Molecular analysis of evolutionary relationships of Phaseolus dumosus with the gene pool of common bean

Valuable genetic variation for bean breeding programs is held within the common bean secondary gene pool which consists of Phaseolus albescens, P. coccineus, P. costaricensis, and P. dumosus. However, the use of close relatives for bean improvement is limited due to the lack of knowledge about genetic variation and genetic plasticity of many of these species. Characterisation and analysis of the genetic diversity is necessary among beans' wild relatives; in addition, conflicting phylogenies and relationships need to be understood and a hypothesis of a hybrid origin of P. dumosus needs to be tested. This thesis research was orientated to generate information about the patterns of relationships among the common bean secondary gene pool, with particular focus on the species Phaseolus dumosus. This species displays a set of characteristics of agronomic interest, not only for the direct improvement of common bean but also as a source of valuable genes for adaptation to climate change. Here I undertake the first comprehensive study of the genetic diversity of P. dumosus as ascertained from both nuclear and chloroplast genome markers. A germplasm collection of the ancestral forms of P. dumosus together with wild, landrace and cultivar representatives of all other species of the common bean secondary gene pool, were used to analyse genetic diversity, phylogenetic relationships and structure of P. dumosus. Data on molecular variation was generated from sequences of cpDNA loci accD-psaI spacer, trnT-trnL spacer, trnL intron and rps14-psaB spacer and from the nrDNA the ITS region. A whole genome DArT array was developed and used for the genotyping of P. dumosus and its closes relatives. 4208 polymorphic markers were generated in the DArT array and from those, 742 markers presented a call rate >95% and zero discordance. DArT markers revealed a moderate genetic polymorphism among P. dumosus samples (13% of polymorphic loci), while P. coccineus presented the highest level of polymorphism (88% of polymorphic loci). At the cpDNA one ancestral haplotype was detected among all samples of all species in the secondary genepool. The ITS region of P. dumosus revealed high homogeneity and polymorphism bias to P. coccineus genome. Phylogenetic reconstructions made with Maximum likelihood and Bayesian methods confirmed previously reported discrepancies among the nuclear and chloroplast genomes of P. dumosus. The outline of relationships by hybridization networks displayed a considerable number of interactions within and between species. This research provides compelling evidence that P. dumosus arose from hybridisation between P. vulgaris and P. coccineus and confirms that P. costaricensis has likely been involved in the genesis or backcrossing events (or both) in the history of P. dumosus. The classification of the specie P. persistentus was analysed based on cpDNA and ITS sequences, the results found this species to be highly related to P. vulgaris but not too similar to P. leptostachyus as previously proposed. This research demonstrates that wild types of the secondary genepool carry a significant genetic variation which makes this a valuable genetic resource for common bean improvement. The DArT array generated in this research is a valuable resource for breeding programs since it has the potential to be used in several approaches including genotyping, discovery of novel traits, mapping and marker-trait associations. Efforts should be made to search for potential populations of P. persistentus and to increase the collection of new populations of P. dumosus, P. albescens and P. costaricensis that may provide valuable traits for introgression into common bean and other Phaseolus crops.

On classical and other methods of discriminant analysis and estimation of log-odds

For two multinormal populations with equal covariance matrices the likelihood ratio discriminant function, an alternative allocation rule to the sample linear discriminant function when n1 ≠ n2 ,is studied analytically. With the assumption of a known covariance matrix its distribution is derived and the expectation of its actual and apparent error rates evaluated and compared with those of the sample linear discriminant function. This comparison indicates that the likelihood ratio allocation rule is robust to unequal sample sizes. The quadratic discriminant function is studied, its distribution reviewed and evaluation of its probabilities of misclassification discussed. For known covariance matrices the distribution of the sample quadratic discriminant function is derived. When the known covariance matrices are proportional exact expressions for the expectation of its actual and apparent error rates are obtained and evaluated. The effectiveness of the sample linear discriminant function for this case is also considered. Estimation of true log-odds for two multinormal populations with equal or unequal covariance matrices is studied. The estimative, Bayesian predictive and a kernel method are compared by evaluating their biases and mean square errors. Some algebraic expressions for these quantities are derived. With equal covariance matrices the predictive method is preferable. Where it derives this superiority is investigated by considering its performance for various levels of fixed true log-odds. It is also shown that the predictive method is sensitive to n1 ≠ n2. For unequal but proportional covariance matrices the unbiased estimative method is preferred. Product Normal kernel density estimates are used to give a kernel estimator of true log-odds. The effect of correlation in the variables with product kernels is considered. With equal covariance matrices the kernel and parametric estimators are compared by simulation. For moderately correlated variables and large dimension sizes the product kernel method is a good estimator of true log-odds.