The seed size and shape of lentil are important traits because they determine the market class, cooking time, and can influence quality and yield of milled lentils. Understanding the genetic control of seed size and shape can help breeders develop varieties with improved seed size and shape characteristics such as seed diameter, seed thickness and seed plumpness. The objectives were to determine the heritability of seed size and shape and identify the genomic regions controlling these traits. This involved i) developing a linkage map for the LR-18 population (CDC Robin x 964a-46) using a recently developed single nucleotide polymorphism (SNP) assay; ii) analyzing the LR-18 population for seed size and shape QTLs; iii) analyzing an association mapping panel for seed size and shape QTLs. Phenotyping trials were grown at two different locations in Saskatchewan, Canada. The mapping population was grown in two different years while the association panel was only grown in one. Seed diameter and thickness were measured using sieves and this data were used to calculate seed plumpness. Days to flowering was also recorded to determine if it had any effect on seed size or shape. A linkage map consisting of 537 SNPs, 10 SSRs and 4 morphological markers on seven linkage groups was constructed and used for the QTL analysis. The heritability estimates were high for seed diameter and seed plumpness (0.92 and 0.94, respectively) while for seed thickness and days to flowering they were more moderate (0.60 and 0.45, respectively). QTL analysis revealed QTLs on five of the seven linkage groups. The association mapping study revealed similar heritability estimates of 0.97, 0.62, 0.94, and 0.62 for seed diameter, seed thickness, seed plumpness and flowering time, respectively. There were 31 different significant marker trait associations, however only 5 of those were significant for both locations. Four of those five markers did not map in the LR-18 linkage map so their genomic locations are still to be determined. Results showed that there are key regions in the genome that control seed size and shape and flowering time in lentil. These markers could be used for marker-assisted selection or for further candidate gene analysis.

This thesis presents an analytical approach using Root-Loci method for designing optimum passive series RC snubbers for continuous-current synchronous buck switch mode power supply (SMPS). Synchronous buck SMPS is the most popular power converter topology found in modern consumer electronics. It offers relatively good efficiency to target the high-current and low-voltage requirements while it is also relatively inexpensive to implement. Passive series RC snubbers are simple, efficient and cost-effective open-loop equalizer circuit for synchronous buck SMPS. Its purpose is to control and to balance between the rate of rise and the overshoots of transient switching waveform in order to optimize efficiency and reliability Existing methods of RC snubber design are solely based on second-order approximation. It is investigated in this research that this approximation is highly inaccurate in SMPS applications because higher order equivalent models are required for the load path of the SMPS. The results using the RC snubbers obtained from existing method are shown to be unsatisfactory without correlation to the calculations and simulations based on second-order approximation. Optimum RC values obtained using Root-Loci approach presented in this thesis are shown to correlate to both Spice simulation and lab measurements.

Domestication is the process by which animals become adapted to the environment provided by humans. The process of domestication has let to a number of correlated behavioural, morphological and physiological changes among many domesticated animal species. An example is the changes of plumage colour in the chicken. Plumage colour is one of the most readily observable traits that make distinction between breeds as well as between strains within a breed. Understanding the genetic architecture of pigmentation traits or indeed any trait is always a great challenge in evolutionary biology. The main aim of this study was to map quantitative trait loci (QTLs) affecting the red and metallic green coloration in the chicken plumage. In this study, a total of 572 F8 intercross chickens between Red Junglefowl and White Leghorn were used. Phenotypic measurements were done using a combination of digital photography and photography manipulating software. Moreover, all birds were genotyped with 657 molecular markers, covering 30 autosomes. The total map distance covered was 11228 cM and the average interval distance was 17 cM. In this analysis, a total of six QTLs (4 for red and 2 for metallic green colour) were detected on four different chromosomes: 2, 3 11 and 14. For red colour, the most significant QTL was detected on chromosome 2 at 165 cM. An additional QTL was also detected on the same chromosome at 540 cM. Two more QTLs were detected on chromosomes 11 and 14 at 24 and 203 cM respectively. Additionally, two epistatic pairs of QTLs were also detected. The identified four QTLs together can explain approximately 36% of the phenotypic variance in this trait. In addition, for metallic green colour, one significant and one suggestive QTLs were detected on chromosomes 2 and 3 at 399 and 247 cM respectively. Moreover, significant epistatic interactions between these two QTLs were detected. Furthermore, these two QTLs together can explain approximately 24% of the phenotypic variance in this trait. These findings suggest that the expression of pigmentation in the chicken plumage is highly influenced by both the epistatic actions and pleiotropic effects of different QTLs located on different chromosomes.

The protein quality of maize can be improved by replacing normal Opaque2 alleles with non-functional recessive alleles opaque2 (o2). The allele o2 produces a severe phenotype with soft endosperm enhancing its protein quality but decreasing its agronomical value. Plant breeders have restored a desirable ratio of hard to soft endosperm in o2 germplasm known as Quality Protein Maize (QPM). Neither the mechanism nor the genetic components by which the modification of the endosperm in QPM lines occurs are well understood. To increase the understanding of the genetics of endosperm modification, a population of 146 recombinant inbred lines derived from a cross between the o2 inbred line B73o2 and the QPM inbred line CML161 was evaluated in two Texas locations from 2004 to 2006. Four traits related to endosperm texture were measured and showed significant effect of the inbred lines, high heritability estimates and high genetic correlations. Relative content of the essential amino acids lysine, tryptophan and methionine were measured and showed significant effects of the lines and considerable high genetic correlations and heritabilities. Negative correlation was observed between endosperm texture traits and amino acid content. Quantitative trait loci (QTL) were mapped for traits related to the modification of endosperm texture and the content of lysine, tryptophan and methionine. QTLs clusters for endosperm texture traits were detected on chromosomes 3, 5, 6 and 8 explaining 62-68% of the variation. QTLs clusters for amino acid contents were located on chromosomes 7 and 8 that explained up to 39% of the observed variation. The product of the O2 gene is a transcription factor that affects the expression of a number of endosperm genes. A group of 29 endosperm genes associated with the O2 activity were evaluated in developing endosperm of the recombinant inbred lines. Genomic regions controlling gene transcript abundance in developing endosperm were identified by expression QTL mapping. Evidence is presented of QTL hot spots that segregate in association with endosperm texture modification or amino acid contents and are associated with the regulation of the expression of a group of endosperm genes.

Heat stress adversely affects wheat production in many regions of the world and is particularly detrimental during reproductive development. The objective of this study was to identify quantitative trait loci (QTL) associated with improved heat tolerance in hexaploid bread wheat (Triticum aestivum). To accomplish this objective, an analysis of both the phenotypic and genetic responses of two recombinant inbred line (RIL) populations was conducted. RIL populations Halberd x Cutter and Halberd x Karl 92 (H/K) both derive heat tolerance from Halberd and segregate in their response to heat stress. A heat susceptibility index (HSI) was calculated from the reduction of three yield components; kernel number, kernel weight, and single kernel weight, following a three-day 38 degrees C heat stress treatment during early grain-filling. The HSI, as well as temperature depression of the main spike and flag leaf were used as measurements of heat tolerance. Genetic linkage maps were constructed for both populations and were used in combination with phenotypic data and statistical software to detect QTL for heat tolerance. In a comparison across the two across populations, seven common QTL regions were identified for HSI, located on chromosomes 1B, 3B, 4A, 5A, 5B, and 6D. Subsequent analysis of temperature depression in the H/K population identified seven QTL that co-localized for both cooler organ temperature and improved HSI. Four of the beneficial alleles at these loci were contributed Halberd. The genetic effect of combining QTL, including QHkw.tam-1B, QHkwm.tam-5A.1, and QHskm.tam-6D showed the potential benefit of selection for multiple heat tolerant alleles simultaneously. Analysis of the H/K population in the field under abiotic stress detected QTL on chromosome 3B and 5A, which were in agreement with results from the greenhouse study. The locus QYld.tam-3B was pleiotropic for both temperature depression and HSI in both experiments and was associated with higher biomass and yield under field conditions. The results presented here represent a comprehensive analysis of both the phenotypic response of wheat to high temperature stress and the genetic loci associated with improved heat tolerance and will be valuable for future understanding and improvement of heat stress tolerance in wheat.

This study reexamines the nuclear microsatellite analysis by Rooney et al. (1999a) of Bering-Chukchi-Beaufort Seas bowhead whales (Balaena mysticetus) to determine if this population underwent a genetic bottleneck as a result of 19th and early 20th Century commercial whaling. This investigation used more accurate laboratory techniques to score alleles, had a larger sample size that was divided into two groups (mainland Alaska and St. Lawrence Island (SLI)), and used a moderately different set of microsatellite loci which are more variable and thus, more informative. The results corroborate the findings of Rooney et al. (1999a) for mainland Alaska showing no evidence of a genetic bottleneck. However, the SLI data analyses provide conflicting conclusions. The Wilcoxon test is significant for a heterozygote excess (p = 0.042) suggesting that a genetic bottleneck has occurred. This is not substantiated by the exact tests of each locus or the table-wide sign test. There is a possibility that a bottleneck has occurred, but due to the small sample size this is not a definitive conclusion and warrants reanalysis with a larger sample size.

Variable selection methods play important roles in modeling high-dimensional data and are key to data-driven scientific discoveries. In this thesis, we consider the problem of variable selection with interaction detection. Instead of building a predictive model of the response given combinations of predictors, we start by modeling the conditional distribution of predictors given partitions based on responses. We use this inverse modeling perspective as motivation to propose a stepwise procedure for effectively detecting interaction with few assumptions on parametric form. The proposed procedure is able to detect pairwise interactions among p predictors with a computational time of \(O(p)\) instead of \(O(p^2)\) under moderate conditions. We establish consistency of the proposed procedure in variable selection under a diverging number of predictors and sample size. We demonstrate its excellent empirical performance in comparison with some existing methods through simulation studies as well as real data examples. Next, we combine the forward and inverse modeling perspectives under the Bayesian framework to detect pleiotropic and epistatic effects in effects in expression quantitative loci (eQTLs) studies. We augment the Bayesian partition model proposed by Zhang et al. (2010) to capture complex dependence structure among gene expression and genetic markers. In particular, we propose a sequential partition prior to model the asymmetric roles played by the response and the predictors, and we develop an efficient dynamic programming algorithm for sampling latent individual partitions. The augmented partition model significantly improves the power in detecting eQTLs compared to previous methods in both simulations and real data examples pertaining to yeast. Finally, we study the application of Bayesian partition models in the unsupervised learning of transcription factor (TF) families based on protein binding microarray (PBM). The problem of TF subclass identification can be viewed as the clustering of TFs with variable selection on their binding DNA sequences. Our model provides simultaneous identification of TF families and their shared sequence preferences, as well as DNA sequences bound preferentially by individual members of TF families. Our analysis may aid in deciphering cis regulatory codes and determinants of protein-DNA binding specificity. / Statistics

This thesis is devoted to the study of holomorphic Poisson structures and Lie algebroids, and their relationship with differential equations, singularity theory and noncommutative algebra. After reviewing and developing the basic theory of Lie algebroids in the framework of complex analytic and algebraic geometry, we focus on Lie algebroids over complex curves and their application to the study of meromorphic connections. We give concrete constructions of the corresponding Lie groupoids, using blowups and the uniformization theorem. These groupoids are complex surfaces that serve as the natural domains of definition for the fundamental solutions of ordinary differential equations with singularities. We explore the relationship between the convergent Taylor expansions of these fundamental solutions and the divergent asymptotic series that arise when one attempts to solve an ordinary differential equation at an irregular singular point. We then turn our attention to Poisson geometry. After discussing the basic structure of Poisson brackets and Poisson modules on analytic spaces, we study the geometry of the degeneracy loci---where the dimension of the symplectic leaves drops. We explain that Poisson structures have natural residues along their degeneracy loci, analogous to the Poincar\'e residue of a meromorphic volume form. We discuss the local structure of degeneracy loci that have small codimensions, and place strong constraints on the singularities of the degeneracy hypersurfaces of log symplectic manifolds. We use these results to give new evidence for a conjecture of Bondal. Finally, we discuss the problem of quantization in noncommutative projective geometry. Using Cerveau and Lins Neto's classification of degree-two foliations of projective space, we give normal forms for unimodular quadratic Poisson structures in four dimensions, and describe the quantizations of these Poisson structures to noncommutative graded algebras. As a result, we obtain a (conjecturally complete) list of families of quantum deformations of projective three-space. Among these algebras is an ``exceptional'' one, associated with a twisted cubic curve. This algebra has a number of remarkable properties: for example, it supports a family of bimodules that serve as quantum analogues of the classical Schwarzenberger bundles.

I examined phenotypic and genetic variation in growth traits in 30 families of commercial Fraser strain Arctic charr (Salvelinus alpinus) reared in freshwater (FRW) and brackish water (BRW) in Eastern Canada. I detected family by treatment interactions for all traits [body weight (BW), condition factor (K) and specific growth rate (SGR)] across all measurement dates and growth intervals, however, mean family BW in FRW was correlated phenotypically with BRW BW. In addition, FRW fish showed significantly greater survival than those transferred to BRW and fish which survived until the conclusion of the experiment were significantly heavier in BW at the baseline assessment than their full-sibs that died. These observations suggest that BW in FRW and BW in BRW should be analyzed as separate but correlated traits in Arctic charr breeding programs. I then tested the potential for genetic improvement in this species by calculating genetic parameters for BW and K, and tested if previously identified quantitative trait loci (QTL) for these traits were detectable across the broodstock. QTL with experiment-wide and chromosome-wide significance for body size and condition factor were detected on multiple linkage groups. Heritability for BW and K was moderate in FRW (0.29-0.38) but lower in BRW (0.14-0.17). Genetic correlations for BW across environments were positive and moderate (0.33-0.67), however equivalent K correlations were weaker (0.24-0.37). This information was then used to predict the rate of genetic change following one generation of selection for BW using phenotypic selection and genomic methodologies including marker-only selection and marker assisted selection. The greatest response in the rate of genetic change was achieved by selecting only from families in which significant BW QTL had been identified. As such, marker assisted selection showed the greatest gain in genetic response with 5.4% in FRW and 4.3% in BRW. These results have applications to commercial aquaculture as the Canadian aquaculture industry is attempting to diversify with alternative species. Such genetic improvement strategies will aid in developing a strain of Arctic charr characterised by increased BW. / Funding provided through the NSERC Strategic grants program. The project was sponsored by CanAqua Seafoods Ltd. in collaboration with the Coastal Zones Research Institute.

This thesis is devoted to the study of holomorphic Poisson structures and Lie algebroids, and their relationship with differential equations, singularity theory and noncommutative algebra. After reviewing and developing the basic theory of Lie algebroids in the framework of complex analytic and algebraic geometry, we focus on Lie algebroids over complex curves and their application to the study of meromorphic connections. We give concrete constructions of the corresponding Lie groupoids, using blowups and the uniformization theorem. These groupoids are complex surfaces that serve as the natural domains of definition for the fundamental solutions of ordinary differential equations with singularities. We explore the relationship between the convergent Taylor expansions of these fundamental solutions and the divergent asymptotic series that arise when one attempts to solve an ordinary differential equation at an irregular singular point. We then turn our attention to Poisson geometry. After discussing the basic structure of Poisson brackets and Poisson modules on analytic spaces, we study the geometry of the degeneracy loci---where the dimension of the symplectic leaves drops. We explain that Poisson structures have natural residues along their degeneracy loci, analogous to the Poincar\'e residue of a meromorphic volume form. We discuss the local structure of degeneracy loci that have small codimensions, and place strong constraints on the singularities of the degeneracy hypersurfaces of log symplectic manifolds. We use these results to give new evidence for a conjecture of Bondal. Finally, we discuss the problem of quantization in noncommutative projective geometry. Using Cerveau and Lins Neto's classification of degree-two foliations of projective space, we give normal forms for unimodular quadratic Poisson structures in four dimensions, and describe the quantizations of these Poisson structures to noncommutative graded algebras. As a result, we obtain a (conjecturally complete) list of families of quantum deformations of projective three-space. Among these algebras is an ``exceptional'' one, associated with a twisted cubic curve. This algebra has a number of remarkable properties: for example, it supports a family of bimodules that serve as quantum analogues of the classical Schwarzenberger bundles.