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Grain protein concentration (GPC) is considered one of the most important quality factors, and it has remained a major culling criterion in the Canadian wheat cultivar development and registration process. However, grain protein composition also plays a critical role in determining the end-use quality of cereal-based products. The objective of this study was to determine whether high-yielding, lower protein Canada Western Red Spring (CWRS) analog wheat lines can exhibit acceptable baking properties (comparable with CWRS cultivars) under contrasting soil nitrogen levels. Five CWRS-analog lines together with four CWRS and one Canada Prairie Spring Red wheat cultivar, representing wide ranges of quality and grain yield potential, were assessed for agronomic and quality traits in multi-environment trials at three locations and five nitrogen fertilizer rates. CWRS analog lines produced significantly higher grain yield and, on average, 0.9% less GPC than the CWRS cultivars. Despite the lower GPC, CWRS-analog lines such as W07786 exhibited suitable and stable baking performance across all nitrogen levels. Based on the genotype × trait biplot analysis, CWRS-analog baking properties were mainly associated with sodium dodecyl sulfate sedimentation and flour water absorption. Our findings revealed that it is possible to develop wheat cultivars with up to 15% higher grain yield than modern CWRS cultivars and comparable end-use characteristics by reducing current GPC requirements (by up to 1%) while simultaneously selecting for improved baking attributes. This would facilitate an increase in CWRS grain yield genetic gains while maintaining favorable end-use quality and improving the crop competitiveness in western Canada.

The $$\gamma $$-graph of a graph G is the graph whose vertices are labelled by the minimum dominating sets of G, in which two vertices are adjacent when their corresponding minimum dominating sets (each of size $$\gamma (G)$$) intersect in a set of size $$\gamma (G)-1$$. We extend the notion of a $$\gamma $$-graph from distance-1-domination to distance-d-domination, and ask which graphs H occur as $$\gamma $$-graphs for a given value of $$d \ge 1$$. We show that, for all d, the answer depends only on whether the vertices of H admit a labelling consistent with the adjacency condition for a conventional $$\gamma $$-graph. This result relies on an explicit construction for a graph having an arbitrary prescribed set of minimum distance-d-dominating sets. We then completely determine the graphs that admit such a labelling among the wheel graphs, the fan graphs, and the graphs on at most six vertices. We connect the question of whether a graph admits such a labelling with previous work on induced subgraphs of Johnson graphs.

A controlled fermentation process using straight-grade wheat flour, commercially milled from a grist of Canada Western Red Spring (CWRS) wheat and English wheat, and fresh yeast (Saccharomyces cerevisiae) was found to be effective for developing a naturally derived product (ferment) that could be used for processing bread with the minimum use of dough improvers. The effects of ferment storage, fermentation time, and fermentation temperature on the quality of ferment and bread were evaluated to establish optimal conditions to produce a mature ferment. Trials were conducted on a pilot scale for greater relevance to industrialized bakeries. Ferment was assessed for total titratable acidity (TTA), pH, and viscosity. Breads made with ferment were evaluated for processing parameters, dough properties, and bread quality and compared to a control prepared without ferment. During fermentation, maximum TTA levels in the ferment were achieved at 100 min, then decreased by the end of fermentation, and increased by 24 h of storage at 4 °C. Viscosity was stable during fermentation but decreased by 24 h of storage. Inclusion of ferment resulted in reduced mixing times and improved dough extensibility and crumb softness. Specific loaf volume was not impacted, a slight reduction in crumb brightness and crumb structure was detected. Fermentation for 240 min at 35 °C was determined as optimal with a storage time for 24 h.

The need to produce wheat with low asparagine concentration is of great importance as a measure to mitigate acrylamide concentration in wheat-based products. The association of asparagine concentration in Canadian bread wheat with cultivar, growing location, fertilizer and their interaction were investigated. Wheat cultivars (8) were grown in 2 locations under 4 fertilizer treatments in triplicate (which consisted of two nitrogen rates (90 or 120 lbs/acre) with or without 15 lbs sulphur per acre). The asparagine concentration ranged from 168.9 to 1050 µg/g and was significantly affected by cultivar, location, and their interaction but not fertilizer treatment. Location and cultivar were responsible for 80% and 14% of the variation, respectively. Some cultivars were not affected by location and maintained their low asparagine accumulation trait. Thus, breeding strategies should aim to identify cultivars that are low asparagine accumulating and are stable across different growing environments.

A $k\ell$-subset partition, or $(k,\ell)$-subpartition, is a $k\ell$-subset of an $n$-set that is partitioned into $\ell$ distinct classes, each of size $k$. Two $(k,\ell)$-subpartitions are said to $t$-intersect if they have at least $t$ classes in common. In this paper, we prove an Erd\H{o}s-Ko-Rado theorem for intersecting families of $(k,\ell)$-subpartitions. We show that for $n \geq k\ell$, $\ell \geq 2$ and $k \geq 3$, the largest $1$-intersecting family contains at most $\frac{1}{(\ell-1)!}\binom{n-k}{k}\binom{n-2k}{k}\cdots\binom{n-(\ell-1)k}{k}$ $(k,\ell)$-subpartitions, and that this bound is only attained by the family of $(k,\ell)$-subpartitions with a common fixed class, known as the \emph{canonical intersecting family of $(k,\ell)$-subpartitions}. Further, provided that $n$ is sufficiently large relative to $k,\ell$ and $t$, the largest $t$-intersecting family is the family of $(k,\ell)$-subpartitions that contain a common set of $t$ fixed classes.