Different Number Of Replicates Research Articles

Dividing out quantification uncertainty allows efficient assessment of differential transcript expression with edgeR.

Differential expression analysis of RNA-seq is one of the most commonly performed bioinformatics analyses. Transcript-level quantifications are inherently more uncertain than gene-level read counts because of ambiguous assignment of sequence reads to transcripts. While sequence reads can usually be assigned unambiguously to a gene, reads are very often compatible with multiple transcripts for that gene, particularly for genes with many isoforms. Software tools designed for gene-level differential expression do not perform optimally on transcript counts because the read-to-transcript ambiguity (RTA) disrupts the mean-variance relationship normally observed for gene level RNA-seq data and interferes with the efficiency of the empirical Bayes dispersion estimation procedures. The pseudoaligners kallisto and Salmon provide bootstrap samples from which quantification uncertainty can be assessed. We show that the overdispersion arising from RTA can be elegantly estimated by fitting a quasi-Poisson model to the bootstrap counts for each transcript. The technical overdispersion arising from RTA can then be divided out of the transcript counts, leading to scaled counts that can be input for analysis by established gene-level software tools with full statistical efficiency. Comprehensive simulations and test data show that an edgeR analysis of the scaled counts is more powerful and efficient than previous differential transcript expression pipelines while providing correct control of the false discovery rate. Simulations explore a wide range of scenarios including the effects of paired vs single-end reads, different read lengths and different numbers of replicates.

Optimized number of suction cups required to predict annual nitrate leaching under varying conditions in Denmark

Nitrate concentrations in soil water leaving the root zone measured by suction cups combined with water transport modeling is a commonly used practice in Denmark for calculating nitrate leaching. Two suction cups installed in one plot giving one water sample and replicated four times, (eight total suction cups) to reduce variability between samples. For practical reasons, it would be beneficial to minimize the number of suction cups used yet maintain reliable predictions. To assess the variability in reducing suction replicates, this study analyzed data from five research sites across Denmark representing annual field nitrate leaching predictions for different combinations of soil, weather conditions, crops, N-fertilizer rates, and winter soil cover, covering a total of 173 annual nitrate leaching experiments. The analysis was conducted having different nitrate leaching predictions using different numbers of replicates of suction cup measurements. Linear regression was used to identify the different influences of leaching year (hydrological year), N rate applied, soil characteristics, and crop sequence on nitrate leaching. The analyses were set up on three 2-yr and two 3-yr field experiments in five different sites. Crop effects showed that cereals and winter cover sown in autumn 2017 had significantly more nitrate leaching than in 2015 and 2016 leaching years due to high precipitation rates in the autumn. Furthermore, decreasing the number of suction cup replicates from four (eight total) to three replicates (six total) did not have a significant effect on nitrate leaching prediction. In contrast, decreasing replicates from four to two (four total) and one (two total) replicates did show a significant difference. Therefore, using three replicates is a viable solution for future sampling strategies and a good trade-off between costs and accuracy.

Rearrangement of incomplete multi-omics datasets combined with ComDim for evaluating replicate cross-platform variability and batch influence

Multi-omics studies can highlight the interrelationships among data across different layers of biological information. However, methods for the unsupervised analysis of multi-block data do not take the individual variability across batches into account and cannot deal with omics datasets when they present different numbers of replicates. We have explored three different data arrangement strategies to tackle these limitations. Several multi-block methods can be used to decipher the common variations across blocks and to determine the contribution of each block to each common component. In this study the ComDim method was used to compare these rearrangement strategies for three multi-omics datasets. We found that arranging the data using the ‘replicate by blocks’ strategy, where each block comprises data from only one replicate independently of its data type, provided the most insightful results. ComDim allowed the evaluation of the variability across the replicate blocks, confirming the existence of batch effects in some of the studies. Moreover, since the contributions of these batch effects were separated from the other contributions, the coordinated biological responses common across the different blocks was characterized for each data type.

Have your cake and eat it too: PLSe2 = ML + PLS

PLSe1 and PLSe2 methods were developed in 2013. While the performance of PLSe1 under normality and non-normality conditions has been confirmed, the performance of PLSe2, proposed to provide an avenue for the resurrection of PLS as a fully justified statistical methodology, has not yet been verified under non-normality condition. For this reason, our study aims at testing the performance of PLSe2 with non-normal data based on a Monte Carlo simulation using a simple and a complex model. In addition, it aims at providing a step-by-step visual guideline on how to apply this method in estimating a simple mediation model using EQS 6.4. The results of the Monte Carlo simulations across different numbers of replications and sample sizes provided substantial support for the performance of PLSe2 under non-normality conditions since the produced estimates were unbiased and virtually identical to the parameters resulted from the traditional ML estimation. In addition, we provided evidence about the suitability of different robust test statistics for the purpose of model evaluation based on our simulation results. Regarding the empirical example, we estimated a mediation model using ML, PLSe2, and PLSc estimators, compared the results across these methods, and provided further support for our PLSe2 and ML results through running a resampling bootstrap simulation. Overall, while we empirically validated the PLSe2 method using Monte Carlo simulations, our findings suggest that PLSe2 has the advantages of both ML and PLS and performs well under non-normality (and normality) conditions, thereby suggesting it as the methodology of choice for model specification, estimation, and evaluation in social sciences empirical studies.

Unravelling heterogeneity of soft bottom communities in littoral zone using cluster analysis: Methodical recommendations

Study of spatial-temporal heterogeneity of the marine benthos is often done using the classification methods, cluster analysis in particular. To date, numerous procedures for determining the number of groups, present in a data set, have been proposed. As a rule, these methods are based on averaged characteristics of the structure of benthic communities, not taking into account the variability of biota abundance or biomass among individual samples. But the number of replicates can strongly affect similarity measures, especially ones, that have often been favored in field studies. The main aim of the present research was to study the effect of different number of replicates on the results of cluster analysis of the benthic community structures. Objects of investigations were the typical soft-bottom associations in the intertidal zone of the White Sea, occupying 9 locations and studied since 2008. The repeated comparisons of community structures described by different number of replicates (10 to 1) in each location were performed. The study showed that the weaker the differences between compared communities, the greater amount of samples were needed to obtain a reliable result. When comparing community structures from different locations at the same year as few as 5 samples were sufficient to obtain relatively reliable community descriptions. However, if the task was analysis of long-term changes in the community structure in the same site, the number of samples should be increased to 11. The reliability of the cluster analysis results depended on 1) similarity level, at which all stations merged into a single group, 2) similarity level, at which clusters were identified, and 3) ratio of these similarity levels.

Choosing sample sizes for various blood parameters of broiler chickens with normal and non-normal observations.

Experimental power is a measure of the ability of an experiment to detect differences between treatment means. Researchers design experiments and then calculate the probability that differences are simply due to chance, the null hypothesis. The objective of the analyses reported here was to determine the appropriate number of samples to demonstrate significant differences of various magnitudes from broiler chicken blood constituents. Over 800 samples were taken for a study of the effects of sample storage time, serum vs. plasma, light intensity, and fed vs. fasted birds on blood cholesterol, triglycerides, uric acid, glucose, total protein (TP), albumin, globulin, alanine aminotransferase (ALT), aspartate aminotransferase, gammaGT, creatinine, alkaline phosphatase, Ca and P. Various transformations increased the QQ plot R2 values from 0.000 to 0.149 or 0.00 to 17.62%. Most of the QQ plot R2 values were at or above 0.90. The 1/x2 transformation of blood P data showed the biggest increase in QQ plot R2 (0.846 to 0.995). The different standard deviations and coefficients of variation (CVs) found for each variable resulted in widely different numbers of replicates needed to detect differences in 2 treatment means. The extremes were glucose with a CV of 6.9% and ALT with a CV of 39.7%. For glucose, 15 replicates are needed to find a 10% difference in 97% of experiments; for ALT, 15 replicates would detect a 50% difference 91% of the time. The use of parameters such as cholesterol, glucose, TP, albumin, and globulin showed low CVs, indicating they may be considered as stable parameters. The lower CVs make it possible to find differences with a smaller number of replicates used in studies. As reported, the phosphorus values did not have a normal distribution of the data, so a transformation of these data could be an alternative to better discuss the results found.

Development of New LSD Formula when Numbers of Observations Are Unequal

In the case of comparison between samples with unequal replications [n1 # n2 # n3 # ... # nk], the statistician should use LSD (Least Significant Difference) many times to achieve these comparisons, this method consumes more time and effort. The purpose of this research is to find out a new method to do easy and reliable comparison between population means when the experiment or data involving different numbers of replications. In order to do this, a new formula was designed; the aim of this new formula is to develop the multiple comparisons into one step instead of doing it with many steps that consume more effort and time. In this work, the researcher used the mean of the replication number in the LDS formula instead of doing the calculation many times for each two means. The results of this study found that the new formula give similar results for multiple comparisons with minimal effort. It was concluded that the new formula (named Al-fahham’s Formula) achieves the same results with less time and efforts. It was recommended that Al-fahham’s Formula can be approved in the statistical textbooks and procedures.

Methodical recommendations for the description of soft bottom communities in the littoral zone

During the study of benthic communities, the choice of a sampling programme is often not given enough attention. Common practice consists of estimating the number of replicates through standard error or coefficient of variation of individual species abundance, but when the object of the study is the whole community, this method is not relevant. We considered the effect of a different number of replicates on the result of community differentiation using different approaches, in particular cluster analysis. Previous studies have shown that five samples did not guarantee a reliable assessment of heterogeneity of benthic biocenosis for long-term monitoring at three control sites in the waters of the Keret archipelago (the White Sea). In 2008 the number of replicates per station was increased to 10. It was shown that the communities that were studied should be identified as the typical biocenosis in the White Sea littoral zone. We estimated the number of replicates that are sufficient to achieve biocenosis differentiation. We therefore carried out repeated macrobenthos comparisons based on a different numbers of samples (10 to 1). It followed that there are differences in the number of replicates required for different approaches for the description of a macrobenthic biocenosis: when community descriptions are based only on dominant taxa, three replicates are sufficient; classification of the data on species composition required five or more samples; for species biomass, four or more samples; and for species abundance, six or more samples.

Assessing the accuracy of the “two-point” dilution technique

The dilution technique is the most commonly used method to measure microzooplankton grazing rates in the ocean. A simplified version of the dilution technique termed the “two-point” dilution technique, has been increasingly used to reduce workload and to increase spatiotemporal coverage. Several variants of the “two-point” dilution technique have been used in the literature. The objective of this study is to assess which one is the best. Three versions of “two-point” dilution experiments with different number of replicates were simulated from a dataset of full dilution series experiments, with the rate estimates from the full dilution series experiments being treated as “true” values. We find that the approach of setting up a highly diluted bottle (the fraction of undiluted seawater ≤ 20%) and treating the net growth rate of phytoplankton of this bottle as the instantaneous growth rate yields the best result, for both experiments with linear and nonlinear behavior. With this approach, significant overestimates or underestimates occurred in only one-fourth of the experiments even if no replicates were set up. Setting up duplicates or more for each dilution level can give more reliable results, very close to those from full dilution series experiments.

Computer-based management of interactive data transformation systems using Taguchi’s robust parameter design

The Taguchi design method, which uses orthogonal arrays to study the quality of characteristics using only a small number of experiments, produces outstanding outcomes when applied to industrial processes. However, nearly all industrial data is concealed via interactive data transformations, for which Box–Cox, arcsine and logit with computer-based management are proposed. The efficiency of each transformation based on the mean and signal-to-noise ratio was investigated for a different number of replicates and noise levels on the response. A total of four simulated scenarios each with 100 noisy data sets were used to examine the system performance. The numerical results indicate that Box–Cox and arcsine transformations are superior to logit transformations. Moreover, the analytical outcomes from the interactive ranges of transformation parameters via the hybridisation of variable neighbourhood search and particle swarm optimisation methods were a close fit to the natural data. In an actual computer-based application of the interactive data transformation system for a ball swaging process, Box–Cox and arcsine transformations followed the simulated numerical data and provided much more appropriate outcomes closer to the natural data. The target of a gram load control was then met via process parameters with higher levels of ranking results of contribution ratio, as expected from the natural data.

Ex-Ante Determination of the Capacity of Field Tests to Detect Effects of Genetically Modified Corn on Nontarget Arthropods

Field trials may be required to assess risks of genetically modified crops (GMCs) for nontarget arthropods. One critical point of these trials is their capacity to detect differences between the density of one taxon in the GMC and that in the comparator. The detection capacity of a trial depends on the abundance and variability of the taxon, the values assumed for type I (alpha) and II (beta) errors, and the characteristics of the trial and statistical design. To determine the optimal trial layout and statistical analysis, 20 field trials carried out in Spain from 2000 to 2009 to assess risks of GMCs on nontarget arthropods were examined with alpha and beta fixed at 0.05 and 0.20, respectively. Under the experimental conditions tested, taxon variability is the most influential component determining test detection capacity; the maximum acceptable values of taxon variability to achieve a certain detection capacity were calculated for different numbers of replicates (blocks), treatments, and years. A close relationship between taxon variability and mean abundance in visual counts, pitfall traps, and yellow sticky traps allowed minimal critical abundance thresholds to be estimated to guarantee a certain detection capacity and to establish abundance criteria for selecting focal taxa. The number of replications (blocks), treatments, sites, and years has a lesser influence on detection capacity once minimal values in taxon abundance in field trials are ensured. Conclusions reached on the detection capacity of field trials with the experimental data obtained under Mediterranean conditions should be contrasted with those of other regions.

Emergência de plântulas de pequizeiro em função da planta matriz e uso de ácido giberélico

Em Goiás, o pequi (Caryocar brasiliense) se destaca, dentre as frutíferas nativas do Cerrado, como promissora para a produção comercial. Um dos obstáculos para a sua produção em grande escala, no entanto, é o fato de que a germinação de sementes seja baixa e irregular. Com o objetivo de avaliar a emergência de sementes de pequizeiro e o desenvolvimento inicial de mudas oriundas de 16 plantas, aos dez meses após a colheita, na presença e ausência de ácido giberélico (GA3), foram conduzidos dois experimentos. O primeiro foi implantado em delineamento de blocos ao acaso, com parcelas subdivididas, tendo as matrizes nas parcelas e, nas subparcelas, um tratamento de imersão por 48 horas, em água pura e em solução de 500 mg L-1 de GA3. Foram realizadas avaliações a cada sete dias, para determinação da percentagem final, tempo médio e índice de velocidade de emergência. Para o segundo experimento, foi utilizado delineamento inteiramente casualizado, com número variado de repetições, de acordo com o número de mudas obtidas no primeiro experimento. Para percentagem, índice de velocidade e tempo médio de emergência, o efeito dos tratamentos foi significativo, sendo que, para os dois primeiros, houve interação significativa entre genótipo e tratamento, para superação da dormência. Observou-se que a utilização de 500 mg L-1 de ácido giberélico pode minimizar a dormência em sementes de Caryocar brasiliense e que o crescimento das matrizes em campo foi linear e contínuo, ao longo do tempo.

Improving the precision of estimating nitrate (NO3 −) concentration in seepage water of forests by prestratification with soil samples

Nitrate (NO3−) concentrations in seepage water (\( {\text{SW}}_{{{\text{NO}}_{ 3} }} \)) of N saturated forests regularly show a high spatial variability. As seepage water sampling is expensive, most studies use small numbers of soil solution samplers. This implies high uncertainties of calculated concentration and flux data. At the N saturated Hoglwald site we investigated, whether a preselection of seepage water sampling places by a prior intensive soil sampling can improve the precision of the estimation of \( {\text{SW}}_{{{\text{NO}}_{ 3} }} \). We implemented 121 suction cups and analyzed the soil, removed with the soil auger during installation at the sampling depth of 40 cm, for water extractable NO3−. The NO3− content in soil (\( {\text{Soil}}_{{{\text{NO}}_{ 3} }} \)) was calculated and \( {\text{SW}}_{{{\text{NO}}_{ 3} }} \) was measured. With this data set we tested the correlation between \( {\text{Soil}}_{{{\text{NO}}_{ 3} }} \) and \( {\text{SW}}_{{{\text{NO}}_{ 3} }} \) and simulated a random selection of sampling places (RS) as well as a prestratified sampling based on \( {\text{Soil}}_{{{\text{NO}}_{ 3} }} \) (PS). With bootstrap statistics different numbers of replications (n) were tested and the 95% confidence interval (95% CI) was used to compare RS with PS. Highly significant correlations between \( {\text{Soil}}_{{{\text{NO}}_{ 3} }} \) and \( {\text{SW}}_{{{\text{NO}}_{ 3} }} \) were found (r = 0.99***). It was even possible to calculate \( {\text{SW}}_{{{\text{NO}}_{ 3} }} \) from \( {\text{Soil}}_{{{\text{NO}}_{ 3} }} \). Here best results where achieved when \( {\text{Soil}}_{{{\text{NO}}_{ 3} }} \) was determined from field moist soil samples. With PS the accuracy of the mean value of \( {\text{SW}}_{{{\text{NO}}_{ 3} }} \) improved considerably. To achieve a 95% CI lower than ±10%, 250 suction cups would be needed for RS compared to n = 20 for PS. Even 6 months after implementation, precision of mean \( {\text{SW}}_{{{\text{NO}}_{ 3} }} \) was higher for suction cup places selected with the PS method. A detailed description is given, how these findings may be applied in studies and monitoring programs focusing on NO3− leaching in forest ecosystems.

Carcass characteristics and meat quality of Aberdeen Angus steers finished on different pastures

The present study was conducted to assess carcass features, physicochemical and sensory parameters of meat from steers finished on three types of pastures: natural pasture; natural pasture improved, fertilized and oversown with winter species; and annual summer grassland. The experiment was conducted from December 14, 2009 to November 30, 2010, with treatments distributed in a completely randomized design with a different number of replicates. Animals were used as experimental units. Experimental animals were Aberdeen Angus steers with twenty months of initial age and 354±27.4 kg of live weight, on average. The highest average daily gains were obtained for the annual summer grassland. There was no effect of treatments on carcass conformation. The highest carcass yield was obtained on the improved natural pasture. Forequarter yield, side cut yield and longissimus muscle area were similar between the pastures. Moisture and total lipids were not affected by the pasture. Thawing and cooking losses were higher in improved natural pasture and lower in sorghum pasture. Regardless of the treatment, the meat had luminosity ranging from intermediate to dark, high in red, high in yellow, and considered within the normal range for beef. Meat of higher shear force was found in natural pasture, and lower shear force was observed in meat from annual summer grassland. Average live weight daily gain explained 18% of the shear force. Sensory evaluation by duo-trio test showed differences between samples from distinct pastures in flavor. All the studied systems allow for desirable characteristics in carcass and meat.

Revisit the Two Sample t-Test with a Known Ratio of Variances

Inference for the difference of two independent normal means has been widely studied in staitstical literature. In this paper, we consider the case that the variances are unknown but with a known relationship between them. This situation arises frequently in practice, for example, when two instruments report averaged responses of the same object based on a different number of replicates, the ratio of the variances of the response is then known, and is the ratio of the number of replicates going into each response. A likelihood based method is proposed. Simulation results show that the proposed method is very accurate even when the sample sizes are small. Moreover, the proposed method can be extended to the case that the ratio of the variances is unknown.

Volumetria e sobrevivência de espécies nativas e exóticas no polo gesseiro do Araripe, PE

Nos setores industriais e comerciais da região do Araripe, em Pernambuco, a utilização de combustíveis lenhosos está dirigida aos processos de desidratação da gipsita e produção de gesso em suas diferentes tecnologias. Dessa forma, o presente estudo teve como objetivo buscar opções para suprir a demanda por lenha no Polo Gesseiro do Araripe pernambucano, por meio da implantação de povoamentos florestais com espécies nativas e exóticas. O experimento foi instalado na Estação Experimental do Instituto Agrônomico de Pernambuco (IPA), utilizando nove espécies, entre nativas e exóticas: (Imburana - Amburana cearense (Allemão) A.C. Sm.; Angico - Anadenanthera colubrina (Vell.) Brenan var. cebil (Griseb.) Altschul; Jurema - Mimosa tenuiflora (Willd.) Poir.; Sabiá - Mimosa caesalpiniaefolia Benth.; Acácia - Senna siamea (Lam.) H.S. Irwin & Barneby; Leucena - Leucaena leucocephala (Lam.) R. de Wit.; Algaroba - Prosopis juliflora (Sw.) D.C.; Ipês - Tabebuia sp.1 e Tabebuia sp.2), em um delineamento inteiramente casualizado com diferentes números de repetições. Foram avaliados os seguintes parâmetros: volume em metro cúbico (m³) e sobrevivência. Com relação ao volume em metro cúbico, o Sabiá teve a melhor produtividade. O Sabiá e a Jurema foram as espécies mais pesadas. E em relação à sobrevivência, Ipê 2 e Imburana tiveram as maiores mortalidades. Desta forma, o Sabiá e a Jurema são as espécies mais indicadas para a produção de lenha em plantios comerciais homogêneos na Chapada do Araripe em Pernambuco.

Micropropagação das bananeiras 'Prata-Anã' e 'FHIA 01' a partir de explantes de plantas tratadas com paclobutrazol

Com o objetivo de avaliar o desenvolvimento in vitro de explantes das bananeiras 'Prata-Anã' e 'FHIA 01' provenientes de plantas tratadas com paclobutrazol (PBZ), conduziu-se este experimento no Laboratório de Cultura de Células e Tecidos Vegetais, Setor de Fruticultura, DFT/UFV. Utilizou-se esquema fatorial 2 x 5, correspondendo às duas cultivares ('Prata-Anã' e 'FHIA 01') e cinco doses de PBZ (0,0; 0,5; 1,0; 1,5 e 2,0 g i.a. planta-1), em delineamento experimental inteiramente ao acaso, com número variável de repetições. Avaliaram-se, na parte aérea: taxa de brotação, altura e diâmetro, número de folhas, massa fresca e seca e intensidade da cor verde; e no sistema radicular: porcentagem de enraizamento, número de raízes, comprimento da maior raiz, massa fresca e seca, e a relação massa da raiz:massa da parte aérea. Foi observado que a altura da parte aérea foi reduzida a partir de 1,13 g i.a. planta-1, em ambas as cultivares. O diâmetro não foi alterado com o aumento das doses, mas nos explantes da 'Prata Anã' os diâmetros foram maiores que 'FHIA 01'. Para o número de folhas, as massas fresca e seca não apresentaram diferenças entre as doses e entre as cultivares. A intensidade da cor verde aumentou linearmente com o aumento das doses, em ambas as cultivares. A partir de 1,07 g i.a. planta-1, a taxa de brotação da 'Prata-Anã' foi inibida, enquanto a da 'FHIA 01' foi estimulada a partir de 0,85 g i.a. planta-1. Houve interação significativa para a porcentagem de enraizamento, onde se observaram valores mais baixos para a cultivar 'Prata-Anã' (64,71%), em relação à 'FHIA 01' (95,83%), na maior dose. Não foi observado efeito das doses de PBZ sobre a porcentagem de enraizamento de explantes da 'Prata-Anã', enquanto para 'FHIA 01' houve aumento linear do enraizamento com o aumento das doses, sendo que o maior valor encontrado foi de 95,18%. As demais características aumentaram linearmente com o aumento das doses de PBZ, para ambas as cultivares.

How Many Bootstrap Replicates Are Necessary?

Phylogenetic bootstrapping (BS) is a standard technique for inferring confidence values on phylogenetic trees that is based on reconstructing many trees from minor variations of the input data, trees called replicates. BS is used with all phylogenetic reconstruction approaches, but we focus here on one of the most popular, maximum likelihood (ML). Because ML inference is so computationally demanding, it has proved too expensive to date to assess the impact of the number of replicates used in BS on the relative accuracy of the support values. For the same reason, a rather small number (typically 100) of BS replicates are computed in real-world studies. Stamatakis et al. recently introduced a BS algorithm that is 1 to 2 orders of magnitude faster than previous techniques, while yielding qualitatively comparable support values, making an experimental study possible. In this article, we propose stopping criteria--that is, thresholds computed at runtime to determine when enough replicates have been generated--and we report on the first large-scale experimental study to assess the effect of the number of replicates on the quality of support values, including the performance of our proposed criteria. We run our tests on 17 diverse real-world DNA--single-gene as well as multi-gene--datasets, which include 125-2,554 taxa. We find that our stopping criteria typically stop computations after 100-500 replicates (although the most conservative criterion may continue for several thousand replicates) while producing support values that correlate at better than 99.5% with the reference values on the best ML trees. Significantly, we also find that the stopping criteria can recommend very different numbers of replicates for different datasets of comparable sizes. Our results are thus twofold: (i) they give the first experimental assessment of the effect of the number of BS replicates on the quality of support values returned through BS, and (ii) they validate our proposals for stopping criteria. Practitioners will no longer have to enter a guess nor worry about the quality of support values; moreover, with most counts of replicates in the 100-500 range, robust BS under ML inference becomes computationally practical for most datasets. The complete test suite is available at http://lcbb.epfl.ch/BS.tar.bz2, and BS with our stopping criteria is included in the latest release of RAxML v7.2.5, available at http://wwwkramer.in.tum.de/exelixis/software.html.

Características quantitativas da carcaça de cordeiros terminados em confinamento e abatidos em diferentes condições corporais

Objetivou-se avaliar os efeitos do grupo genético e da condição corporal sobre os rendimentos de carcaça de cordeiros terminados em confinamento. Foram utilizados 24 cordeiros Santa Inês e 24 cordeiros ½ Dorper × ½ Santa Inês com peso médio de 19,8 kg e idade média de 103 dias. O período de adaptação às instalações e à dieta foi de 14 dias. Os animais receberam ração completa com 30% de feno de maniçoba (Manihot pseudoglaziovii) e 70% de concentrado. O delineamento experimental foi o inteiramente casualizado em esquema fatorial 2 × 3, composto de dois grupos genéticos e três condições corporais, com diferentes números de repetições. Não houve diferença entre os grupos genéticos para as características quantitativas estudadas, exceto o percentual de gordura interna, a espessura de gordura subcutânea na condição gorda e os rendimentos de perna e costela na condição corporal intermediária. O efeito da condição corporal dentro do grupo genético aumenta o percentual de gordura interna, a espessura de gordura subcutânea, o índice de compacidade da carcaça e os pesos dos cortes, exceto do pescoço, nos cordeiros Dorper × Santa Inês.

MEASUREMENT OF FIRMNESS OF FRESH‐CUT SLICED TOMATO USING PUNCTURE TESTS – STUDIES ON SAMPLE SIZE, PROBE SIZE AND DIRECTION OF PUNCTURE

ABSTRACT In order to investigate the firmness of tomato slices, two experiments were performed. In the first one, Monte Carlo simulation was used to study the variation in firmness within and between slices. Adding more slices and more measurements per slice reduced the SD, but in general, the efficiency of adding more slices was higher. In the second experiment, the firmness of tomato slices was measured by puncture test during storage, using one of three flat‐tipped cylindrical probes (3.5‐, 2.5‐ and 1.5‐mm diameter) in two directions, along or perpendicular to the main axis of the fruit. Changes in firmness were studied by nonlinear regression analysis. The same model could be applied to all combinations of probe size and direction with the same correction for shear and compression. It suggests that shear and compression forces decay with storage time according to the same mechanism, irrespective of the measurement direction. PRACTICAL APPLICATIONSMethodologies for both firmness evaluation and data analysis were presented. Monte Carlo simulation was used to optimize the number of samples for firmness assays. After calculating the experimental SD from preliminary experimental results, simulations were performed with different numbers of replicates and measurements per replicate, to find an optimal experimental design where the SD is minimized. Using nonlinear regression, the effects on firmness of probe size, puncture direction in relation to the plant tissue and storage time can be analyzed simultaneously. The incorporation of a correction factor to account for differences in firmness due to probe size was proposed. The relative influence of shear (s) and compression force (c) on the observed force is estimated. Results of interest for the industry were presented, confirming previous findings that the firmness of ripened tomato slices measured by puncture analysis does not change significantly during short‐term storage at low temperature.