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.

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.

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.

Selection indices, used in animal and plant breeding to select the best individuals for the next breeding cycle, are based on phenotypic observations of traits recorded in candidate individuals. The restrictive selection index (RSI) facilitates maximizing the genetic progress of some characters, while leaving others unchanged. Recently a selection index (SI) was proposed based on the eigen analysis method (ESIM), in which the first eigenvector (from the largest eigenvalue) is used as the SI criterion, and its elements determine the proportion of the trait that contributes to the SI. However, the current ESIM, which has two main limitations, is based on the assumption that the vector of coefficients of the index is equal to the genotypic variance-covariance matrix among the traits multiplied by the vector of economic weights, and does not allow one to restrict the number of traits. In this study, we develop a more general ESIM that has two main features, namely, it makes no assumption concerning the coefficients of the index and it can be generalized to a restrictive ESIM (RESIM). We use two datasets to illustrate the theoretical results and practical use of ESIM and RESIM, and to compare them with standard unrestrictive and restrictive selection indices. The main advantages of RESIM over traditional unrestrictive and restrictive SIs are that its statistical sampling properties are known; its selection responses are equal to or greater than those estimated from the traditional restrictive SI; and 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 (traditional SIs cannot improve several traits simultaneously if economic weights are not available). Finally, we prove that the coefficients of the traditional RSI belong to the space generated by the eigenvectors of RESIM.