Statistical Designs and Response Models for Mixtures of Cultivars¹

A generalized statistical framework to assess mixing ability from incomplete mixing designs using binary or higher order variety mixtures and application to wheat

“…By assessing a set of p genotypes in all possible hybrid combinations, the combining ability can be estimated and partitioned between the general combining ability of the genotypes and the specific ability of each particular combination (Griffing 1956). The analogy has first been proposed for the study of plant interactions between rows of genotypes (Jensen and Federer 1965) and has then been broadly applied to the study of binary mixtures for estimating mixing ability, both when the performance of each component is accessible in the mixture (McGilchrist 1965;Chalbi 1967;Gallais 1970;Federer 1979;Federer et al 1982), or when only the mixture performance is surveyed (Federer 1979;Federer et al 1982;Gizlice et al 1989;Knott and Mundt 1990;Gallandt et al 2001). The work developed hereafter deals with this second case, where only the global performance of each mixture is available.…”

Harnessing monocrop breeding strategies for intercrops

“…This approach, initially used for studying plant interactions, has been widely applied to predict the agronomic performance of binary mixtures. The methodology has been developed and refined over several decades, with significant contributions from researchers such as (Sprague and Tatum, 1942;Griffing, 1956;Jensen and Federer, 1965), and others throughout the 1960s and beyond, highlighting its broad applicability and refinement over time (McGilchrist, 1965;Chalbi, 1967;Gallais, 1970;Federer, 1979;Federer et al, 1982;Gizlice et al, 1989;Knott and Mundt, 1990;Gallandt et al, 2001;Forst et al, 2019;Haug et al, 2021). Reciprocal mixing ability refers to the compatibility between different crop species or varieties to support each other's growth when planted together.…”

Statistical Design and Analysis for Intercropping Experiments

“…Using some of the ideas from the above plus others, biological modeling for intercropping experiments was developed (see Chapters 6 and 7 of Federer, 1991, Federer, 1979, and Federer and Raghavarao, 1987. For the models proposed, particular treatment designs are necessary.…”

“…are discussed in Federer (1979 and1991, Chapters 6 and7). General mixing ability (gma) refers to ~he ability of a crop or line to mix well with all others in the experiment.…”