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

Abstract

Statistical analyses for variety mixtures have made little progress in recent years • Novel models are proposed to study mixing ability in incomplete designs • The models account for inter and intra-genotypic interactions within mixtures • The framework handles mixtures with any order and proportions of components • This framework was shown to be relevant on wheat mixture trial analysis

Advances in Breeding for Mixed Cropping – Incomplete Factorials and the Producer/Associate Concept

“…Besides having been suggested for calibration of genomic prediction models for hybrid breeding ( Seye et al, 2020 ), incomplete designs have been used to estimate GMA and SMA effects in wheat cultivar mixtures ( Forst et al, 2019 ). The findings of Forst et al (2019) could be applied to hybrid breeding as well as to breeding for mixed cropping: in the early development of a hybrid selection scheme for a crop, a broad range of genotypes could be tested in an incomplete diallel, similar to the one in Forst et al (2019) that identified suitable material to form “pools” in cultivar mixtures. In mixed cropping, in early stages of breeding, where the size of the GMA variances of the two species are yet unknown and both species are of equal interest, an incomplete factorial with equal sizes of m and n would be advisable to subsequently design a breeding scheme based on the results.…”

“…Incomplete factorial designs have been suggested to mitigate the limitations of (i) and (ii) by expanding the numbers of m and n while maintaining a feasible number of experimental plots. Previously, they have been applied to assess GMA and SMA effects in wheat ( Triticum aestivum L.) cultivar mixtures ( Forst et al, 2019 ) and found recent application in genomic prediction in corn ( Zea mays L.) hybrid breeding ( Seye et al, 2020 ).…”

Multi-Species Genomics-Enabled Selection for Improving Agroecosystems Across Space and Time

“…Investigating all possible combinations of genotypes between any diverse set of germplasm from one species (or population), and a diverse set of another interacting species (or population), is intractable. Borrowing methodology from maize hybrid breeding [reciprocal recurrent selection ( Comstock et al, 1949 )], ( Wright, 1985 ) developed an interspecies selection scheme, which partitions plot-level performance into main effects for each species (general mixing ability; GMA) and an interaction (specific mixing ability; SMA) ( Federer, 1993 ; Forst et al, 2019 ; Sampoux et al, 2020 ; Haug et al, 2021 ). We note that a GMA is estimated for each genotype of each single crop, but that these GMAs refer to emergent plot-level properties (e.g., erosion protection) that can only be measured on crop combinations.…”

Table_1.DOCX

“…Besides having been suggested for calibration of genomic prediction models for hybrid breeding (Seye et al, 2020), incomplete designs have been used to estimate GMA and SMA effects in wheat cultivar mixtures (Forst et al, 2019). The findings of Forst et al (2019) could be applied to hybrid breeding as well as to breeding for mixed cropping: in the early development of a hybrid selection scheme for a crop, a broad range of genotypes could be tested in an incomplete diallel, similar to the one in Forst et al (2019) that identified suitable material to form "pools" in cultivar mixtures. In mixed cropping, in early stages of breeding, where the size of the GMA variances of the two species are yet unknown and both species are of equal interest, an incomplete factorial with equal sizes of m and n would be advisable to subsequently design a breeding scheme based on the results.…”

“…Incomplete factorial designs have been suggested to mitigate the limitations of (i) and (ii) by expanding the numbers of m and n while maintaining a feasible number of experimental plots. Previously, they have been applied to assess GMA and SMA effects in wheat (Triticum aestivum L.) cultivar mixtures (Forst et al, 2019) and found recent application in genomic prediction in corn (Zea mays L.) hybrid breeding (Seye et al, 2020).…”