arXiv subjects

Hans-Peter Piepho

Publications and source records attributed to Hans-Peter Piepho.

11 recordsLinked to original sources

arXiv2026

Fisher's ideas and the design of field experiments in agronomy and plant breeding

R. A. Fisher was one of the greatest scientists of the last century. He made many ground-breaking contributions, so many indeed that it seems almost impossible to list all of them. His revolutionary contributions to the design of experiments can mostly be traced to the early part of his academic career, and they are inextricably linked to his involvement with agricultural field experiments at Rothamsted Experiment Station. In this talk I will review Fisher's key ideas on experimental design and relate them to some of the work I am involved in, most of which directly focuses on field experiments in agriculture. Topics covered include systematic designs, row-column designs, augmented row-column designs, multi-environment trials, partially replicated designs, optimal allocation of trials to zones in sub-divided target populations of environments, and the connection of trialling systems across countries.

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arXiv2026

Optimal allocation of trials to sub-regions in crop variety testing with multiple years and correlated genotype effects

Plant breeding and variety trials are usually conducted in multiple environments sampled from a defined target population of environments in order to characterize the performance of breeding lines or varieties. When the population is large and heterogeneous, it may be sub-divided into sub-regions or zones according to administrative and agro-ecological criteria. Analysis then focuses on prediction of performance in the individual sub-regions. Modelling the genotype effect in each sub-region as random, information can be borrowed across sub-regions using best linear unbiased prediction based on a suitable variance-covariance matrix for the genotype-zone effects. Here, we consider the important case where kinship of pedigree information is available for the genotypes under test. This information can be integrated into the variance-covariance matrix for genotype-zone effects. The objective we pursue here is to determine the optimal allocation of a fixed budget of trials to sub-regions. This design problem is solved using a combination of theory and explicit equations on one hand and numerical optimization on the other hand. Our proposed novel approach allows obtaining the optimal allocation when the number of genotypes is in the hundreds, a common setting in large plant breeding programs as well as in variety testing for economically important crops.

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arXiv2026

A Bayesian Updating Framework for Long-term Multi-Environment Trial Data in Plant Breeding

In variety testing, multi-environment trials (MET) are essential for evaluating the genotypic performance of crop plants. A persistent challenge in the statistical analysis of MET data is the estimation of variance components, which are often still inaccurately estimated or shrunk to exactly zero when using residual (restricted) maximum likelihood (REML) approaches. At the same time, institutions conducting MET typically possess extensive historical data that can, in principle, be leveraged to improve variance component estimation. However, these data are rarely incorporated sufficiently. The purpose of this paper is to address this gap by proposing a Bayesian framework that systematically integrates historical information to stabilize variance component estimation and better quantify uncertainty. Our Bayesian linear mixed model (BLMM) reformulation uses priors and Markov chain Monte Carlo (MCMC) methods to maintain the variance components as positive, yielding more realistic distributional estimates. Furthermore, our model incorporates historical prior information by managing MET data in successive historical data windows. Variance component prior and posterior distributions are shown to be conjugate and belong to the inverse gamma and inverse Wishart families. While Bayesian methodology is increasingly being used for analyzing MET data, to the best of our knowledge, this study comprises one of the first serious attempts to objectively inform priors in the context of MET data. This refers to the proposed Bayesian updating approach. To demonstrate the framework, we consider an application where posterior variance component samples are plugged into an A-optimality experimental design criterion to determine the average optimal allocations of trials to agro-ecological zones in a sub-divided target population of environments (TPE).

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arXiv2025

Automatic Quality Control for Agricultural Field Trials -- Detection of Nonstationarity in Grid-indexed Data

A common assumption in the spatial analysis of agricultural field trials is stationarity. In practice, however, this assumption is often violated due to unaccounted field effects. For instance, in plant breeding field trials, this can lead to inaccurate estimates of plant performance. Based on such inaccurate estimates, breeders may be impeded in selecting the best performing plant varieties, slowing breeding progress. We propose a method to automatically verify the hypothesis of stationarity. The method is sensitive towards mean as well as variance-covariance nonstationarity. It is specifically developed for the two-dimensional grid-structure of field trials. The method relies on the hypothesis that we can detect nonstationarity by partitioning the field into areas, within which stationarity holds. We applied the method to a large number of simulated datasets and a real-data example. The method reliably points out which trials exhibit quality issues and gives an indication about the severity of nonstationarity. This information can significantly reduce the time spent on manual quality control and enhance its overall reliability. Furthermore, the output of the method can be used to improve the analysis of conducted trials as well as the experimental design of future trials.

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arXiv2025

Rectangular augmented row-column designs generated from contractions

Row-column designs play an important role in applications where two orthogonal sources of error need to be controlled for by blocking. Field or greenhouse experiments, in which experimental units are arranged as a rectangular array of experimental units are a prominent example. In plant breeding, the amount of seed available for the treatments to be tested may be so limited that only one experimental unit per treatment can be accommodated. In such settings, augmented designs become an interesting option, where a small set of treatments, for which sufficient seed is available, are replicated across the rectangular layout so that row and column effects, as well as the error variance can be estimated. Here, we consider the use of an auxiliary design, also known as a contraction, to generate an augmented row-column design. We make use of the fact that the efficiency factors of the contraction and the associated augmented design are closely interlinked. A major advantage of this approach is that an efficient contraction can be found by computer search at much higher computational speed than is required for direct search for an efficient augmented design. Two examples are used to illustrate the proposed method.

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arXiv2025

Regression approaches for modelling genotype-environment interaction and making predictions into unseen environments

In plant breeding and variety testing, there is an increasing interest in making use of environmental information to enhance predictions for new environments. Here, we will review linear mixed models that have been proposed for this purpose. The emphasis will be on predictions and on methods to assess the uncertainty of predictions for new environments. Our point of departure is straight-line regression, which may be extended to multiple environmental covariates and genotype-specific responses. When observable environmental covariates are used, this is also known as factorial regression. Early work along these lines can be traced back to Stringfield & Salter (1934) and Yates & Cochran (1938), who proposed a method nowadays best known as Finlay-Wilkinson regression. This method, in turn, has close ties with regression on latent environmental covariates and factor-analytic variance-covariance structures for genotype-environment interaction. Extensions of these approaches - reduced rank regression, kernel- or kinship-based approaches, random coefficient regression, and extended Finlay-Wilkinson regression - will be the focus of this paper. Our objective is to demonstrate how seemingly disparate methods are very closely linked and fall within a common model-based prediction framework. The framework considers environments as random throughout, with genotypes also modelled as random in most cases. We will discuss options for assessing uncertainty of predictions, including cross validation and model-based estimates of uncertainty, the latter one being estimated using our new suggested approach. The methods are illustrated using a long-term rice variety trial dataset from Bangladesh.

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arXiv2025

Change of some cropping systems in a long-term trial comparing different systems: rationale and implications for statistical analysis

The project Agriculture 4.0 without chemical synthetical plant protection (NOcsPS) tests a number of cropping systems that avoid the use of chemical synthetical pesticides while at the same time using mineral fertilizers. The experiment started in 2020 (sowing fall 2019). In 2024 (sowing fall 2023), some of the cropping systems were modified. Analysis of this experiment may be done using linear mixed models. In order to include the data from 2020-2023 in joint analyses with the data collected for the modified systems from 2024 onwards, the mixed modelling approach needs to be reconsidered. In this paper, we develop models for this purpose. A key feature is the use of network meta-analytic concepts that allow a combination of direct and indirect comparisons among systems from the different years. The approach is first illustrated using a toy example. This is followed by detailed analyses of data from two the two trials sites Dahnsdorf and Hohenheim.

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arXiv2021

Hierarchical Bayesian state-space modeling of age- and sex-structured wildlife population dynamics

Biodiversity is declining at alarming rates worldwide, including for large wild mammals. It is therefore imperative to develop effective population conservation and recovery strategies. Population dynamics models can provide insights into processes driving declines of particular populations of a species and their relative importance. We develop an integrated Bayesian state-space population dynamics model for wildlife populations and illustrate it using a topi population inhabiting the Masai Mara Ecosystem in Kenya. The model is general and integrates ground demographic survey with aerial survey monitoring data. It incorporates population age- and sex-structure and life-history traits and relates birth rates, age-specific survival rates and sex ratio with meteorological covariates, prior population density, environmental seasonality and predation risk. The model runs on a monthly time step, enabling accurate characterization of reproductive seasonality, phenology, synchrony and prolificacy of births and juvenile recruitment. Model performance is evaluated using balanced bootstrap sampling and comparing predictions with aerial population size estimates. The model is implemented using MCMC methods and reproduces several well-known features of the Mara topi population, including striking and persistent population decline, seasonality of births and juvenile recruitment. It can be readily adapted for other wildlife species and extended to incorporate several additional useful features.

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arXiv2021

Regression Models for Order-of-Addition Experiments

The purpose of order-of-addition (OofA) experiments is to identify the best order in a sequence of m components in a system or treatment. Such experiments may be analysed by various regression models, the most popular ones being based on pairwise ordering (PWO) factors or on component-position (CP) factors. This paper reviews these models and extensions and proposes a new class of models based on response surface (RS) regression using component position numbers as predictor variables. Using two published examples, it is shown that RS models can be quite competitive. In case of model uncertainty, we advocate the use of model averaging for analysis. The averaging idea leads naturally to a design approach based on a compound optimality criterion assigning weights to each candidate model.

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arXiv2020

Optimizing the allocation of trials to sub-regions in multi-environment crop variety testing

New crop varieties are extensively tested in multi-environment trials in order to obtain a solid empirical basis for recommendations to farmers. When the target population of environments is large and heterogeneous, a division into sub-regions is often advantageous. When designing such trials, the question arises how to allocate trials to the different subregions. We consider a solution to this problem assuming a linear mixed model. We propose an analytical approach for computation of optimal designs for best linear unbiased prediction of genotype effects and pairwise linear contrasts and illustrate the obtained results by a real data example from Indian nation-wide maize variety trials. It is shown that, except in simple cases such as a compound symmetry model, the optimal allocation depends on the variance-covariance structure for genotypic effects nested within sub-regions.

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arXiv2018

A Coefficient of Determination (R2) for Linear Mixed Models

Extensions of linear models are very commonly used in the analysis of biological data. Whereas goodness of fit measures such as the coefficient of determination (R2) or the adjusted R2 are well established for linear models, it is not obvious how such measures should be defined for generalized linear and mixed models. There are by now several proposals but no consensus has yet emerged as to the best unified approach in these settings. In particular, it is an open question how to best account for heteroscedasticity and for covariance among observations induced by random effects. This paper proposes a new approach that addresses this issue and is universally applicable. It is exemplified using three biological examples.

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