Hervé Monod

A CATALOGUE OF EFFICIENT NEIGHBOUR-DESIGNS WITH BORDER PLOTS

We consider designs in linear blocks with border plots, in which a treatment may affect the response on the two adjacent plots. Three series of designs are given: (i) neighbour-balanced designs in complete blocks; (ii) neighbour-balanced designs in blocks each of which lacks one treatment; (iii) partially neighbour-balanced designs in few complete blocks. Complete methods of construction and randomization are given. Optimality properties are discussed.

Pseudofactors : normal use to improve design and facilitate analysis

SUMMARY Pseudofactors are an inherently simple device to aid the construction and analysis of designed experiments. Although they were introduced over 50 years ago, they still puzzle many statisticians. After a historical introduction a worked example is used to demonstrate how pseudofactors are used to construct the design, to obtain the analysis-of-variance table and table of means and to calculate standard errors of contrasts. Then the algebraic and algorithmic roles of pseudofactors are explained and reviewed, with particular emphasis on Genstat. Finally, a section on standard designs shows how pseudofactors may be used to construct more efficient designs, and to give simpler or better analyses, than those recommended in the current literature.

The Influence of Design on Validity and Efficiency of Neighbour Methods

SUMMARY Neighbour methods have often been shown to be apparently more efficient than analysis of variance for the analysis of field experiments. This means that the precision of the analysis estimated by the statistical method itself is smaller for the neighbour method than for the classical one. This comparison is meaningful only if the analysis is valid in the sense that it estimates its own precision without bias. Although precise validity properties are known for the analysis of variance of randomized designs, no analogous properties are known for neighbour analyses. In this paper, we investigate the validity and efficiency of some neighbour methods and their relations with the design. First, we give precise definitions of the desirable properties of the combination of design (including randomization) and method of analysis; then we report on a simulation study. We show that neighbour methods are often valid or conservative with higher efficiency than classical ones. To better ensure these properties, we advocate the use of randomized neighbour designs and corrections to degrees of freedom. Finally, we discuss how these results can be used to assess neighbour methods for routine trials.

Automatic generation of generalised regular factorial designs

The R package planor enables the user to search for, and construct, factorial designs satisfying given conditions. The user specifies the factors and their numbers of levels, the factorial terms which are assumed to be non-zero, and the subset of those which are to be estimated. Both block and treatment factors can be allowed for, and they may have either fixed or random effects, as well as hierarchy relationships. The designs are generalised regular designs, which means that each one is constructed by using a design key and that the underlying theory is that of finite abelian groups. The main theoretical results and algorithms on which planor is based are developed and illustrated, with the emphasis on mathematical rather than programming details. Sections 3–5 are dedicated to the elementary case, when the numbers of levels of all factors are powers of the same prime. The ineligible factorial terms associated with users’ specifications are defined and it is shown how they can be used to search for a design key by a backtrack algorithm. Then the results are extended to the case when different primes are involved, by making use of the Sylow decomposition of finite abelian groups. The proposed approach provides a unified framework for a wide range of factorial designs.

Market analyses of livestock trade networks to inform the prevention of joint economic and epidemiological risks

Conventional epidemiological studies of infections spreading through trade networks, e.g. via livestock movements, generally show that central large-size holdings (hubs) should be preferentially surveyed and controlled in order to reduce epidemic spread. However, epidemiological strategies alone may not be economically optimal when costs of control are factored in together with risks of market disruption from targeting core holdings in a supply chain. Using extensive data on animal movements in supply chains for cattle and swine in France, we introduce a method to identify effective strategies for preventing outbreaks with limited budgets while minimizing the risk of market disruptions. Our method involves the categorization of holdings based on position along the supply chain and degree of market share. Our analyses suggest that trade has a higher risk of propagating epidemics through cattle networks, which are dominated by exchanges involving wholesalers, than for swine. We assess the effectiveness of contrasting interventions from the perspectives of regulators and the market, using percolation analysis. We show that preferentially targeting minor, non-central agents can outperform targeting of hubs when the costs to stakeholders and the risks of market disturbance are considered. Our study highlights the importance of assessing joint economic–epidemiological risks in networks underlying pathogen propagation and trade.

A Bayesian approach to model dispersal for decision support

In agricultural and environmental sciences dispersal models are often used for risk assessment to predict the risk associated with a given configuration and also to test scenarios that are likely to minimise those risks. Like any biological process, dispersal is subject to biological, climatic and environmental variability and its prediction relies on models and parameter values which can only approximate the real processes. In this paper, we present a Bayesian method to model dispersal using spatial configuration and climatic data (distances between emitters and receptors; main wind direction) while accounting for uncertainty, with an application to the prediction of adventitious presence rate of genetically modified maize (GM) in a non-GM field. This method includes the design of candidate models, their calibration, selection and evaluation on an independent dataset. A group of models was identified that is sufficiently robust to be used for prediction purpose. The group of models allows to include local information and it reflects reliably enough the observed variability in the data so that probabilistic model predictions can be performed and used to quantify risk under different scenarios or derive optimal sampling schemes. A Bayesian approach is proposed to model dispersal and to make probabilistic predictions which account for uncertainty.16 statistical gene flow models were designed, calibrated and compared within the Bayesian framework.Models with Zero-inflated Poisson distribution and with exponential decay turn out to provide the most reliable predictions.The proposed approach allows to set up context-specific isolation distances by providing accurate probabilistic predictions.Thanks to precise predictions of intra-field variability, our models allow to design optimal stratified sampling schemes.

Adaptive diversification in heterogeneous environments

The role of environmental heterogeneity in the evolution of biological diversity has been studied only for simple types of heterogeneities and dispersals. This article broadens previous results by considering heterogeneities and dispersals that are structured by several environmental factors. It studies the evolution of a metapopulation, living in a network of patches connected by dispersal, under the effects of mutation, selection and migration. First, it is assumed that patches are equally connected and that they carry habitats characterized by several factors exerting selection pressures on several individual traits. Habitat factors may vary in the environment independently or they may be correlated. It is shown that correlations between habitat factors promote adaptive diversification and that this effect may be modified by trait interactions on survival. Then, it is assumed that patches are structured by two crossed factors, called the row and column factors, such that patches are more connected when they occur in the same row or in the same column. Environmental patterns in which each habitat appears in each row the same number of times and appears in each column the same number of times are found to hinder adaptive diversification.