Evaluating the performance of genomic selection on purebred population by incorporating crossbred data in pigs

Genomic selection(GS)has been widely used in livestock,which greatly accelerated the genetic progress of complex traits.The population size was one of the significant factors affecting the prediction accuracy,while it was limited by the purebred population.Compared to directly combining two uncorrelated purebred populations to extend the reference population size,it might be more meaningful to incorporate the correlated crossbreds into reference population for genomic prediction.In this study,we simulated purebred offspring(PAS and PBS)and crossbred offspring(CAB)base on real genotype data of two base purebred populations(PA and PB),to evaluate the performance of genomic selection on purebred while incorporating crossbred information.The results showed that selecting key crossbred individuals via maximizing the expected genetic relationship(REL)was better than the other methods(individuals closet or farthest to the purebred population,CP/FP)in term of the prediction accuracy.Furthermore,the prediction accuracy of reference populations combining PA and CAB was significantly better only based on PA,which was similar to combine PA and PAS.Moreover,the rank correlation between the multiple of the increased relationship(MIR)and reliability improvement was 0.60-0.70.But for individuals with low correlation(Cor(Pi,PA or B),the reliability improvement was significantly lower than other individuals.Our findings suggested that incorporating crossbred into purebred population could improve the performance of genetic prediction compared with using the purebred population only.The genetic relationship between purebred and crossbred population is a key factor determining the increased reliability while incorporating crossbred population in the genomic prediction on pure bred individuals.

Rule acquisition of three-way semi-concept lattices in formal decision context

Three-way concept analysis is an important tool for information processing,and rule acquisition is one of the research hotspots of three-way concept analysis.However,compared with three-way concept lattices,three-way semi-concept lattices have three-way operators with weaker constraints,which can generate more concepts.In this article,the problem of rule acquisition for three-way semi-concept lattices is discussed in general.The authors construct the finer relation of three-way semi-concept lattices,and propose a method of rule acquisition for three-way semi-concept lattices.The authors also discuss the set of decision rules and the relationships of decision rules among object-induced three-way semi-concept lattices,object-induced three-way concept lattices,classical concept lattices and semi-concept lattices.Finally,examples are provided to illustrate the validity of our conclusions.

Absolute copy number differences of Y chromosomal genes between crossbred (Bos taurus×Bos indicus) and Indicine bulls

Background: The Y chromosome in mammal is paternally inherited and harbors genes related to male fertility and spermatogenesis. The unique intra-chromosomal recombination pattern of Y chromosome and morphological difference of this chromosome between Bos taurus and Bos indicus make it an ideal model for studying structural variation, especially in crossbred(Bos taurus × Bos indicus) bulls. Copy Number Variation(CNV) is a type of genomic structural variation that gives information complementary to SNP data. The purpose of this study was to find out copy number differences of four Y chromosomal spermatogenesis-related candidate genes in genomic DNA of crossbred and purebred Indicine bulls. Result: Four Y chromosomal candidate genes of spermatogenesis namely, sex determining gene on Y chromosome(SRY), DEAD box polypeptide 3-Y chromosome(DDX3Y), Ubiquitin specific peptidase 9, Y-linked(USP9Y), testis-specific protein on Y chromosome(TSPY) were evaluated. Absolute copy numbers of Y chromosomal genes were determined by standard curve-based quantitative real time PCR. Copy numbers of SRY and TSPY genes per unit amount of genomic DNA are higher in crossbred than Indicine bulls. However, no difference was observed in DDX3Y and USP9Y gene copy numbers between two groups. Conclusion: The present study demonstrates that the structural organization of Y chromosomes differs between crossbred and Indicine bulls which are reproductively healthy as observed from analysis of semen attributes. The absolute copy numbers of SRY and TSPY genes in unit mass of genomic DNA of crossbred bulls are significantly higher than Indicine bulls. No alteration in absolute copies of DDX3Y and USP9Y gene was found between the genome of crossbred and Indicine bulls. This study suggests that the DDX3Y and USP9Y are likely to be single copy genes in the genome of crossbred and Indicine bulls and variation in Y chromosome length between crossbred and Indicine bulls may be due to the copy number variation of SRY gene and TSPY array.

Factors affectingin-vivo fertility of crossbred Egyptian - Italian buffalo semen

Objective:To assess the effect of region, season and year of insemination onin-vivo fertility of Italian-Egyptian crossbred buffalo semen.Methods: A total number of 4799 female buffaloes were inseminated by frozen semen with at least 50% post-thaw motility of Egyptian-Italian crossbred bulls in three localities in Delta, lower Egypt (El-Behira, El-Sharkia and Damietta) during the period of 2013, 2014 and 2015. The pregnancy rate after two months was evaluated during the four seasons.Results:The rate of pregnancy was significantly (P<0.0001) differ among the three localities. The effect of year of insemination on pregnancy rate was significantly higher during 2014 and 2015 than 2013 in El-Sharkia and El-Behira. But in Damietta, the rate of pregnancy was significantly higher in 2014 than 2013 and 2015. There were no significant differences among seasons in El-Behira and Damietta governorates but there was significant (P<0.05) differences in pregnancy rate in El-Sharkia. It was higher in summer, spring and autumn than in winter.Conclusions:Localities, year of insemination and season of the year have effects on fertility of crossbred Egyptian-Italian buffalo semen.

Trans-10,cis-12 conjugated linoleic acid reduces neutral lipid content and may affect cryotolerance of in vitro-produced crossbred bovine embryos

Background:Due to high neutral lipids accumulation in the cytoplasm,in vitro-produced embryos from Bos primigenius indicus and their crosses are more sensitive to chilling and cryopreservation than those from Bos primigenius taurus.The objective of the present study was to evaluate the effects of trans-10,cis-12 conjugated linoleic acid(CLA) on the development and cryotolerance of crossbred Bos primigenius taurus x Bos primigenius indicus embryos produced in vitro,and cultured in the presence of fetal calf serum.Bovine zygotes(n = 1,692)were randomly assigned to one of the following treatment groups:1) Control,zygotes cultured in Charles Rosenkrans 2 amino acid(CR2aa) medium(n = 815) or 2) CLA,zygotes cultured in CR2 aa medium supplemented with 100 μmol/L of trans-10,cis-12 CLA(n =877).Embryo development(cleavage and blastocyst rates evaluated at days 3 and 8 of culture,respectively),lipid content at morula stage(day 5) and blastocyst cryotolerance(re-expansion and hatching rates,evaluated 24 and 72 h post-thawing,respectively) were compared between groups.Additionally,selected mRNA transcripts were measured by Real-Time PCR in blastocyst stage.Results:The CLA treatment had no effect on cleavage and blastocyst rates,or on mRNA levels for genes related to cellular stress and apoptosis.On the other hand,abundance of mRNA for the 1-acylglycerol-3-phosphate0-acyltransferase-encoding gene(AGPAT),which is involved in triglycerides synthesis,and consequently neutral lipid content,were reduced by CLA treatment.A significant increase was observed in the re-expansion rate of embryos cultured with trans-10,cis-12 CLA when compared to control(56.3 vs.34.4%,respectively,P = 0.002).However,this difference was not observed in the hatching rate(16.5 vs.14.0%,respectively,P=0.62).Conclusions:The supplementation with trans-10,ds-12 CLA isomer in culture medium reduced the lipid content of in vitro produced bovine embryos by reducing the gene expression of 1-acylglycerol 3-phosphate 0-acyltransferase(AGPAT) enzyme.However,a possible improvement in embryo cryotolerance in response to CLA,as suggested by increased blastocyst re-expansion rate,was not confirmed by hatching rates.

Three-Way Behavioral Decision Making With Hesitant Fuzzy Information Systems:Survey and Challenges

Three-way decision(T-WD)theory is about thinking,problem solving,and computing in threes.Behavioral decision making(BDM)focuses on effective,cognitive,and social processes employed by humans for choosing the optimal object,of which prospect theory and regret theory are two widely used tools.The hesitant fuzzy set(HFS)captures a series of uncertainties when it is difficult to specify precise fuzzy membership grades.Guided by the principles of three-way decisions as thinking in threes and integrating these three topics together,this paper reviews and examines advances in three-way behavioral decision making(TW-BDM)with hesitant fuzzy information systems(HFIS)from the perspective of the past,present,and future.First,we provide a brief historical account of the three topics and present basic formulations.Second,we summarize the latest development trends and examine a number of basic issues,such as one-sidedness of reference points and subjective randomness for result values,and then report the results of a comparative analysis of existing methods.Finally,we point out key challenges and future research directions.

Meat Production Performances of Geese in Different Crossbred Combinations

[Objective] To study the meat production performance of geese in different crossbred combination, and provide a reference for cultivating new multiplication strains of meat geese. [Method] A total of five goose breeds including Taihu goose (T), Wulong goose (WL), Wanxi white goose (WX), Sichuan white goose (SC) and Sanhua goose (SH) were used as research objects, and eight crossbred combinations were designed. The body measurements, slaughter performance, conventional meat quality and muscle composition of 90-day-old geese in eight crossbred combinations were determined and comparatively analyzed. [Result] All the body measurement indexes except thurl width of WXSC combination were the biggest in the eight crossbred combinations. Contrarily, the body measurement indexes of SHSC combination, including average body weight, body slope length, breast depth, breast width, shank length, neck length and half-diving depth were the lowest in the eight crossbred combinations. The live weight, slaughter weight and abdomen fat weight of WXSC combinations ware 3 291.36, 2 956.46 and 77.84 g, respectively, which were the biggest in eight crossbred combinations. The slaughter rate of SHWL combinations was 92.96%, and more than other crossbred combinations. The shear force of SHT and WXWL combinations were the lowest (3.09 kg) and the highest (3.78 kg), respectively. The water holding capacities of SCWL and WXSC combinations were the highest (66.46%) and the lowest (61.48%), respectively. The percentage of moisture content of SHWL and SCT combinations were the highest (73.05%) and the lowest (66.77%), respectively. The crude protein content of SHT and SHWL combinations were the highest (23.32%) and the lowest (21.94%), respectively. The percentage of crude fat content of SHT and SCWL combinations were the highest (3.06%) and the lowest (1.67%), respectively. [Conclusion] The growth rate of WXSC combination is the fastest, and the meat performance of SHT combination is the best.

蒸汽压片玉米对肉牛生长性能、屠宰性能和肉品质的影响

为了研究蒸汽压片玉米对肉牛生长性能、屠宰性能和肉品质的影响,试验拟选用40头体重(224.05±14.56)kg的西门塔尔杂交肉牛,随机分为4组,每组5个重复,每个重复2头肉牛。对照组饲粮中添加粉碎玉米,试验Ⅰ组~Ⅲ组分别用33%、66%、100%的蒸汽压片玉米替代粉碎玉米。预试期7 d,正式试验期120 d。结果显示,试验Ⅱ组和试验Ⅲ组末重比对照组分别提高了6.27%(P<0.05)和10.64%(P<0.01),试验Ⅰ组~Ⅲ组总增重比对照组分别提高了7.56%(P<0.05)、21.29%(P<0.01)和33.45%(P<0.01),试验Ⅰ组~Ⅲ组宰前活重比对照组分别提高了2.64%(P<0.05)、6.59%(P<0.01)和10.25%(P<0.01),试验Ⅱ组和Ⅲ组料重比极显著低于对照组(P<0.01)。试验Ⅱ组和Ⅲ组胴体重、净肉重均极显著高于对照组(P<0.01)。试验Ⅱ组和Ⅲ组牛肉中粗蛋白的含量极显著高于对照组(P<0.01),试验Ⅲ组粗脂肪显著高于对照组(P<0.05),试验Ⅲ组的pH_(45 min)值和失水率显著低于对照组(P<0.05)。试验Ⅰ组~Ⅲ组养殖效益比对照组分别提高了15.36%、48.04%和77.98%。研究表明,用蒸汽压片玉米替代肉牛饲粮中普通粉碎玉米可以提高西门塔尔杂交肉牛的生长性能和屠宰性能,改善牛肉品质,提高了肉牛养殖的经济效益,在饲粮中使用100%的蒸气压片玉米替代普通粉碎玉米效果较好。

发酵玉米芯对肉牛生长性能、瘤胃发酵参数及菌群的影响

本试验旨在研究发酵玉米芯对肉牛生长性能、瘤胃发酵参数及菌群的影响。选用60头体况良好、13月龄左右、体重[(395±32)kg]相近的西门塔尔杂交牛,随机分为3组,每组20个重复,每个重复1头牛。对照组饲喂不添加发酵玉米芯的全混合日粮,试验1组饲喂添加10%发酵玉米芯的全混合日粮,试验2组饲喂添加20%发酵玉米芯的全混合日粮,预试期7 d,正试期93 d。结果显示:1)试验1、2组的平均日采食量和平均日增重显著高于对照组(P<0.05),料重比显著低于对照组(P<0.05)。2)试验1、2组瘤胃液氨态氮(NH_(3)-N)浓度与对照组相比均显著升高(P<0.05),试验2组瘤胃液微生物蛋白(MCP)浓度与对照组和试验1组相比显著提高(P<0.05);各组瘤胃液pH无显著差异(P>0.05);2个试验组瘤胃液总挥发性脂肪酸(TVFA)浓度均显著低于对照组(P<0.05),但乙酸、丙酸、戊酸摩尔百分比及乙酸/丙酸值没有显著变化(P>0.05);2个试验组瘤胃液丁酸摩尔百分比显著低于对照组(P<0.05),而异丁酸和异戊酸摩尔百分比均显著高于对照组(P<0.05)。3)门水平上,拟杆菌门(Bacteroidetes)和厚壁菌门(Firmicutes)为3组肉牛瘤胃菌群中的主要优势菌门。试验1、2组Bacteroidetes的相对丰度显著高于对照组(P<0.05),试验2组Firmicutes的相对丰度显著低于对照组(P<0.05)。属水平上,3组的主要优势菌属均为普雷沃氏菌属(Prevotella)、拟杆菌目未鉴定属(unidentified Bacteroidales)。试验1、2组普雷沃氏菌科未鉴定属(unidentified Prevotellaceae)的相对丰度显著高于对照组(P<0.05),同时试验1组还显著高于试验2组(P<0.05);对照组Ruminococcus和甲烷短杆菌属(Methanobrevibacter)的相对丰度显著高于试验1、2组(P<0.05);试验2组的梭菌目未分类属(unclassified Clostridiales)和毛螺菌科未鉴定属(unidentified Lachnospiraceae)的相对丰度显著低于对照组和试验1组(P<0.05)。综上所述,饲粮中添加发酵玉米芯能够提高肉牛的生长性能,改善瘤胃发酵环境,同时影响瘤胃菌群在门水平和属水平上的组成。

糜草黄贮替代全株玉米青贮饲喂西门塔尔杂交牛效果的研究

为探究糜草黄贮替代全株玉米青贮饲喂西门塔尔杂交牛对其生长性能、血清生化指标、抗氧化指标和经济效益的影响,选用西门塔尔杂交公牛36头,随机分为4组,每组9头。对照组试验牛饲喂全混合日粮,试验组以10%、30%和50%糜草黄贮替代全株玉米青贮。试验期为75 d。结果表明:(1)各组试验牛初始体重、终末体重、平均日增重和料重比差异不显著(P>0.05)。(2)试验组西杂牛血清尿素氮含量均显著低于对照组(P<0.05);10%和50%糜草黄贮替代组谷胱甘肽-过氧化物酶活性比对照组显著高10.93%和11.68%(P<0.05);50%糜草黄贮替代组血清丙二醛含量比对照组显著低11.18%(P<0.05)。(3)在60 d育肥期内,糜草黄贮替代组中30%替代组的总利润最高,分别比10%和50%替代组高72元和138元。综上所述,日粮中用糜草黄贮替代全株玉米青贮不影响西门塔尔杂交牛生长性能和血清生化指标,替代50%可提高西门塔尔杂交牛机体抗氧化能力,替代30%的育肥效益最高。

南瓜籽壳对不同生长阶段西杂肉牛生长性能、血清生化和免疫指标及激素水平的影响

[目的]研究日粮中添加南瓜籽壳对不同生长阶段西杂肉牛生长性能、血清生化和免疫指标及激素水平的影响。[方法]选取体况良好的西门塔尔杂交公牛共40头,按照体重分为5组,分别为试验1组(300 kg左右)、试验2组(400 kg左右)、试验3组(500 kg左右)、试验4组(600 kg左右)和试验5组(700 kg左右),每组8头,分栏饲养,基础日粮中均添加10%的南瓜籽壳。试验期为90 d,预试期20 d,正试期70 d。记录各组肉牛试验期间体重及采食情况,计算平均日增重、平均日采食量和平均料重比;试验结束时采集血液样本制备血清,测定血清生化指标、免疫指标及激素水平。[结果]随着肉牛体重的增加,日采食量逐渐增加,试验4组和5组平均日采食量显著(P<0.05)高于其他组;试验1组平均料重比最低,显著(P<0.05)低于其他组。试验4组血清总蛋白(TP)、尿素氮(BUN)含量显著(P<0.05)高于试验1组、3组。试验2组血清免疫球蛋白M(IgM)含量显著(P<0.05)高于其他组。试验1组血清皮质醇(COR)水平显著(P<0.05)高于试验3组、4组、5组,试验5组血清降钙素(CT)水平显著(P<0.05)高于其他各组,试验4组、5组C反应蛋白水平显著(P<0.05)高于试验1组。[结论]西杂肉牛日粮中添加南瓜籽壳,可增加采食量,提高机体蛋白质利用率,对增强动物免疫力具有一定作用,可作为一种粗饲料资源进行开发利用。

Angle estimation for bistatic MIMO radar with unknown mutual coupling based on three-way compressive sensing

The problem of angle estimation for bistatic multipleinput multiple-output radar in the present of unknown mutual coupling(MC) is investigated, and a three-way compressive sensing(TWCS) estimation algorithm is developed. To exploit the inherent multi-dimensional structure of received data, a trilinear tensor model is firstly formulated. Then the de-coupling operation is followed. Thereafter, the high-order singular value decomposition is applied to compress the high dimensional tensor to a much smaller one. The estimation of the compressed direction matrices are linked to the compressed trilinear model, and finally two overcomplete dictionaries are constructed for angle estimation. Also,Cramer-Rao bounds for angle and MC estimation are derived. The proposed TWCS algorithm is effective from the perspective of estimation accuracy as well as the computational complexity, and it can achieve automatically paired angle estimation. Simulation results show that the proposed method has much better estimation accuracy than the existing algorithms in the low signal-to-noise ratio scenario, and its estimation performance is very close to the parallel factor analysis(PARAFAC) algorithm at the high SNR regions.

Stress and Fracture Strength Analysis for Three-Way Pipes

Three-way pipes, T and Y pipes, are very important connecting components in pipeline systems, their strength are related to the safety of pipelines. In the case that crack is not detected in the three-way pipe, ANSYS finite element program version 5.6 is applied to study the stress distribution of the three-way pipe and to obtain the optimum fillet radius in the crotch region of the two pipes. The reasonable intersection angle of the two pipes is also obtained. In the case that a surface crack is detected in the three-way pipe, the maximum stress intensity factor (SIF) near the front of the surface crack is studied.

An adaptive dwell time scheduling model for phased array radar based on three-way decision

Real-time resource allocation is crucial for phased array radar to undertake multi-task with limited resources,such as the situation of multi-target tracking,in which targets need to be prioritized so that resources can be allocated accordingly and effectively.A three-way decision-based model is proposed for adaptive scheduling of phased radar dwell time.Using the model,the threat posed by a target is measured by an evaluation function,and therefore,a target is assigned to one of the three possible decision regions,i.e.,positive region,negative region,and boundary region.A different region has a various priority in terms of resource demand,and as such,a different radar resource allocation decision is applied to each region to satisfy different tracking accuracies of multi-target.In addition,the dwell time scheduling model can be further optimized by implementing a strategy for determining a proper threshold of three-way decision making to optimize the thresholds adaptively in real-time.The advantages and the performance of the proposed model have been verified by experimental simulations with comparison to the traditional twoway decision model and the three-way decision model without threshold optimization.The experiential results demonstrate that the performance of the proposed model has a certain advantage in detecting high threat targets.

Energy Optimization Oriented Three-Way Clustering Algorithm for Cloud Tasks

Cloud computing has developed as an important information technology paradigm which can provide on-demand services. Meanwhile,its energy consumption problem has attracted a grow-ing attention both from academic and industrial communities. In this paper,from the perspective of cloud tasks,the relationship between cloud tasks and cloud platform energy consumption is established and analyzed on the basis of the multidimensional attributes of cloud tasks. Furthermore,a three-way clustering algorithm of cloud tasks is proposed for saving energy. In the algorithm,f irst,t he cloud tasks are classified into three categories according to the content properties of the cloud tasks and resources respectively. Next,cloud tasks and cloud resources are clustered according to their computation characteristics( e. g. computation-intensive,data-intensive). Subsequently,greedy scheduling is performed. The simulation results showthat the proposed algorithm can significantly reduce the energy cost and improve resources utilization,compared with the general greedy scheduling algorithm.

Influences of (Ce-Zr-La-Pr)O Contents on Three-Way Catalyst Performances

A series of catalysts with (Ce-Zr-La-Pr)O contents range from 0 to 50% in coating and single-palladium loads on substrates were prepared to study effects of (Ce-Zr-La-Pr)O contents on catalytic activities and durability by contrasting the characteristics of light-off, A/F and catalytic conversions of the fresh catalysts with that of the aged catalysts. The results show that (Ce-Zr-La-Pr)O can enhance the catalysts light-off characteristics, widen A/F windows and increase catalytic conversions at a certain extent through optimizing physical structural and chemical property of the mixed coating. However, (Ce-Zr-La-Pr)O contents influence greatly on the catalysts activities and durability, and the catalysts with contents ranging from 10% to 30% exhibited better integrative properties in all samples, and 10% was the optical content to make the catalyst performance highest in this thesis. It is indicated that an suitable content of (Ce-Zr-La-Pr)O plays an important role in assisting catalysis, enhancing durability and increasing oxygen storage capability.

Regulated and Speciated Hydrocarbon Emissions from a Dual Fuel Light Duty Vehicle with and Without a Three-Way Catalyst

The regulated pollutants (CO,HC and NOx) and unregulated pollutants (volatile organic compounds and carbonyl compounds),emitted from a dual fuel vehicle fueled with gasoline and E10 fuel,are measured under a transient cycle and steady modes.The impacts of a three-way catalyst (TWC) are investigated for the two types of fuels.The measured results show that NOx and acetaldehyde emitted from the E10-fueled car are much more than that from the gasoline-fueled car under the same modes.On the basis of maximum incremental reactivity (MIR) factors and emissions of organic gases,the ozone specific reactivity of the tailpipe gases are evaluated.

INVESTIGATION ON THE DYNAMIC RESPONSE PERFORMANCE OF A NOVEL THREE-WAY SOLENOID VALVE

Objective A novel high-speed three-way solenoid valve is developed, which is used for the common-rail injection system equipped on DME powered engine. In order to improve the dynamic response performance of the three-way solenoid. Methods Experimental studies have been conducted to investigate the effects of spool stroke, drive voltage, negative demagnetizing pulse and two drive schemes on the dynamic response performance of the three-way solenoid valve. Results The results show that the dynamic response performance of the three-way solenoid valve can be remarkably improved by shortening the spool stroke and increasing the drive voltage. Simultaneously, the difference between the response time of closing valve and that of opening valve decreases. At each different drive voltage, there exists an optimal negative demagnetizing pulse corresponding to the same positive exciting pulse. At this optimal pulse, the dynamic response performance of the three-way solenoid valve is the best. In addition, the high drive voltage can lead to the smaller optimal negative demagnetizing pulse. It is also indicated from the experiments that the dynamic response performance of the three-way solenoid valve is better when the NO.1 drive scheme is adopted. The lower drive voltage results in the larger difference between the dynamic response performances for the two drive schemes. Conclusion The dynamic response performance of a novel three-way solenoid valve is good.

Anti-Robinson Structures for Analyzing Three-Way Two-Mode Proximity Data

Multiple discrete (non-spatial) and continuous (spatial) structures can be fitted to a proximity matrix to increase the information extracted about the relations among the row and column objects vis-à-vis a representation featuring only a single structure. However, using multiple discrete and continuous structures often leads to ambiguous results that make it difficult to determine the most faithful representation of the proximity matrix in question. We propose to resolve this dilemma by using a nonmetric analogue of spectral matrix decomposition, namely, the decomposition of the proximity matrix into a sum of equally-sized matrices, restricted only to display an order-constrained patterning, the anti-Robinson (AR) form. Each AR matrix captures a unique amount of the total variability of the original data. As our ultimate goal, we seek to extract a small number of matrices in AR form such that their sum allows for a parsimonious, but faithful reconstruction of the total variability among the original proximity entries. Subsequently, the AR matrices are treated as separate proximity matrices. Their specific patterning lends them immediately to the representation by a single (discrete non-spatial) ultrametric cluster dendrogram and a single (continuous spatial) unidimensional scale. Because both models refer to the same data base and involve the same number of parameters, estimated through least-squares, a direct comparison of their differential fit is legitimate. Thus, one can readily determine whether the amount of variability associated which each AR matrix is most faithfully represented by a discrete or a continuous structure, and which model provides in sum the most appropriate representation of the original proximity matrix. We propose an extension of the order-constrained anti-Robinson decomposition of square-symmetric proximity matrices to the analysis of individual differences of three-way data, with the third way representing individual data sources. An application to judgments of schematic face stimuli illustrates the method.