The association of genetic distance and heterosis was investigated in dry edible bean (Phaseolus vulgaris L.) and faba bean (Viciafaba L.). Dry bean materials consisted of 28 F2 populations of an 8 × 8 diallel, and their respective parents, grown in eight replications in the field at East Lansing, Mich. in 1981. Faba bean materials comprised the 64 F1's and parents of an 8 × 8 diallel grown in 1975, and 120 populations grown in 1976 como prised of F1's, F2's, and parents of the same diallel, grown in four replications at the Agricultural Research Center at Giza, Egypt. Mahalanobis' D2 was used to estimate genetic distance between parents. Heterosis was measured as deviation from midparent. Correlations in dry beans between heterotic effects and parental distances were positive and highly significant for yield at harvest and for two of the three yield components, namely, number pods/plant and number seeds/pod. No relationship was found for 100‐seed weight. A highly significant positive correlation was obtained for leaf weight. Both significantly positive and negative correlations were found in faba beans for an array of “number” traits related to yield, but heterosis for yield of seed per se in faba beans was not associated with the Mahalanobis D2's

Forty‐one genotypes (seven cultivars and 34 breeding lines) of winter wheat (Triticum aestivum L.) were planted in eight locations in each of 2 years. Test weight data were used to group locations according to their similarity of genotype ✕ location (G✕L) effects by cluster analysis. The results indicated that deletion of only one location from the variance analysis resulted in a group within which G ✕ L interaction was not significant. Such an analysis would be useful for the selection of testing sites for early generation testing and for development of genotypes with wide or narrow adaptability.The cultivars were also grouped into 10 clusters with respect to their test weight similarity across the 16 environments (2 years and eight locations). Further, stability parameters, i.e., mean, regression coefficient, and deviations from regression were calculated for each genotype. Cluster analysis effectively grouped genotypes according to their stability responses. Three broad categories of genotypes were identified with respect to their stability characteristics. Cluster analysis could be a useful supplementary tool for the analysis of adaptation reactions of wheat genotypes for test weight.

Test weight is defined as the weight of grain that fills a given volume. It is the product of kernel density and volume of grain occupying the container. The latter component, when expressed as percentage of the volume of the container, is referred to as packing efficiency and was shown to be a cultivar characteristic. Of the two components packing efficiency has a greater effect on test weight when comparing soft winter wheats (Triticum aestivum L. em Thell).There was a negative correlation between test weight and the kernel length‐width ratio (kernel shape). When the length‐width ratio remained constant, there was no increase in test weight when kernel volume increased. Kernel width was correlated more than length with kernel volume. Test weight and flour yield were not correlated within or among cultivars. Kernel protein was related to kernel size within cultivars.

A principal factor analysis was applied to data for yield and 16 sensory and physico-chemical traits measured on 25 strains of blackseeded dry beans (Phaseolus vulgaris L.) grown in Michigan in 1978 and 1979. Five principal factors were extracted from the correlation matrix of traits. The principal factors extracted described "soaking," "cooked color," "thermal," "dry color," and "general color" constructs. The soaking, cooked color, and thermal factors are related to culinary quality and accounted for 67.1, 73.0 and 67.8% of the variance in the 1978, 1979 and combined data, respectively. The factors themselves did not provide an image by which culinary quality could be interpreted in a developmental sense from the physico-chemical traits of dry, soaked, or cooked bean seeds. Major traits did not appear in more than one factor in any of the analyses. When the loadings were examined from the point of view of the tests rather than factors, the constructs which emerged were coherent in a physico-chemical or technological sense and reasonable biologically. "Soaking", "cooked color", and "thermal" constructs can be measured by the hydration coefficient, L color value and Kramer shear press, respectively. These tests were able to differentiate culinary quality among test samples. Yield and protein content were independent of culinary quality.Key words: Phaseolus vulgaris L., consumer acceptance, seed coat color, soaking characteristics, cookability, protein content

In solid mechanics, data-driven approaches are widely considered as the new paradigm that can overcome the classic problems of constitutive models such as limiting hypothesis, complexity, and accuracy. However, the implementation of machine-learned approaches in material modeling has been modest due to the high-dimensionality of the data space, the significant size of missing data, and limited convergence. This work proposes a framework to hire concepts from polymer science, statistical physics, and continuum mechanics to provide super-constrained machine-learning techniques of reduced-order to partly overcome the existing difficulties. Using a sequential order-reduction, we have simplified the 3D stress–strain tensor mapping problem into a limited number of super-constrained 1D mapping problems. Next, we introduce an assembly of multiple replicated neural network learning agents (L-agents) to systematically classify those mapping problems into a few categories, each of which were described by a distinct agent type. By capturing all loading modes through a simplified set of dispersed experimental data, the proposed hybrid assembly of L-agents provides a new generation of machine-learned approaches that simply outperform most constitutive laws in training speed, and accuracy even in complicated loading scenarios. Interestingly, the physics-based nature of the proposed model avoids the low interpretability of conventional machine-learned models.