growth-Related Traits of Hevea brasiliensis Cultivated Under Suboptimal Temperature and Humidity Conditions.

Rubber tree (Hevea brasiliensis) cultivation is the main source of natural rubber worldwide and has been extended to areas with suboptimal climates and lengthy drought periods; this transition affects growth and latex production. High-density genetic maps with reliable markers support precise mapping of quantitative trait loci (QTL), which can help reveal the complex genome of the species, provide tools to enhance molecular breeding, and shorten the breeding cycle. In this study, QTL mapping of the stem diameter, tree height, and number of whorls was performed for a full-sibling population derived from a GT1 and RRIM701 cross. A total of 225 simple sequence repeats (SSRs) and 186 single-nucleotide polymorphism (SNP) markers were used to construct a base map with 18 linkage groups and to anchor 671 SNPs from genotyping by sequencing (GBS) to produce a very dense linkage map with small intervals between loci. The final map was composed of 1,079 markers, spanned 3,779.7 cM with an average marker density of 3.5 cM, and showed collinearity between markers from previous studies. Significant variation in phenotypic characteristics was found over a 59-month evaluation period with a total of 38 QTLs being identified through a composite interval mapping method. Linkage group 4 showed the greatest number of QTLs (7), with phenotypic explained values varying from 7.67 to 14.07%. Additionally, we estimated segregation patterns, dominance, and additive effects for each QTL. A total of 53 significant effects for stem diameter were observed, and these effects were mostly related to additivity in the GT1 clone. Associating accurate genome assemblies and genetic maps represents a promising strategy for identifying the genetic basis of phenotypic traits in rubber trees. Then, further research can benefit from the QTLs identified herein, providing a better understanding of the key determinant genes associated with growth of Hevea brasiliensis under limiting water conditions.

Linkage Disequilibrium and Population Structure in Wild and Cultivated Populations of Rubber Tree (Hevea brasiliensis).

Among rubber tree species, which belong to the Hevea genus of the Euphorbiaceae family, Hevea brasiliensis (Willd. ex Adr.de Juss.) Muell. Arg. is the main commercial source of natural rubber production worldwide. Knowledge of the population structure and linkage disequilibrium (LD) of this species is essential for the efficient organization and exploitation of genetic resources. Here, we obtained single-nucleotide polymorphisms (SNPs) using a genotyping-by-sequencing (GBS) approach and then employed the SNPs for the following objectives: (i) to identify the positions of SNPs on a genetic map of a segregating mapping population, (ii) to evaluate the population structure of a germplasm collection, and (iii) to detect patterns of LD decay among chromosomes for future genetic association studies in rubber tree. A total of 626 genotypes, including both germplasm accessions (368) and individuals from a genetic mapping population (254), were genotyped. A total of 77,660 and 21,283 SNPs were detected by GBS in the germplasm and mapping populations, respectively. The mapping population, which was previously mapped, was constructed with 1,062 markers, among which only 576 SNPs came from GBS, reducing the average interval between two adjacent markers to 4.4 cM. SNPs from GBS genotyping were used for the analysis of genetic structure and LD estimation in the germplasm accessions. Two groups, which largely corresponded to the cultivated and wild populations, were detected using STRUCTURE and via principal coordinate analysis. LD analysis, also using the mapped SNPs, revealed that non-random associations varied along chromosomes, with regions of high LD interspersed with regions of low LD. Considering the length of the genetic map (4,693 cM) and the mean LD (0.49 for cultivated and 0.02 for wild populations), a large number of evenly spaced SNPs would be needed to perform genome-wide association studies in rubber tree, and the wilder the genotypes used, the more difficult the mapping saturation.

A Review of a Century of Studies on South American Leaf Blight of the Rubber Tree.

In the past, South American leaf blight (SALB) of the rubber tree has been responsible for very severe damage in rubber plantations in South America. It is still the main obstacle holding back the development of rubber cultivation on the American continent and is a major risk for Asia and Africa, which are still exempt from this scourge. However, knowledge about the disease and about rubber tree resistance factors has progressed over the last decade, suggesting some solutions, notably for varietal improvement. This article is an overview of knowledge on this subject, particularly the most recent achievements.

Genetic Determinism of Sensitivity to Corynespora cassiicola Exudates in Rubber Tree (Hevea brasiliensis).

An indirect phenotyping method was developed in order to estimate the susceptibility of rubber tree clonal varieties to Corynespora Leaf Fall (CLF) disease caused by the ascomycete Corynespora cassiicola. This method consists in quantifying the impact of fungal exudates on detached leaves by measuring the induced electrolyte leakage (EL%). The tested exudates were either crude culture filtrates from diverse C. cassiicola isolates or the purified cassiicolin (Cas1), a small secreted effector protein produced by the aggressive isolate CCP. The test was found to be quantitative, with the EL% response proportional to toxin concentration. For eight clones tested with two aggressive isolates, the EL% response to the filtrates positively correlated to the response induced by conidial inoculation. The toxicity test applied to 18 clones using 13 toxinic treatments evidenced an important variability among clones and treatments, with a significant additional clone x treatment interaction effect. A genetic linkage map was built using 306 microsatellite markers, from the F1 population of the PB260 x RRIM600 family. Phenotyping of the population for sensitivity to the purified Cas1 effector and to culture filtrates from seven C. cassiicola isolates revealed a polygenic determinism, with six QTL detected on five chromosomes and percentages of explained phenotypic variance varying from 11 to 17%. Two common QTL were identified for the CCP filtrate and the purified cassiicolin, suggesting that Cas1 may be the main effector of CCP filtrate toxicity. The CCP filtrate clearly contrasted with all other filtrates. The toxicity test based on Electrolyte Leakage Measurement offers the opportunity to assess the sensitivity of rubber genotypes to C. cassiicola exudates or purified effectors for genetic investigations and early selection, without risk of spreading the fungus in plantations. However, the power of this test for predicting field susceptibility of rubber clones to CLF will have to be further investigated.

Genetic Diversity Strategy for the Management and Use of Rubber Genetic Resources: More than 1,000 Wild and Cultivated Accessions in a 100-Genotype Core Collection.

The rubber tree [Hevea brasiliensis (Willd. ex Adr. de Juss.) Muell. Arg.] is the only plant species worldwide that is cultivated for the commercial production of natural rubber. This study describes the genetic diversity of the Hevea spp. complex that is available in the main ex situ collections of South America, including Amazonian populations that have never been previously described. Genetic data were analyzed to determine the genetic structure of the wild populations, quantify the allelic diversity and suggest the composition of a core collection to capture the maximum genetic diversity within a minimal sample size. A total of 1,117 accessions were genotyped with 13 microsatellite markers. We identified a total of 408 alleles, 319 of which were shared between groups and 89 that were private in different groups of accessions. In a population structure and principal component analysis, the level of clustering reflected a primary division into the following two subgroups: cluster 1, which consisted of varieties from the advanced breeding germplasm that originated from the Wickham and Mato Grosso accessions; and cluster 2, which consisted of the wild germplasm from the Acre, Amazonas, Pará and Rondônia populations and Hevea spp. The analyses revealed a high frequency of gene flow between the groups, with the genetic differentiation coefficient (GST) estimated to be 0.018. Additionally, no distinct separation among the H. brasiliensis accessions and the other species from Amazonas was observed. A core collection of 99 accessions was identified that captured the maximum genetic diversity. Rubber tree breeders can effectively utilize this core collection for cultivar improvement. Furthermore, such a core collection could provide resources for forming an association panel to evaluate traits with agronomic and commercial importance. Our study generated a molecular database that should facilitate the management of the Hevea germplasm and its use for subsequent genetic and genomic breeding.

De novo transcriptome analysis of Hevea brasiliensis tissues by RNA-seq and screening for molecular markers.

BACKGROUND: The rubber tree, Hevea brasiliensis, is a species native to the Brazilian Amazon region and it supplies almost all the world's natural rubber, a strategic raw material for a variety of products. One of the major challenges for developing rubber tree plantations is adapting the plant to biotic and abiotic stress. Transcriptome analysis is one of the main approaches for identifying the complete set of active genes in a cell or tissue for a specific developmental stage or physiological condition. RESULTS: Here, we report on the sequencing, assembling, annotation and screening for molecular markers from a pool of H. brasiliensis tissues. A total of 17,166 contigs were successfully annotated. Then, 2,191 Single Nucleotide Variation (SNV) and 1.397 Simple Sequence Repeat (SSR) loci were discriminated from the sequences. From 306 putative, mainly non-synonymous SNVs located in CDS sequences, 191 were checked for their ability to characterize 23 Hevea genotypes by an allele-specific amplification technology. For 172 (90%), the nucleotide variation at the predicted genomic location was confirmed, thus validating the different steps from sequencing to the in silico detection of the SNVs. CONCLUSIONS: This is the first study of the H. brasiliensis transcriptome, covering a wide range of tissues and organs, leading to the production of the first developed SNP markers. This process could be amplified to a larger set of in silico detected SNVs in expressed genes in order to increase the marker density in available and future genetic maps. The results obtained in this study will contribute to the H. brasiliensis genetic breeding program focused on improving of disease resistance and latex yield.

QTL mapping of growth-related traits in a full-sib family of rubber tree (Hevea brasiliensis) evaluated in a sub-tropical climate.

The rubber tree (Hevea spp.), cultivated in equatorial and tropical countries, is the primary plant used in natural rubber production. Due to genetic and physiological constraints, inbred lines of this species are not available. Therefore, alternative approaches are required for the characterization of this species, such as the genetic mapping of full-sib crosses derived from outbred parents. In the present study, an integrated genetic map was obtained for a full-sib cross family with simple sequence repeats (SSRs) and expressed sequence tag (EST-SSR) markers, which can display different segregation patterns. To study the genetic architecture of the traits related to growth in two different conditions (winter and summer), quantitative trait loci (QTL) mapping was also performed using the integrated map. Traits evaluated were height and girth growth, and the statistical model was based in an extension of composite interval mapping. The obtained molecular genetic map has 284 markers distributed among 23 linkage groups with a total length of 2688.8 cM. A total of 18 QTLs for growth traits during the summer and winter seasons were detected. A comparison between the different seasons was also conducted. For height, QTLs detected during the summer season were different from the ones detected during winter season. This type of difference was also observed for girth. Integrated maps are important for genetics studies in outbred species because they represent more accurately the polymorphisms observed in the genitors. QTL mapping revealed several interesting findings, such as a dominance effect and unique segregation patterns that each QTL could exhibit, which were independent of the flanking markers. The QTLs identified in this study, especially those related to phenotypic variation associated with winter could help studies of marker-assisted selection that are particularly important when the objective of a breeding program is to obtain phenotypes that are adapted to sub-optimal regions.