Generalized Row-Column Designs for Crop and Animal Experiments

Abstract

In field and animal experiments, where there are two sources of variation in experimental units that may influence the response variable, row-column designs are used. Most of the row-column designs developed in the literature have only one unit corresponding to the intersection of row and column i.e. in a single cell. However, for the instances when the number of treatments is large with limited experimental resources, Generalized Row-Column (GRC) designs are used where there is more than one unit in each row-column intersection. The presence of missing observations, outliers in the data, etc. are some of the disturbances that may occur during experimentation. These disturbances may lead to less precise comparisons among treatments. Robustness of different classes of GRC designs against missing of one or more observations has been investigated. It is found that the efficiency is quite high (more than 90%) for most of the designs and the designs are robust and there is a decreasing trend in efficiency with increase in number of missing observations. Series of GRC designs balanced for spatial effects have been developed. The information matrices for estimating the contrasts pertaining to direct effect and spatial effect have been derived. The designs developed ensure that within a cell every treatment has every other treatment appearing as neighbour a constant number of times. Further, in order to give a readymade solution to the experimenters, a SAS macro has been developed that generates the layout of the designs. For easy accessibility of GRC designs, a web solution named WebGRC has been developed that provides the online generation of randomized layout of these designs along with an online catalogue within a permissible range.These designs can be advantageously used for obtaining mating plans like Partial diallel cross (PDC) or Partial triallel cross (PTC) plans by considering treatments in the design as individual parental lines in the breeding programme and by making crosses between lines within each cell. Here, methods of obtaining PDC and PTC plans using different classes of GRC designs have been described. The plans obtained using these designs will yield smaller degree of fractionation thereby reducing the resources and reduce the heterogeneity present in the experimental field, simultaneously.