Row-column Designs Research Articles

Construction of Partially Balanced Semi-Latin Rectangles with Block Size 4

Semi-Latin rectangles represent row-column designs where each row-column intersection contains the same number of experimental units, denoted as k >1. Additionally, each treatment appears an equal number of times in each row ( r n , say) and in each column ( c n , say) ( 1 r n ≥ and 1 c n ≥ may or may not be same). Partially Balanced Semi-Latin rectangles (PBSLR) constitute a subset of Semi-Latin rectangles (SLR), serving as generalizations of Latin squares and Semi-Latin squares (SLS). These designs find utility in various agricultural and industrial experiments, particularly situations where one effect is considered a column effect and the other a row effect, with the intersection (block/cell) accommodating precisely four units. This article introduces two methods for constructing PBSLR designs with a block size of 4. Also, R package has been developed for generating the designs.

Construction of 2fi-optimal row–column designs

Row–column designs that provide unconfounded estimation of all main effects and the maximum number of two-factor interactions (2fi’s) are called 2fi-optimal. This issue has been paid great attention recently for its wide application in industrial or physical experiments. The constructions of 2fi-optimal two-level and three-level full factorial and fractional factorial row–column designs have been proposed. However, the results for higher prime levels have not been achieved yet. In this paper, we give theoretical constructions of 2fi-optimal sn full factorial row–column designs for any odd prime level s and any parameter combination, and theoretical constructions of 2fi-optimal sn−1 fractional factorial row–column designs for any prime level s and any parameter combination.

236 The effects of replacing dried distiller’s grains with solubles with heat-treated soybean meal on nutrient intake and digestibility in forage-based diets

Abstract Cattle growth is calculated through dry matter intake, average daily gain and gain:feed measures that assume performance and digestibility are correlated. Hence, evaluating nutrient digestibility and flow provides additional explanations for subsequent growth performance. Therefore, five fistulated Jersey steers [Initial body weight (BW) = 288 ± 22 kg) fitted with ruminal, duodenal, and ileal cannulas were utilized in a 4 × 5 row-column design to determine intake and total tract nutrient digestibility when replacing dried distiller’s grains plus solubles (DDGS) with heat-treated soybean meal (TSBM) in forage-based growing diets. The 56-d study contained 4 periods, each period lasting 14 d [9 d of adaptation and 5 d of collection (d 0 to 4)]. Dietary treatments partially replaced DDGS, included at 16% diet dry matter (DM), with TSBM at increasing inclusion levels of 0 (TSBM0), 4 (TSBM4), 8 (TSBM8), and 12% (TSBM12) DM. Basal diets contained 43.5% corn silage, 36.5% oat hay, and 4% meal supplement (DM). Chromic oxide was incorporated into the diet daily at 0.25% DM as a digesta marker. Steers were housed in individual tie stalls during the 5-d collection period. Treatment diets were fed daily at 0800 h with orts being weighed at 0730 h and subsampled on d 0 to d 4 each period. Fecal collection bags were harnessed to each steer from d 0 to d 4 to collect fecal weight and subsampled twice daily (0700 and 1900 h). Digestibility and feed intake were analyzed utilizing the MIXED procedure of SAS with treatment and period as fixed effects and animal as a random effect. There were no differences (P ≥ 0.14) in DM, organic matter (OM), neutral detergent fiber (NDF), starch and nitrogen (N) intakes among treatments. Fecal DM, OM, NDF, starch, and N output resulted in no treatment effects (P ≥ 0.24). Subsequently, total tract apparent digestibility differences (P ≥ 0.32) were not detected for DM, OM, NDF, and starch content. However, N total tract apparent digestibility was significantly different (P < 0.03) with TSBM0 resulting in less N digestibility than TSBM12 (65.54% and 71.59%, respectively). Replacing a portion of DDGS with TSBM does not result in deleterious digestive effects in forage-based growing diets. As a result, the utilization of DDGS or TSBM as the primary protein source will depend on growth performance, feedstuff availability and economics.

Clonal Evaluation and Genetic Divergence Studies in Mulberry Genotypes

Aims: This study aims to evaluate the wood quality and leaf quality traits of selected mulberry clones and assess the genetic divergence among them, providing valuable insights for the development of superior genotypes with enhanced economic value for the sericulture and agroforestry sectors.
 Study design: Twenty-one genetic resources of mulberry were collected from various regions in India and evaluated through clonal test in a Row Column Design to assess growth attributes and genetic divergence.
 Place and Duration of Study: The study was conducted in India, and the systematic progeny test and clonal evaluation were carried out in Forest College and Research Institute, Mettupalayam during 2018-2022.
 Methodology: The selected clones were evaluated for growth attributes such as plant height, diameter at breast height (DBH), volume, number of branches, leaf length, leaf width, petiole length, number of leaves, and leaf area. Genetic divergence was estimated using D2 statistics, and clustering of clones was performed using the 'GENRES' statistical package.
 Results: The study identified several clones with significantly higher growth attributes, highlighting their potential for selection in breeding and cultivation programs. Variability and heritability studies indicated that volume exhibited the highest heritability, suggesting strong genetic control and potential for improvement.
 Conclusion: Clones MI-0718, MI-0807, and MI-0845 showed superior growth performance and genetic divergence, indicating their suitability for further breeding and improvement programs. The study provides insights into the genetic variability of mulberry clones and emphasizes selecting superior clones for enhancing wood volume and overall productivity.

Construction of structurally incomplete row-column designs for comparing test treatments with control treatments

Construction of structurally incomplete row-column designs for comparing test treatments with control treatments

Registration of New Bread Wheat Variety (Biftu) for Low to Mid-Altitude Wheat-Producing Areas of Ethiopia

In Ethiopia, wheat (Triticum Sp.) is cultivated on a total area of 2.1 million (1.7 million ha for rain fed and 0.4 million ha for irrigated areas) hectares of land; the annual total production is 6.7 million tons of grains during 2022. Recently released commercial wheat varieties have higher genetic gain for economic trait than the older varieties. Forty-seven advanced genotypes and three standard checks were tested across different environments from 2019 to 2020 in Ethiopia. The genotypes were arranged in row column design with three replications. Analysis of variance and mean separation were carried out to differentiate the significance difference in genotypes. The results revealed that the advanced genotypes viz. BW173528 and EBW17-365 had significantly higher for grain yield than the other genotypes. In addition, BW173528 has better diseases resistance than the checks; Deka, Kakaba and Kingbird. Therefore, this genotype was tested and verified on farmers’ fields in 2021. Based on its performance and good quality traits the advanced line BW173528 was released for production in low moisture stress areas of Ethiopia and named as: Biftu.

Spatial model selection and design evaluation in the Ethiopian sorghum breeding program

AbstractIn plant breeding field experiments, proper statistical design and analysis improve precision of genotype comparisons. The focus of this study was to compare the precision of different spatial techniques in estimating genotypic effects using sorghum [Sorghum bicolor (L.) Moench] breeding data from Ethiopia and to investigate alternative design strategies maintaining overall field layout of the current trials while modifying the blocking (replicate, rows, and columns) structures compared to the current practice. The current trials comprise both partially replicated and fully replicated row–column designs where the field layout has short rows and long columns. For model comparison, six partially replicated row–column trials and 10 fully replicated row–column trials of sorghum were used. Relative efficiency calculations for the designs indicate that in most of the trials, alpha designs with block sizes of five, six, 10 and 15, and the alternative row–column designs were more efficient than the current design practice. Moreover, overall model comparison showed that augmenting the baseline model by a two‐dimensional nonlinear spatial model plus nugget improves the precision, while the randomization‐based plus two‐dimensional linear variance model and the randomization based plus a two‐dimensional nonlinear spatial model are also good candidate models. If row and column coordinates are available for all plots, the post‐blocking approach used here can be used in any breeding program and crop to explore alternative design options.

Generating designs for comparative experiments with two blocking factors.

Often, comparative experiments involve a single treatment factor and two blocking factors, for example, augmented row-column, two-phase, and incomplete row-column experiments. These experiments are widely used in agriculture. Finding good designs for these experiments is a major challenge when the number of treatments is large and the blocking structure is complex. In this paper, we first propose a new search algorithm that is combined with efficient update formulae, so that optimal designs with two blocking factors can be found within a reasonable time. Second, we compare augmented row-column designs generated with our new method to those obtained from CycDesigN, DiGGer, and the OPTEX procedure of SAS in terms of computing times as well as the quality of solutions. Third, we illustrate our proposed approach with four applications. We show an example where our efficient update formulae work while existing update formulae cannot be applied, and we use our search framework to generate augmented row-column, two-phase, and incomplete row-column designs. We end the paper with a conclusion along with suggestions for potentialapplications.

Root system architecture analysis of sorghum genotypes and its effect on drought adaptation

Sorghum is a crucial crop in semi-arid regions because of its capacity to resume photosynthesis and physiological growth after being subjected to drought stress. Although it is one of the most resilient crops to drought stress, recurrent drought is affecting its productivity. It is thus of paramount importance to explore genes contributing to drought stress adaptation, thereby increasing the productivity of sorghum. A study was initiated to evaluate and determine the effect of root systems, particularly root angle traits, on drought stress adaptation and grain yield performance. A total of 428 sorghum genotypes from the Ethiopian breeding program were evaluated for their performance in three drought-stress environments. The experimental materials include stay-green, non-stay-green genotypes and released sorghum varieties. A row-column design with three replications was used for the field trials. For root system screenings a high throughput phenotyping platform were used and a row-column design with two replications applied for root trait analysis. The mean grain yield for non-stay green genotypes ranged from 1.63 to 3.1 tons/ha. However, for stay-green genotypes, it ranged from 2.4 to 2.9 tons per hectare. The analysis of the root system architecture showed highly significant variations among the genotypes. The root angle of non-stay-green genotypes ranged from 8.0 to 30.5°, while for stay-green sorghum genotypes it varied from 12.0 to 29.0°. At the same time, for improved varieties, it exhibited between 14.04 and 19.50°. The result of the principal component for stay-green genotypes was computed, and the largest variations were 52.7% and the least were 10.4%. The most contributing traits in dimension one were shoot dry weight and shoot fresh weight, followed by leaf width and shoot length. Positive and significant correlations were observed between leaf areas and shoot dry weight and leaf width and shoot dry weight at phenotypic and genotypic levels. Negative correlations were observed between root angle and leaf area. Root angle and root length traits had a negative phenotypic correlation (r = −0.018). In conclusion, in drought-stressed conditions, narrow root angle genotypes produced the highest grain production. Therefore, narrow root angle genotypes should be taken into account in sorghum breeding to boost sorghum gain yield in drought-stressed areas. Secondly, the association of the narrow root angle trait with grain yield revealed a connection between the two traits to maximize the productivity of sorghum, both for stay-green and non-stay-green sorghum genotypes. However, the productivity of narrow root angle genotypes was higher for stay-green gene introgressed sorghum genotypes. Finally, the negative correlation obtained between the root angle and grain yield traits for stay-green genotypes has justified the possibility of using the stay-green trait to select sorghum genotypes with narrow root angles.

Genetic diversity in Ethiopian sorghum germplasm for root system architecture and trait association

Sorghum productivity in arid and semi-arid regions of Africa is very low, mainly due to limited water availability. Roots are the primary conduit for plants to access moisture and nutrients. Root growth angle determines the direction of root elongation in the soil profile and is an important trait for adaptation to water-limited environments. Information on the extent of genetic variation in root system architecture (RSA) and its relationship with drought response is critical for improving the performance of the crop under drought stress. The objective of this study was to examine the degree of genetic variability for root and shoot traits in sorghum germplasm during the seedling stage. Two hundred and ninety-one sorghum germplasm adapted to different agroecologies of Ethiopia were phenotyped for root and shoot traits using a purpose-built root chamber in the greenhouse at Jimma University. The experiment was set up in a row-column design with three replicates. Significant genetic variation (P < 0.01) was observed for all traits examined except root hair number and shoot dry weight. Root angle varied from 9° to 21.3° with an average of 14.9° and showed moderate heritability of 44.38%. Root dry weight also exhibited moderate heritability (49.3%). Correlation and path coefficient analysis revealed that root angle (RA) was uncorrelated with other RSA traits. Cluster analysis using the RSA traits grouped the 291 genotypes into four different clusters. The first three principal components accounted for about 50% of the total variation. The results demonstrate that the Ethiopian sorghum germplasm exhibits large variation in RSA traits that can be harnessed in breeding programs to enhance sorghum productivity under drought stress.

Correction to: Optimality of Some Row–Column Designs

Correction to: Optimality of Some Row–Column Designs

Design of Agricultural Field Experiments Accounting for both Complex Blocking Structures and Network Effects

We propose a novel model-based approach for constructing optimal designs with complex blocking structures and network effects for application in agricultural field experiments. The potential interference among treatments applied to different plots is described via a network structure, defined via the adjacency matrix. We consider a field trial run at Rothamsted Research and provide a comparison of optimal designs under various different models, specifically new network designs and the commonly used designs in such situations. It is shown that when there is interference between treatments on neighboring plots, designs incorporating network effects to model this interference are at least as efficient as, and often more efficient than, randomized row–column designs. In general, the advantage of network designs is that we can construct the neighbor structure even for an irregular layout by means of a graph to address the particular characteristics of the experiment. As we demonstrate through the motivating example, failing to account for the network structure when designing the experiment can lead to imprecise estimates of the treatment parameters and invalid conclusions.Supplementary materials accompanying this paper appear online.

Small Youden Rectangles, Near Youden Rectangles, and Their Connections to Other Row-Column Designs

In this paper we first study $k \times n$ Youden rectangles of small orders. We have enumerated all Youden rectangles for a range of small parameter values, excluding the almost square cases where $k = n-1$, in a large scale computer search. In particular, we verify the previous counts for $(n,k) = (7,3), (7,4)$, and extend this to the cases $(11,5), (11,6), (13,4)$ and $(21,5)$. For small parameter values where no Youden rectangles exist, we also enumerate rectangles where the number of symbols common to two columns is always one of two possible values, differing by 1, which we call \emph{near Youden rectangles}. For all the designs we generate, we calculate the order of the autotopism group and investigate to which degree a certain transformation can yield other row-column designs, namely double arrays, triple arrays and sesqui arrays. Finally, we also investigate certain Latin rectangles with three possible pairwise intersection sizes for the columns and demonstrate that these can give rise to triple and sesqui arrays which cannot be obtained from Youden rectangles, using the transformation mentioned above.

Amino acid digestibility and metabolizable energy of soybean meal of different origins in cecectomized laying hens

This study investigated the variation in amino acid (AA) digestibility and MEn of 18 samples of solvent-extracted soybean meal (SBM; 6 European, 7 Brazilian, 2 Argentinian, 2 North American, 1 Indian) in cecectomized laying hens. The experimental diets contained either 300 g/kg of cornstarch or one of the SBM samples. Pelleted diets were fed to 10 hens in two 5×10 row-column designs so that 5 replicates were obtained from each diet during 5 periods. A regression approach and the difference method were used to determine AA digestibility and MEn, respectively. The variation in the digestibility of SBM differed among AA with ranges in digestibility of 6 to 12%-units for most AA. Among the first-limiting AA, the digestibility was 87 to 93%, 63 to 86%, 85 to 92%, 79 to 89%, and 84 to 95% for Met, Cys, Lys, Thr, and Val, respectively. The range of MEn for the SBM samples was 7.5 to 10.5 MJ/kg DM. Indicators of SBM quality (including trypsin inhibitor activity, KOH solubility, urease activity, and in vitro N solubility) and analyzed SBM constituents were significantly correlated (P ≤ 0.05) with AA digestibility or MEn only in a few cases. No differences were observed in AA digestibility and MEn between countries of origins, except low digestibility of some AA and MEn for the 2 Argentinian SBM samples. These results suggest that the precision of feed formulation benefits from considering the variations in AA digestibility and MEn. Often used indicators for SBM quality and analyzed constituents were not suitable to explain variations in AA digestibility and MEn, suggesting that AA digestibility and MEn are determined by other factors.

Correction to: ‘Optimal row-column designs’

Correction to: ‘Optimal row-column designs’

Optimality of Some Row–Column Designs

Optimality of Some Row–Column Designs

Advanced row-column designs for animal feed experiments

Inappropriate statistical designs may misinterpret results of animal feed experiments. Thus complete statistical designs can make animal feed research more appropriate and cost effective. Usually factorial row-column designs are used when the heterogeneity in the experimental material is in two directions and the experimenter is interested in studying the effect of two or more factors simultaneously. Attempts have been to develop the method of construction of balanced nested row column design under factorial setup. Factorial experiments are used in designs when two or more factors have same levels or different levels. The designs that are balanced symmetric factorials nested in blocks are called block designs with nested row-column balanced symmetric factorial experiments. These designs were constructed by using confounding through equation methods.Construction of confounded asymmetrical factorial experiments in row-column settings and efficiency factor of confounded effects was worked out. The design can be used in animal feed experiment with fewer resources by not compromising the test accuracy.

Research Note: Influence of monocalcium phosphate and phytase in the diet on phytate degradation in cecectomized laying hens

This study investigated the effects of phytase and monocalcium phosphate supplementation on the dephosphorylation of phytic acid [myo-inositol 1,2,3,4,5,6-hexakis (dihydrogen phosphate); InsP6] in cecectomized laying hens using total excreta collection. Four corn-soybean meal-rapeseed meal-based diets were mixed with or without 6 g of monocalcium phosphate/kg, with or without supplementation of 1,500 FTU phytase/kg, and had the same calcium concentration at 39 g/kg of feed. Each diet was tested in 5 replicates using a row-column design with 10 cecectomized laying hens in 2 periods. The hens received 120 g/d of feed while being housed individually in metabolism units, and total excreta were collected for a period of 4 d. The monocalcium phosphate × phytase interaction was not significant for InsP6 degradation (P = 0.054). Phytase increased InsP6 disappearance from 13% to 83% (P < 0.001), whereas monocalcium phosphate had no effect. Concentrations of most of the lower inositol phosphate isomers in excreta were higher when monocalcium phosphate was added to the diets. The concentration of Ins(1,2,5,6)P4 in excreta was the highest among the studied partially dephosphorylated inositol phosphates with phytase supplementation and was higher than in diets without phytase supplementation (P < 0.001). Supplementation with phytase increased myo-inositol concentration in excreta (P = 0.002), whereas monocalcium phosphate had no effect. Phosphorus utilization ranged from 4% to 18% and was not significantly affected by the treatments. These results suggest that phytase supplementation markedly increased InsP6 degradation in laying hens. The cecectomized laying hen assay may be suitable for studying the effects of phytase supplementation on phytate dephosphorylation under dietary conditions when performance and phosphorus excretion are unlikely to be affected.

Effect of dietary calcium concentration and exogenous phytase on inositol phosphate degradation, mineral digestibility, and gut microbiota in growing pigs.

Variations in the dietary Ca concentration may affect inositol phosphate (InsP) degradation, and thereby, P digestibility in pigs. This study assessed the effects of dietary Ca concentration and exogenous phytase on InsP degradation, nutrient digestion and retention, blood metabolites, and microbiota composition in growing pigs with ileal cannulation. In a completely randomized row-column design with four periods, eight ileal-cannulated barrows (initial body weight 27 kg) were fed four corn-soybean- and rapeseed meal-based diets containing 5.5 or 8.5 g Ca/kg dry matter (DM), with or without 1,500 FTU of an exogenous hybrid-6-phytase/kg diet. No mineral P was added and the P concentration in the feed was 4.8 g P/kg DM. Prececal InsP6 disappearance in pigs fed diets containing exogenous phytase was lower (P = 0.022) with additional Ca than without. Concentrations of InsP2-4 isomers and myo-inositol in the distal ileal digesta and prececal P digestibility were greater (P < 0.001) with exogenous phytase than without exogenous phytase. In feces, InsP6 disappearance was lower (P < 0.002) and concentration of InsP5 and InsP4 isomers was higher (P ≤ 0.031) with additional Ca compared to without additional Ca. The prececal amino acid digestibility, energy digestibility, and hindgut disappearance of energy did not differ. The Shannon diversity index of the microbiota in the distal ileal digesta and feces was similar among the diets but was lower in the distal ileal digesta than in the feces (P < 0.001). Permutation analysis of variance revealed no dietary differences between the bacterial groups within the ileal digesta and fecal samples (P > 0.05). In conclusion, additional Ca reduced the effect of exogenous phytase on prececal InsP6 degradation. Endogenous InsP degradation was impaired by additional Ca only in the hindgut but the abundance of bacterial genera in feces was not affected.

Performance Evaluation of Elite Durum Wheat Genotypes for Yield and Stem Rust Response

Durum wheat is one of the most important crops worldwide and Ethiopia is the major producer in sub-Saharan Africa (SSA). However, there is a huge gap between domestic production and demand in Ethiopia. Hence, getting high yielder with resistant for multiple races of rusts especially for stem rust became challenging. This could be due to limited availability of resistance to multiple stem rust races coupled with the rapid occurrence and spread of virulent races of stem rust. Hence, objective of this study is to identify high yielding and stem rust resistant genotypes and use them as parents in the breeding program and advance to national variety trial to select for wide adaptability. Sixty advanced genotypes were evaluated across three locations during 2020/21 cropping season. The trial was set up using row-column design in two replications. Data on grain yield, yield related traits and stem rust were collected. Stem rust was scored following the modified Cobb’s scale. Under high disease pressure the genotypes showed disease response and severity variations from RMR to S and from 5% to 100%, respectively indicating the presenece of variation for stem rust response. There were also genotypes which showed suceptable reaction and high grain yield and yield related traits. Hence, this may be due to minor gene resistance to stem rust. Generally, about 13 genotypes had good grian yield, thousand kernel weight and stem rust resistance. We can recommend these genotypes to test across country for their wide adaptability and as a parents for crossing.