<abstract xmlns="http://www.w3.org/1999/xhtml"> A common problem in multi-environment trials arises when some genotypeby- environment combinations are missing. In Arciniegas-Alarcón et al. (2010) we outlined a method of data imputation to estimate the missing values, the computational algorithm for which was a mixture of regression and lower-rank approximation of a matrix based on its singular value decomposition (SVD). In the present paper we provide two extensions to this methodology, by including weights chosen by cross-validation and allowing multiple as well as simple imputation. The three methods are assessed and compared in a simulation study, using a complete set of real data in which values are deleted randomly at different rates. The quality of the imputations is evaluated using three measures: the Procrustes statistic, the squared correlation between matrices and the normalised root mean squared error between these estimates and the true observed values. None of the methods makes any distributional or structural assumptions, and all of them can be used for any pattern or mechanism of the missing values.</abstract>

Departamento de Ciências Exatas, Universidade de São Paulo/ESALQ, Cx.P.09, CEP.13418-900, Piracicaba, SP - Brasil

College of Engineering, Mathematics and Physical Sciences, Harrison Building, University of Exeter, North Park Road, Exeter, EX4 4QF, United Kingdom

An alternative methodology for imputing missing data in trials with genotype-by-environment interaction: some new aspects

<abstract xmlns="http://www.w3.org/1999/xhtml"> The genotype by environment interaction (GEI)) has an influence on the selection and recommendation of cultivars. The aim of this work is to study the effect of GEI and evaluate the adaptability and stability of productivity (kg/ha) of nine maize genotypes using AMMI model (Additive Main effects and Multiplicative Interaction). The AMMI model is one of the most widely used statistical tools in the analysis of multiple-environment trials. It has two purposes, namely understanding complex GEI and increasing accuracy. Nevertheless, the AMMI model is a widely used tool for the analysis of multiple-environment trials, where the data are represented by a two-way table of GEI means. In the complete tables, least squares estimation for the AMMI model is equivalent to fitting an additive two-way ANOVA model for the main effects and applying a singular value decomposition to the interaction residuals. It assumes equal weights for all GEI means implicitly. The experiments were conducted in twenty environments, and the experimental design was a randomized complete block design with four repetitions. The AMMI model identified the best combinations of genotypes and environments with respect to the response variable. This paper concerns a basic and a common application of AMMI: yield-trial analysis without consideration of special structure or additional data for either genotypes or environments.</abstract>

Programa de Pos-graduação em Estatística e Experimentação Agronômica, Universidade de São Paulo, Brazil

Departamento de Estatística, Universidade Federal de Mato Grosso, Av. Fernando Corrêa da Costa, no 2367 - Bairro Boa Esperança. 78060-900, Cuiabá - MT - Brazil

Departamento de Estatística, Universidade Federal de Uberlândia, MG, Brazil

Departamento de Ciências Exatas, Universidade de São Paulo, Brazil

Statistical analysis of yield trials by AMMI analysis of genotype × environment interaction

<abstract xmlns="http://www.w3.org/1999/xhtml"> In this paper we consider a set of T repeated measurements on p characteristics on each of n individuals. The n individuals themselves may be divided and randomly assigned to K groups. These data are analyzed using a mixed effect MANOVA model, assuming that the data on an individual have a covariance matrix which is a Kronecker product of two positive definite matrices. Results are illustrated on a data set obtained from experiments with varieties of winter rye.</abstract>

Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznan, Poland

Plant Breeding and Acclimatization Institute, National Research Institute, Radzików, 05-870 Błonie, Poland

Analysis of multivariate repeated measures data using a MANOVA model and principal components

<abstract xmlns="http://www.w3.org/1999/xhtml"> This paper deals with two-factor experiments with split units. The whole plot treatments occur in a repeated Latin square, modified Latin square or Youden square, while subplot treatments occur in a block design within the whole plots. The statistical properties of the considered designs are examined. Special attention is paid to the case where one of the treatments is an individual control or an individual standard treatment. In addition, we give a brief overview of work on the design of experiments using the considered designs, as well as possible arrangements of controls in the experiments.</abstract>

Department of Mathematical Sciences, Graduate School of Engineering,Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531, Japan

Department of Mathematical and Statistical Methods, Poznan University of Life Sciences, Wojska Polskiego 28, PL-60-637 Poznań, Poland

Department of Nursing, Gifu College of Nursing, Hashima, Gifu 501-6295, Japan

Control treatments in designs with split units generated by Latin squares

<abstract xmlns="http://www.w3.org/1999/xhtml"> Annual height increments are a very important characteristic of Scots pine. They have a direct effect on the determination of the dendrometric properties of a stand, such as volume increment. In the present study the data concern height increments of the main shoot in selected age classes of trees (age 72 to 92 years). A relationship is determined between the values of the increments and meteorological conditions such as temperature, precipitation and sunshine. On the basis of lasso regression analysis, precipitation in the year preceding the incremental season was shown to have the greatest effect on height increments of Scots pine.</abstract>

Department of Forest Management, Poznań University of Life Sciences, Wojska Polskiego 28, 60-637 Poznań, Poland

Department of Mathematical and Statistical Methods, Poznań University of Life Sciences, Wojska Polskiego 28, 60-637 Poznań, Poland

The influence of weather conditions on annual height increments of Scots pine

<abstract xmlns="http://www.w3.org/1999/xhtml"> Breeding work using European rye populations has resulted in a considerable reduction of genetic variation in breeding materials of that species. Many taxa from the genus Secale may constitute a potential source of genetic variation in rye breeding. A source of new genetic variation can be found in such species as Secale montanum and Secale vavilovii, which are sources of resistance to fusarium ear blight and septoria leaf blotch, while Secale vavilovii may also be a source of sterilising cytoplasm. The aim of this study was to assess the efficiency of crossing the wild species Secale vavilovii and the rye subspecies Secale cereale subsp. afghanicum, Secale cereale subsp. ancestrale, Secale cereale subsp. dighoricum, Secale cereale subsp. segetale with the crop species Secale cereale ssp. cereale, and to produce F1 hybrids and describe selected morphological traits. Observations of biometric traits indicate that the F1 crosses produced may be potential sources of variation for common rye. The greatest variation in terms of all analysed phenotypic traits combined was found for the cross combinations S. c. ssp. cereale cv. Amilo × S. c. ssp. ancestrale and S. c. ssp. cereale cv. Dańkowskie Diament × S. c. ssp. dighoricum. The hybrids showed considerable variation in the analysed biometric traits within individual cross combinations.</abstract>

Department of Genetics and Plant Breeding, Poznań University of Life Sciences, Dojazd 11, 60-632 Poznań, Poland

Biometric characteristics of interspecific hybrids in the genus Secale

<abstract xmlns="http://www.w3.org/1999/xhtml"> A nonlinear statistical approach was used to evaluate the efficiency of plant protection products. The methodology presented can be implemented when the observations in an experiment are recorded as success or failure. This occurs, for example, when following the application of a herbicide or pesticide, a single weed or insect is classified as alive (failure) or dead (success). Then a higher probability of success means a higher efficiency of the tested product. Using simulated data sets, a comparison was made of three methods based on the logit, probit and threshold models, with special attention to the effect of sample size and number of replications on the accuracy of the estimation of probabilities.</abstract>

An evaluation of the efficiency of plant protection products via nonlinear statistical methods – a simulation study

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Biometrical Letters

 Biometrical Letters is the official journal of the Polish Biometric Society, founded in 1964, now published with the financial support of the Ministry of Science and Higher Education. The anonymous double-blind peer review by the two independent reviewers is applied to all the papers.  The purposes of Biometrical Letters are:   publishing papers dealing with various aspects of the analysis and interpretation of results from biometrical experiments, using mathematical and statistical methods;  promoting and extending the use of statistical and mathematical methods in the principal disciplines of life sciences by reporting on the development and application of these methods;  presenting statistical and mathematical tools useful in biometry. Methodological developments should be motivated by interesting problems from life sciences, applied or applicable;  publishing review papers and papers presenting practical use of various methods of data analysis and statistical inference.   The core of most Biometrical Letters articles is statistical inference that sets scientific or policy objectives, motivates methodological development and demonstrates the operation of new methods.  The paper should include a description of the biometrical problem and a section detailing the application of the new methodology.  The Journal welcomes the submission of manuscripts from bioscience, mathematical and statistical theory, biology, genetics, medical statistics, agriculture, forestry, ecology, environmental sciences, biometrics and clinical trials. Case studies and articles on the use and development of statistical software are also welcome.  Rejection Rate   20%   Archiving  Sciendo archives the contents of this journal in Portico - digital long-term preservation service of scholarly books, journals and collections.  Plagiarism Policy  The editorial board is participating in a growing community of Similarity Check System's users in order to ensure that the content published is original and trustworthy. Similarity Check is a medium that allows for comprehensive manuscripts screening, aimed to eliminate plagiarism and provide a high standard and quality peer-review process. 