Inbreeding and Genetic Erosion from a Finite Model of a Synthetic Formed with Single Crosses.

When a seed produced by a single-cross (SC) maize hybrid is sown, the resulting grain yield is usually lower than that of the hybrid due to the inbreeding generated. However, if a seed from a mixture of s hybrids were sown instead, the synthetic variety thus formed (SynSC) would have a lower inbreeding coefficient (FSynSC) and a higher grain yield. The grain yield s, the finite number of representatives of each parent SC (m) and the inbreeding coefficient of the parent lines of the SCs (F) are related to the FSynSC. In addition, randomness and the finite size of m can cause the loss of genes and genotypes and increase the FSynSC. The objectives of this study were to derive formulas for (1) expressing FSynSC in terms of m, F, and s, and (2) calculating the probability of the occurrence of gene and genotype loss. It was found that for the probability of no genotype being missing from the progeny representing a parent to be at least 0.95, it is necessary that m ≥ 15. It was also found that a sample size of 7 is sufficient for FSynSC to stabilize, more visibly as F is larger, and for the probability of the occurrence of erosion to be practically zero.

Haploid Induction in Tomato (Solanum lycopersicum L.) via Gynogenesis.

The generation of new hybrid varieties of tomato (Solanum lycopersicum L.) is the most widely used breeding method for this species and requires at least seven self-fertilization cycles to generate stable parent lines. The development of doubled haploids aims at obtaining completely homozygous lines in a single generation, although, to date, routine commercial application has not been possible in this species. In contrast, obtaining doubled haploid lines via gynogenesis has been successfully implemented in recalcitrant crops such as melon, cucumber, pumpkin, loquat and walnut. This review provides an overview of the requirements and advantages of gynogenesis as an inducer of haploidy in different agricultural crops, with the purpose of assessing the potential for its application in tomato breeding. Successful cases of gynogenesis variants involving in vitro culture of unfertilized ovules, use of 60Co-irradiated pollen, in vivo haploid inducers and wide hybridization are presented, suggesting that these methodologies could be implemented in tomato breeding programs to obtain doubled haploids.

Distribution and Climatic Adaptation of Wild Tomato (Solanum lycopersicum L.) Populations in Mexico.

Tomato (Solanum lycopersicum L.) is a vegetable with worldwide importance. Its wild or close related species are reservoirs of genes with potential use for the generation of varieties tolerant or resistant to specific biotic and abiotic factors. The objective was to determine the geographic distribution, ecological descriptors, and patterns of diversity and adaptation of 1296 accessions of native tomato from Mexico. An environmental information system was created with 21 climatic variables with a 1 km2 spatial resolution. Using multivariate techniques (Principal Component Analysis, PCA; Cluster Analysis, CA) and Geographic Information Systems (GIS), the most relevant variables for accession distribution were identified, as well as the groups formed according to the environmental similarity among these. PCA determined that with the first three PCs (Principal Components), it is possible to explain 84.1% of the total variation. The most relevant information corresponded to seasonal variables of temperature and precipitation. CA revealed five statistically significant clusters. Ecological descriptors were determined and described by classifying accessions in Physiographic Provinces. Temperate climates were the most frequent among tomato accessions. Finally, the potential distribution was determined with the Maxent model with 10 replicates by cross-validation, identifying areas with a high probability of tomato presence. These results constitute a reliable source of useful information for planning accession sites collection and identifying accessions that are vulnerable or susceptible to conservation programs.

Climatic Diversity and Ecological Descriptors of Wild Tomato Species (Solanum sect. Lycopersicon) and Close Related Species (Solanum sect. Juglandifolia y sect. Lycopersicoides) in Latin America.

Conservation and sustainable use of species diversity require a description of the environment where they develop. The objectives were to determine ecological descriptors and climatic diversity of areas along the distribution range of 12 species of wild tomatoes (Solanum sect. Lycopersicon) and four wild species of phylogenetically related groups (Solanum sect. Juglandifolia and sect. Lycopersicoides), as well as their ecological similarity in Latin America. With 4228 selected tomato accessions and an environmental information system (EIS) composed of 21 climatic variables, diversity patterns of the distribution areas were identified for each species, as well as ecological descriptors through the use of geographic information systems (GIS). The contribution of climatic variables to the species geographical distribution was identified by principal component analysis (PCA), and similarity in species distribution as a function of the variables identified with cluster analysis (CA). Climatic characteristics and the environmental amplitude of wild tomatoes and related species along their distributional range were satisfactorily determined by ecological descriptors. Eleven climate types were identified, predominantly BSk (arid, steppe, cold), BWh (arid, desert, hot), and Cfb (temperate, no dry season, warm summer). PCA determined 10 most important variables were the most important for the geographical distribution. Six groups of species were identified according to CA and climatic distribution similarity. This approach has shown promissory applications for biodiversity conservation of valuable genetic resources for tomato crop breeding.

Edaphoclimatic Descriptors of Wild Tomato Species (Solanum Sect. Lycopersicon) and Closely Related Species (Solanum Sect. Juglandifolia and Sect. Lycopersicoides) in South America.

Wild species related to cultivated tomato are essential genetic resources in breeding programs focused on food security to face future challenges. The ecogeographic analysis allows identifying the species adaptive ranges and most relevant environmental variables explaining their patterns of actual distribution. The objective of this research was to identify the diversity, ecological descriptors, and statistical relationship of 35 edaphoclimatic variables (20 climatic, 1 geographic and 14 edaphic variables) from 4,649 accessions of 12 wild tomato species and 4 closely related species classified in Solanum sect. Lycopersicon and clustered into four phylogenetic groups, namely "Lycopersicon group" (S. pimpinellifolium, S. cheesmaniae, and S. galapagense), "Arcanum group" (S. arcanum, S. chmielewskii, and S. neorickii), "Eriopersicon group" (S. habrochaites, S. huaylasense, S. corneliomulleri, S. peruvianum, and S. chilense), "Neolycopersicon group" (S. pennellii); and two phylogenetically related groups in Solanum sect. Juglandifolia (S. juglandifolium and S. ochranthum), and section Lycopersicoides (S. lycopersicoides and S. sitiens). The relationship between the climate and edaphic variables were determined by the canonical correlation analysis, reaching 89.2% of variation with the first three canonical correlations. The most significant climatic variables were related to humidity (annual evapotranspiration, annual precipitation, and precipitation of driest month) and physicochemical soil characteristics (bulk density, pH, and base saturation percentage). In all groups, ecological descriptors and diversity patterns were consistent with previous reports. Regarding edaphoclimatic diversity, 12 climate types and 17 soil units were identified among all species. This approach has promissory applications for biodiversity conservation and uses valuable genetic resources related to a leading crop.

A molecular selection index method based on eigenanalysis.

The traditional molecular selection index (MSI) employed in marker-assisted selection maximizes the selection response by combining information on molecular markers linked to quantitative trait loci (QTL) and phenotypic values of the traits of the individuals of interest. This study proposes an MSI based on an eigenanalysis method (molecular eigen selection index method, MESIM), where the first eigenvector is used as a selection index criterion, and its elements determine the proportion of the trait's contribution to the selection index. This article develops the theoretical framework of MESIM. Simulation results show that the genotypic means and the expected selection response from MESIM for each trait are equal to or greater than those from the traditional MSI. When several traits are simultaneously selected, MESIM performs well for traits with relatively low heritability. The main advantages of MESIM over the traditional molecular selection index are that its statistical sampling properties are known and that it does not require economic weights and thus can be used in practical applications when all or some of the traits need to be improved simultaneously.

Propuesta para la formulación de soluciones nutritivas en estudios de nutrición vegetal / Formulation of nutrient solutions for plant nutrition studies: a proposal

Para evaluar el efecto de uno o más nutrientes de las soluciones nutritivas en el crecimiento, desarrollo, rendimiento, calidad del producto y absorción de los nutrientes por los cultivos se han llevado a cabo numerosas investigaciones, sin que exista una técnica con aceptación general. Lo más común es que se modifique la concentración del nutriente en cuestión (anión o catión) y, en el mejor de los casos, se controle que los demás nutrientes restantes mantengan una concentración constante. El uso de soluciones nutritivas que contienen N-NH4+ y N-NO3- son un buen ejemplo de soluciones con cambios simultáneos en los nutrientes del tipo anión y catión. Por otra parte, con base en algunos estudios sistemáticos acerca de las características químicas de las soluciones nutritivas, y cómo éstas afectan a su vez dichas características de los cultivos, se analizó un número de estudios acerca del uso del N-NH4+ y/o del N-NO3-. Se encontró que dichos estudios no permiten hacer inferencias sobre los efectos directos del N-NH4+, o del N-NO3-, así como de su interacción. Se propone el empleo de soluciones nutritivas que correspondan, por su estructura, al diseño experimental factorial completo; con combinaciones de soluciones nutritivas (tratamientos) de un grupo de relaciones de concentración NH4+:cationes, con otro grupo de relaciones similares NO3-:aniones. Dichos tratamientos permiten evaluar los efectos directos del N-NH4+ y el N-NO3- y de su interacción, sin interferencias de otra índole (eg., presión osmótica y pH de la solución nutritiva)