Rectangular Lattice Design Research Articles

A preliminary evaluation of phenotypic traits of tepary bean (Phaseolus acutifolius A. Gray)

Background: Tepary bean (Phaseolus acutifolius A. Gray) is an underutilised grain legume crop and important source of food, nutrition and income. To date, there are no significant breeding efforts aimed at cultivar development and the crop remains under-utilised and under-researched.Aim: Therefore, the aim of this study was to evaluate eight phenotypic traits and their relationships among 42 genotypes of tepary bean in a controlled drought screening greenhouse environment.Setting: Agricultural Research Council – Vegetable, Industrial and Medicinal Plants, South Africa in drought screening glasshouse.Method: A 6 × 7 rectangular lattice design replicated three times was used in the study.Results: There were highly significant (p 0.01) differences in all the phenotypic traits that were measured. The highest number (30) of secondary roots was recorded for genotype ‘Ac-39’, which exceeded the trial, mean value by 62.87%. In comparison with the check, only Ac-33’, ‘Ac-39’, ‘Ac-40’ and ‘Ac-7’, ‘Ac-8’, ‘Ac-40’, ‘Ac-41’ genotypes achieved a significantly (p 0.05) higher secondary root length (SRL) and shoot dry weight (SDW), respectively. A highly significant (p 0.01) positive association was observed between the shoot fresh weight and the SDW suggesting that there was a strong linear relationship between the two parameters. Similarly, at least 68.0% of the changes in root dry weight were attributed to the changes in the SRL.Conclusion: These results suggested that the observed phenotypic variability in this germplasm which could be exploited for the enhancement of tepary bean.Contribution: There will be merit in validating these results on a field basis together with grain yield evaluation and genotyping over multiple locations and seasons to determine elite germplasm for production and utilisation by growers.

RGB-image method enables indirect selection for leaf spot resistance and yield estimation in a groundnut breeding program in Western Africa.

Early Leaf Spot (ELS) caused by the fungus Passalora arachidicola and Late Leaf Spot (LLS) also caused by the fungus Nothopassalora personata, are the two major groundnut (Arachis hypogaea L.) destructive diseases in Ghana. Accurate phenotyping and genotyping to develop groundnut genotypes resistant to Leaf Spot Diseases (LSD) and to increase groundnut production is critically important in Western Africa. Two experiments were conducted at the Council for Scientific and Industrial Research-Savanna Agricultural Research Institute located in Nyankpala, Ghana to explore the effectiveness of using RGB-image method as a high-throughput phenotyping tool to assess groundnut LSD and to estimate yield components. Replicated plots arranged in a rectangular alpha lattice design were conducted during the 2020 growing season using a set of 60 genotypes as the training population and 192 genotypes for validation. Indirect selection models were developed using Red-Green-Blue (RGB) color space indices. Data was collected on conventional LSD ratings, RGB imaging, pod weight per plant and number of pods per plant. Data was analyzed using a mixed linear model with R statistical software version 4.0.2. The results showed differences among the genotypes for the traits evaluated. The RGB-image method traits exhibited comparable or better broad sense heritability to the conventionally measured traits. Significant correlation existed between the RGB-image method traits and the conventionally measured traits. Genotypes 73–33, Gha-GAF 1723, Zam-ICGV-SM 07599, and Oug-ICGV 90099 were among the most resistant genotypes to ELS and LLS, and they represent suitable sources of resistance to LSD for the groundnut breeding programs in Western Africa.

Traits that define yield and genetic gain in East African highland banana breeding

East African highland bananas (Musa spp. AAA group) are an important staple in the Great Lakes region of East Africa. Their production has declined due to pests and diseases. Breeding for host plant resistance is a sustainable option for addressing this challenge. Understanding the relationships between growth parameters and bunch weight (i.e., yield) is crucial to guide breeding efforts for this crop. We investigated cause-effect relationships, through path analysis, in bunch weight of East African highland banana derived hybrids, their parents and grandparents. These family structures were planted in a 7 × 8 rectangular lattice design, replicated twice. Genetic gains for bunch weight (kg plant−1) and yield potential (t ha−1 year−1) were estimated. Significant increases of bunch weight and yield potential were noted from the landrace triploid germplasm, their derived primary tetraploid hybrids and secondary triploid bred-germplasm. Path analysis revealed that fruit length, circumference and number, number of hands and plant cycle number had a direct positive effect on the bunch weight. Days to fruit filling, days to maturity and index of non-spotted leaves had indirect effects on bunch weight. The average genetic gains for bunch weight and yield potential were 1.4% and 1.3% per year, respectively. This is the first report about genetic gains in banana breeding. Our findings may be useful for assessing progress and directing future breeding efforts in banana breeding.

Genetic variation in some Iranian bitter vetch (Vicia ervilia L.) landraces based on agronomic-morphological traits for use in breeding program in Rafsanjan

The aims of this research were to generate information on agro-morphological variability among 42 bitter vetch (Vicia ervilia L.) landraces collected from major growing areas of North West of Iran. The landraces were grown according to rectangular lattice design in the field across 2 years (2018 and 2019) in the Research Farm at Vali-e-Asr University of Rafsanjan (Rafsanjan, Iran). Observations were recorded days to 50% flowering, days to maturing start, days to 50% maturing, height to first flower node, plant height in flowering stage, plant height in maturity stage, root length in maturity stage, number of lateral branch, one, two and three seed pod length, number of pod per plant, number of seed per pod, number of seed per plant, thousand kernel weight, biomass and grain yield. Analysis of variance revealed significant variation among landraces for the majority of the traits. Using principal component analysis, the first five PCs with eigenvalues > 1 contributed 74.4% of the variability among landraces. PC1, which is the most important component, explained 28. 9% of the total variation and was positively related to days to 50% maturing, plant height in maturity stage, days to maturing start, plant height in flowering stage, height to first flower node and biomass, respectively and PC2 accounted for 20.6% of the total variation and the traits with the greatest weight on this component were number of seed per plant, number of pod per plant, grain yield and two seed pod length, respectively. Cluster analysis using Ward method divided landraces into four groups. Based on cluster analysis and mean comparison among four groups, promising landraces were identified with superior traits such as number of pod per plant, number of seed per plant, thousand kernel weight, biomass and grain yield. The results demonstrated bitter vetch landraces of North West of Iran are a useful source of diversity in desirable traits that can be exploited in future breeding programs.

The Estimation of Missing Values in Rectangular Lattice Designs

<p>Algebraic expressions for estimating missing data when one or more observation(s) are missing in Rectangular lattice designs with repetition were derived using the method of minimizing the residual sum of squares. Results showed that the estimated value(s) were significantly approximate to that of the actual value(s).</p>

General and specific combining ability in sweet sorghum

In breeding of sweet sorghum hybrids, non-additive genetic effects are important in phenotypic expression of the traits of interest. The aim of this study was to evaluate the general combining ability (GCA) of sweet sorghum lines and the specific combining ability (SCA) of the hybrids for agronomic and technological traits. Five fertility restorer lines, four male-sterile lines, and their hybrids from partial diallel crosses were evaluated in experiments laid out in a 5 x 6 triple rectangular lattice design in the municipalities of Lavras, MG and Sete Lagoas, MG, Brazil. Diallel analysis was performed using the Griffing model adapted to partial diallel crosses. There was a significant effect of GCA and SCA for most of the traits evaluated, indicating the participation of additive or dominant genes in inheritance. The restorer lines CMSX508, BRS 511, CMSXS643, and CMSXS646 show potential for use as parents in sorghum breeding programs.

On the Comparison of Methods of Estimating Missing Values in Rectangular Lattice Designs

Missing values occur in almost all research which lead to ambiguity in data analysis. It becomes necessary that appropriate consideration is made in order to provide an efficient and valid analysis. Researchers have developed and compared a variety of methods of estimating missing values in experimental designs; however, no research work has derived and compared methods of estimating missing values, particularly for rectangular lattice designs. In this study, the Least Square Method (LSM) and the Analysis of Covariance (ANCOVA) method for estimating missing value in rectangular lattice designs, with and without repetitions, were derived and compared based on four (4) statistical criteria: estimated values, standard errors, p-values and coefficients of determination respectively. Results from the comparison between the derived LSM and the ANCOVA methods showed that the estimates of the LSM appeared more approximate and better than the ANCOVA method in terms of their estimated values, standard errors, p-values and coefficients of determination.

The robustness of resolvable block designs against the loss of whole blocks or replicates

This paper considers the robustness of resolvable incomplete block designs in the event of two patterns of missing observations: loss of whole blocks and loss of whole replicates. The approach used to assess designs is based on the concept of block intersection which exploits the resolvability property of the design. This improves on methods using minimal treatment concurrence which have been used previously. It is shown that several classes of designs, including affine resolvable designs, square and rectangular lattice designs and two-category concurrence α-designs and αn-designs, are maximally robust; some of these classes of designs are also shown to be most replicate robust.

Tolerance of 42 Bread Wheat Genotypes to Drought Stress after Anthesis

The present research characterized yield and yield components of 42 wheat genotypes after terminal drought stress. The experiment was in twice replicated simple rectangular lattice design, conducted at irrigated and terminal stress conditions during 2006-2007. These study genotypes had significant differences for grain yield at level of 1%. Genotypes 4057, Viking/5/Gds/4.., Sabalan and 5041 respectively with 6.313, 6.159, 5.793 and 5.774 t ha(-1) had the highest yield and Gascogen has the lowest yield with 2.561 t ha(-1). Mean of total grain yield for under study genotypes was 5.628 t ha(-1) in non-stress and 3.305 t ha(-1) in drought stress conditions. Drought stress decreased amount of grain yield 2.323 t ha(-1) that was noticeable. Interaction of Genotype x environmental conditions was significant at probability level of 1% for grain yield. Yield of all genotypes in drought condition was lower than non-stress condition. Genotypes Viking/5/Gds/4/Anza/3/Pi.., Sabalan, 4061,4057 and 4041 had more yield in non-stress condition and MV17/Zrn, Sabalan, Saysonz and 4032 in stress condition. Stress intensity pay attention to total grain yield was 42%. Genotypes Viking/5/Gds/4/.. and Sabalan had high grain yield and was better than other genotypes and controls (Toos and Crosse Shahi), according to GMP, STI and MSTI. And had the most amount of stress tolerance index as compared with other genotypes confirms this subject. Correlation of yield with other traits was not significant in non-stress condition. In drought condition, correlation of grain yield with 1000 grain weight and total number of tillers per plant was positively significant. ANOVA showed significant differences between osmotic pressures for coleoptile length, between genotypes for mean and maximum coleoptile length and between interactions of genotypes x osmotic pressures for mean and maximum coleoptile length. Mean comparisons showed the highest total, mean and maximum coleoptile length in -7 bar PEG+I ml L(-1) potassium humate treatments. Genotypes Sardari and Sabalan had the highest amounts of total, mean and maximum coleoptile length. With due attention to interaction genotype x osmotic pressures, genotypes Sardari, Sabalan and 4057 in -7 bar PEG+1 ml L(-1) potassium humate had the most amounts of noted characters than others. In conditions of this experiment, potassium humate caused increase in tolerance rate of genotypes against drought stress.

Incorporating different proportions of exotic maize germplasm into two adapted populations

Maize breeders frequently wish to use exotic germplasm in their breeding programs without losing specific characteristics of their adapted material. The objective of this study was to determine the optimal proportions of exotic germplasm to incorporate into adapted populations (F2 = 50% exotic, BC1 = 25% exotic, BC2 = 12.5% exotic and BC3 = 6.25% exotic) to form the initial foundation population and to determine the heterosis between adapted x exotics. We used six exotic populations of different origins and two adapted populations representing a Brazilian heterotic pattern. In 1993-94 and 1994-95, the parents, F1, F2, BC1, BC2, BC3 and four checks were evaluated in six environments in central Brazil using an 8 x 9 simple rectangular lattice design. Higher mean values for yield were obtained as the proportion of exotic germplasm decreased. Some backcrosses produced more than the adapted populations BR 105 (7.59 ton/ha) and BR 106 (8.43 ton/ha). The best results were obtained when incorporating 6.25 or 12.5% of exotic genes. This trend was true for root lodging, stalk lodging and ear diseases but not for plant and ear height. The midparent heterosis for yield varied from -16.1 to 40.3%. Midparent heterosis with positive and negative values were also found for the other traits. The results indicate the potential of exotic germplasm for developing good hybrids. After choosing the best exotic source, some recurrent selection might be appropriate in order to adapt and improve the exotic populations.

Construction of a genetic map and location of quantitative trait loci for dwarf trait in maize by RFLP markers

Using F2 population derived from the cross of tall inbred 7922 by dwarf inbred 5003, an RFLP linkage map of maize has been constructed, on which 85 markers are distributed among 10 linkage groups and span maize genome about 1827.8 cM with an average distance (24.4 cM) between markers. 106 F2:3 lines of the population were grown in a 10 × 11 simple rectangular lattice design of one-raw plots with two replications and evaluated for plant height (PH). With interval mapping procedure, 5 QTLs controlling plant height have been identified and their genetic effects and gene action determined. 2 major QTLs with opposite effect have been discovered. One for increasing plant height isph1 which is located at chromosome 2 and accounts for 51.8% of the total phenotypic variation; the other for decreasing plant height isph3 which is located at chromosome 5 and accounts for 38.6% of the total phenotypic variation. The chromosomal location ofph3 might be the same as or close to the position ofbv1, a dwarf mutant of maize.

Rectangular lattice designs

This paper describes methods of constructing rectangular lattice designs for any number of treatments of the form s( s − l) with block size k = s − l and l < s.

Rectangular Lattice Designs: Efficiency Factors and Analysis

Rectangular lattice designs are shown to be generally balanced with respect to a particular decomposition of the treatment space. Efficiency factors are calculated, and the analysis, including recovery of interblock information, is outlined. The ideas are extended to rectangular lattice designs with an extra blocking factor.

A Note on Rectangular Lattice Designs

A Note on Rectangular Lattice Designs

ITERATIVE ANALYSIS OF GENERALIZED LATTICE DESIGNS

SummaryGeneralized lattice designs are defined. They include as special cases the square and rectangular lattice designs, and the α‐designs defined by Patterson and Williams (1976). An iterative procedure is given for the combined estimation of variety effects in generalized lattice designs with optimal or near optimal efficiency factors. This procedure, together with an approximate variance matrix, enables the analysis of efficient generalized lattice designs to be carried out on mini computers.

A method for estimating combining ability components of variance in incomplete block designs

A method is described for estimating components of variance for specific and general combining ability from breeding experiments arranged in incomplete block designs. Utilizing published results estimates of these components of variances were computed for a potato breeding experiment arranged in a rectangular lattice design with the parameters v=200 entries, k=10 entries per incomplete block, r=6 complete blocks, and b/r=20 incomplete blocks within each complete block. The experiment was grown at three different locations thus yielding three estimates of the components of variance for combining ability. These results were used in the computations of expected genetic progress in the preceding paper of this Journal.

Factorial Treatments in Rectangular Lattice Designs

Abstract This paper reports how factorial treatment combinations may be used in rectangular lattice designs. The analysis of variance is obtained both with and without recovery of inter-block information. Explicit formulae are presented for the variances and covariances of the treatment effects as well as single degree-of-freedom comparisons. In fact, this paper extends all the uses of factorial treatment combinations in complete block designs to rectangular lattice designs.

Factorial Treatments in Rectangular Lattice Designs

Abstract This paper reports how factorial treatment combinations may be used in rectangular lattice designs. The analysis of variance is obtained both with and without recovery of inter-block information. Explicit formulae are presented for the variances and covariances of the treatment effects as well as single degree-of-freedom comparisons. In fact, this paper extends all the uses of factorial treatment combinations in complete block designs to rectangular lattice designs.

Analysis of Covariance for a 3 x 4 Triple Rectangular Lattice Design (3 Associate P.B.I.B.)

The technique of analysis of covariance which was first introduced by R. A. Fisher [1934] has received detailed appraisal and extensive broadening of scope in a special issue of Biometrics published in September 1957. In that issue the nature and principal uses of the analysis of covariance are discussed with exceptional clarity in an article by W. G. Cochran [1957]; H. F. Smith [19571 offers an exposition on the theory, interpretation, and relationship of analysis of covariance with regression analysis; and the general case of r concomitant variables with special reference to incomplete block designs-both intraand inter-block analyses included-is presented by M. Zelen [1957]; other papers appearing in that special issue include those by W. T. Federer [1957], G. N. Wilkinson [1957], D. J. Finney [1957] and I. Coons [1957]. B. Harshbarger [1946, 1947, and 1949] developed a set of incomplete block designs in which the number of varieties (or treatments) is the product of two consecutive integers and the number of replications of each variety is either 2 or 3 and their multiples. He called them simple and triple rectangular lattices respectively. An early report on the analysis of such designs was put forth by Robinson and Watson [1949]. A few years later K. R. Nair [1951, 1952] showed that a 3 X 4 triple rectangular lattice is a 3-associate partially balanced incomplete block design. V. N. Murty [1953] has given a numerical illustration of the analysis for such a design following the methods of K. R. Nair. It is not generally realized, as pointed out by M. Zelen [1957] and others, that regardless of the experimental incomplete block design in question the problem of analysis of covariance is directly dependent upon the solution of the ordinary problem of analysis of variance for that design. Hence, once the analysis of variance solution is obtained,

Multiple Range Tests for Correlated and Heteroscedastic Means

Miultiple range tests have been developed by several writers, for example, D. Newmiian [8], M. Keuls [5], J. W. Tukey [10] anid D. B. Duincani [3], for testinig differenices between several treatmenlt means in cases inl which all such differences are of equal a priori interest. These tests, which are also described in recent textbooks, for example, W. T. Federer [4, chapter 2], have been worked out for data in which the treatment means are homoscedastic (have equal variances) and are uncorrelated. Recently, C. Y. Kramer [6] has presented a simple miethod for extending these procedures to give useful tests for differences between means with unequal replications, the method being applicable to aniy set of heteroscedastic unicorrelated means. In a subsequent paper [7], the same authorl has given further extensions to tests of mneanis which are also correlated, such as the adjusted means from analyses of covariance or from incomplete block designs. Similar work has also been done by E. Bleicher [1] and P. G. Sanders [9] in extendinig a multiple F test to making tests in lattice and rectangular lattice designs. One purpose of this paper is to present a more complete method for these extensions which lnecessarily sacrifices a little in simplicity but is more powerful, especially in cases in which the differences between the mneans have appreciably different varianices. Another purpose is to incdicate briefly the closeniess of the properties of these complete tests of heteroscedastic and correlated meanis to those of the corresponding tests of homoscedastic and unicorrelated mieans. Incidcental to these main ptirposes, a shor t-cut skippinig priniciple, useful in applyilng multiple ranige tests to a large lntum-ber of treatmenit means (or totals), is also presented.